CHEM120A Traditional LabManual S2012

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CHEMISTRY120A

LABORATORY

MANUALSeventeenth Edition

Fall 2011

California State University, FullertonDepartment of Chemistry and Biochemistry


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TABLE OF CONTENTSGrading Information

Laboratory Grade 1

Laboratory Reports 2

Academic Honesty 3Background Information

Why Do Experiments? 4

Safety in the Laboratory 5

Waste Disposal 8

The Laboratory Notebook 9

Quantitative Observations

Precision of Measurements 11

Scientific Notation 12

Relative and Absolute Precision 13

Rounding Off 16

Accuracy and Error 20

Averaging 22

Statistical Analysis: the Rule of Four 23

Exploration A1: Is Volume Conserved?

Objectives and Introduction 25

Graph of Water Density 28

Procedure 29

Calculations 34

Report 36

Data Sheets 37


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Exploration A2: Chemistry of Aluminum


Procedure: Formation of an Aluminum Compound 47

Procedure: Displacement Reactions of Aluminum 49

Procedure: Determining the Empirical Formula 52

Calculations 58

Report 61

Data and Results Sheets 62

Exploration A3: An Emission Spectroscope


Procedure: Construction of the Spectroscope 70

Procedure: Measurements 74

Calculations 76

Report 76

Exploration A4: Equivalent Mass of an Acid


Procedure 80

Report 83-84

Data and Results Sheet 85

Exploration A5: Preparation and Analysis of a Compound


Procedure 88-89

Analysis of the Compound 90-93

Calculations 93

Report 95

Data and Results Sheets 96

Appendix Results Reporting Forms 99


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LABORATORY GRADE

Your work in the laboratory will generate a point total that will be added to your

lecture points to generate an overall point total for the course. Consult the syllabus ofyour lecture instructor for details. The laboratory is worth 200 points, broken down asfollows:

1. Laboratory quizzes (25 points each): 502. Laboratory reports and Quality of results:

A.1 36B.2 25

A.4 36A.5 40

Total: 187

1. Laboratory Quizzes (50 points)A quiz testing your preparation and understanding of the laboratoryexperience will be administered at the beginning of the lab session Weeks4 and 14.

2. Quality of Results:Your results for each experiment will be graded for accuracy andreproducibility. Accurate and reproducible results require that you takecare and pay attention to detail while doing the experiment, and that youdevelop and master the laboratory and technical skills required for each

experiment. Care and good technique will yield good results scores.3. Laboratory Reports:

See the next page for general information concerning laboratory reportpreparation. In addition, your laboratory manual contains specificinstructions for preparing the report for each experiment at the end of thedescription of that experiment.


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LABORATORY REPORTS

You are required to submit a laboratory report for each experiment.

Contents: Each laboratory report should contain three parts:

1.) A copy of the Results Reporting Form for the experiment (see Appendix),

filled out neatly and completely. (3 points)

2.) A written narrative, addressing the points described in the instructions for the

experiment, see each individual experiment for details (6 points).

3.) A data and calculations section containing the data from your experiment,

appropriately organized, and a sample of each different type of calculation

you made in obtaining the results from your data (5 points).

In addition, your instructor will have the following, which will be graded as part ofyour report:

4.) The carbon copies of your laboratory notebook pages, turned in to your

laboratory instructor at the end of each laboratory period (2 points).

Grading: Reports are graded for organization, clarity, readability and completeness.

General Rules: Write clearly and concisely. Avoid the use of "I" except when stating your opinion. Do not repeat what is in the laboratory manual.

Follow the instructions for each report.

Due Dates: Laboratory reports generally are due in the Department Office (MH-580) at5:00 p.m. on a specified day, usually one week after the completion of the experiment.Consult the laboratory schedule for exact due dates. It is a good idea to plan aheadand write parts of your laboratory report before you have finished the experiment. Thiswill keep you from falling behind and will also help you to understand the experimentwhile it is still in progress.


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WHY DO EXPERIMENTS?

Our General Chemistry course includes a laboratory component because all ofchemistry is based on observations. You may get the idea from your textbook that

chemistry is mostly theory. There is much theory in chemistry, but all chemical theory

explains the observations that chemists have made, and theories must agree with

experimental observations. In Chemistry 120A, we ask you to complete five

explorations. Each of these involves experiments designed to generate data and

results of the same sort that chemists obtain when they do research. These

explorations differ from chemical research in that the results that you will obtain are

already known, whereas research explores the unknown. Still, we expect you to learn

how chemists obtain the experimental information that underlies chemical theories.

The interplay between theory and observations can be described by a general

method, a scientific method. First, a scientist makes observations under controlled

conditions (does an experiment). When the scientist has enough results, he or she then

proposes a general conclusion regarding these results (frames a hypothesis). If the

hypothesis is sufficiently general, the scientist then uses it to deduce what should occur

under other conditions (makes predictions). To check the validity of the hypothesis, the

scientist then makes more observations (tests the predictions). When the newexperiments agree with the predictions, the hypothesis is supported, and enough such

support causes it to be accepted as a scientific law. When the experiments do not

agree, the hypothesis is incorrect and must be revised. In either case, experiments

occupy a central role in any science. They are both the starting point of information

gathering and the ultimate test of whether hypotheses are correct.

Chemistry provides particularly instructive examples of experiments in science

because observations can be made in a chemistry laboratory under controlled

conditions. In designing the explorations that constitute the laboratory portion of

Chemistry 120A, we had several goals. You can learn much about chemistry as you

carry out these explorations.

l. You can learn something about how chemists learn.

2. You can learn some facts and laws of chemistry.


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3. You can learn some important laboratory techniques.

4. You can learn to work quantitatively.

5. You can learn to think like a scientist.

Every good scientist is an active observer. To become skilled at observations,

you must pay attention and ask questions. Why are we doing this particular

procedure? What would be the effect of changing a condition? What might go wrong

with the procedure? What is the meaning of the observations? Good laboratory workers

are always thinking about what is going on, asking questions and modifying their

thinking as they go. Form the habit of being an active, questioning laboratory worker.

Every good scientist also is a careful record keeper. Complete records must be

kept of all procedures and observations. An experiment is no better than the written

records of what happened during that experiment. For that purpose, every good

experimenter keeps a laboratory notebook, in which all significant observations are

written down. Form the habit of recording everyobservation that might be important.

SAFETY IN THE LABORATORY

Every good scientist takes appropriate safety precautions. A chemistry

laboratory is like a freeway -- it is safe for all, provided all understand and obey the

rules. But just like a freeway, it can be dangerous for all ifanyone ignores the rules.

There are basic safety rules for working in the laboratory that are analogous to traffic

laws. You are expected to know them and obey them whenever you are working on an

experiment. Form the habit of learning safety rules and living by them.

Like any other human endeavor that is worth doing, chemistry experiments

involve a certain amount of risk, particularly when the unknown is being explored. The

Curies, for example, eventually died of cancer brought on by exposure to theradioactivity which they discovered and studied. Nevertheless, risks are minimized and

the laboratory made as safe as any other work place when everyone uses caution and

common sense. The following are general safety rules that must always be observed.


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1. KNOW YOUR EXPERIMENT. The more you know about the procedures and

chemicals you are working with, the easier it is to avoid accidents. Read the exploration

before coming to the laboratory. Become familiar with a procedure, instrument, or

chemical before you do experiments with it. There is no excuse for not knowing asmuch as possible before beginning to work.

2. ALWAYS BE CAREFUL. Along with ignorance, the worst enemy of safety is

carelessness. Care in the laboratory includes staying alert, observing what is going on,

and not taking anything for granted.

3. WEAR SAFETY GOGGLES, LAB COATS, CLOSED SHOES. The eye is a

marvelous instrument, but it is vulnerable to injury. Accidents in a chemistry laboratory

frequently involve flying materials -- splashing liquids, splintered glass, etc. -- which can

seriously injure the eyes. Full goggles must be worn at all times in all chemistry

laboratories and when picking up materials at the chemicals stockroom. Note: this is

not a local rule. State law requires that eye protection must be worn wherever

potentially harmful chemicals are stored.

We strongly recommend that you not wear contact lenses! They readily

absorb chemical vapors that can lead to eye irritation and damage without you realizing

it. If you must wear contact lenses, notify your laboratory instructor.

4. KEEP WORK AREAS CLEAN. Chemicals used in the laboratory are safe as

long as they are kept in their appropriate place, but they can be very dangerous if

allowed to contact the wrong materials. This is particularly true of strong acids and

bases and human skin. Chemicals become particularly dangerous when we are

unaware of what they are. A spill on a bench top may look like water but be strong acid.

Always clean up any spilled material immediately.

Mercury spills must be carefully cleaned up using a special air suction apparatus.

If you are unfortunate enough to break a thermometer, immediately inform your

instructor. Do not try to recover spilled mercury by yourself.

5. LABEL ALL MATERIALS. Any time you are working with more than one

substance of similar appearance, there is a possibility of a mix-up. Just as newborn


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babies are given name tags to prevent inadvertent confusion, samples in the laboratory

should be uniquely identified.

6. DON'T EAT or DRINK. Too many chemicals are harmful when takeninternally for it to be safe to eat or drink in the laboratory.

7. WEAR SENSIBLE CLOTHING. High-heeled or open-toed shoes, long floppy

sleeves and the like are invitations for accidents to happen. These are prohibited in the

laboratory. If you must wear fashionable and/or expensive clothing, wear a protective

lab coat or apron over it. If you have long hair, tie it back on lab days. Hair very

easily catches fire!

8. BEWARE OF FIRES. Chemistry experiments frequently involve the use of

open flames for heating. Always check around you (l) before lighting a Bunsen burner

to be certain no one is using a volatile flammable solvent such as acetone, and (2)

before using a flammable solvent to be certain no one has an open flame nearby.

9. KNOW WHERE SAFETY EQUIPMENT IS. If you are careful, accidents will

be very rare. If they do happen, though, a quick response may be crucial to avoiding

disaster. Be sure you know the location of the following, and how to use them:

eye wash first aid kit

safety shower emergency telephones

fire extinguisher all exits

If you get any chemical in your eyes, begin an eye rinse at the eyewash

immediately. Eye damage can occur very quickly.

10. BE AWARE OF SENSITIVITY TO CHEMICALS. The chemicals used in

General Chemistry are safe for general use, but many chemicals can cause adverse

reactions for those who are especially sensitive. If you are pregnant, suffer from

allergies, or know of any special sensitivity, please notify your laboratory

instructor or the laboratory coordinator before the beginning of laboratory work.

If, during a laboratory, you experience unusual symptoms such as persistent itching or

shortness of breath, immediately stop what you are doing and consult your instructor.


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In addition to these general rules, some specific precautions apply when working in the

general chemistry laboratory.

l. Put nothing in drying ovens unless specifically instructed to.

2. When diluting strong acids, always add the acid to water. Adding water tostrong acid can liberate enough heat to boil the solution, causing splattering or

"spitting" of hot acid solution in random directions.

3. Handle volatile, toxic, and obnoxious materials in the fume hood.

4. Never return excess chemicals to their original container. Discard excess

chemicals in the appropriate waste container. To minimize waste disposal, follow

the procedure and do not take more than is needed.

5. Never perform unauthorized or unsupervised experiments.

6. Never pipet liquids by mouth suction. Instead, use a rubber pipet bulb.

7. Never push glass into a stopper without protection. When inserting glass into

a stopper, wet the glass with water or glycerol, wrap the glass with a towel, and

hold the glass near the stopper.

8. Never taste or smell laboratory chemicals.

WASTEDISPOSAL

There are separate containers for different types of waste. Place each kind of waste

only in its proper container. Your laboratory procedure describes which container to

use for each type of waste that you generate during an exploration. When in doubt,

consult your laboratory instructor.

Glass wastecontainer is for glass waste. Dont put paper or chemicals in

this container!

Solid chemical waste containeris for solid waste. Dont put glass or liquids

in this container!

Non-Halogenated Liquid waste container is for organic liquids such as

ethanol and acetone. Dont put solids or aqueous solutions in this container! Aqueous waste containeris for aqueous solutions that contain toxic materials.


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THELABORATORYNOTEBOOK

Your laboratory notebook is the most important document in the laboratory,

becaise it is where you record all observations that you make while doing explorations.

A good laboratory notebook is organized in a way that makes it easy for you to locate

and identify an observation that you made at an earlier date. In the General Chemistry

laboratory, we expect you to keep a complete notebook, following the rules that are

given below.

Type of Notebook: You are required to make duplicate copies of all your

notebook pages, so your laboratory notebook must produce a duplicate page for each

original page. These notebooks have pages in alternating colors. The originals shouldbe on the white pages, duplicates on the yellow or blue pages.

Instructor Verification: At the end of each laboratory period, have your

instructor date and initial your data pages for that day. Before leaving for the day, turn

in the duplicate copies of your data pages to your laboratory instructor.

Table of Contents: Reserve the first four pages of your notebook for a table of

contents. This table should have four columns: Date, Exploration number, Description,

and Page number. The description should briefly identify the procedure. For example,

your first entry may be described "Preparation of Solution." Update your table of

contents after each laboratory period, so that it always shows all of the data that have

been entered in it.

Data Pages: At the top of each data page, enter the exploration number and the

date. On the first page of each exploration, be sure to begin with the title of the

exploration.

Your laboratory notebook is the only place where the observations that you make

in the laboratory should be recorded. Do not record data or observations on stray

pieces of paper or in the laboratory manual.


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Types of Data: You should include the following:

Numerical data (temperatures, masses, volumes, etc.): identify the data fully,

include units, and give the correct number of significant figures. For example: "Mass ofempty flask and stopper: 27.4586 g."

Observations: record anything that you notice that might turn out to be important.

For example: "When the 2 solutions were mixed, a white precipitate formed." "Balance

#5 had to be re-zeroed before making this weighing." When in doubt, record an

observation. An observation that turns out not to be important can always be ignored,

but an unrecorded observation is lost forever.

Preliminary calculations: when the procedure calls for you to do a calculation

before proceeding, enter the calculation in your laboratory notebook.

Comments and speculations: anything that you think of which may help you in

interpreting the data and results can be included as a comment. For example: "This

calibration doesn't agree with the first one, but I think there were water droplets on the

flask walls." Be sure to identify these as opinions by using words like "I think", "Maybe",

"It appears", etc.

Special Instructions: Write only on the numbered side of the pages. Be sure to

use carbon paper to make a duplicate copy of your data or have a notebook with paper

that automatically produces a carbon copy. Write only in ink (ball point pen). Never

erase errors. If a small mistake is made, draw a line through the mistake and write the

correct information above or next to the mistake. If an entire page needs correcting,

draw a large X across the entire page and write VOID in large letters. When you void

data, write an explanation of why it is invalid. Here are two examples: "The balance

was miscalibrated." "I used the wrong reagent in preparing my solution."


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PRECISION OF MEASUREMENTS

Chemistry is a quantitative science. Most of the time, a chemist wants to know

not only what is happening but also to what extent (how much). Chemical observations

must be expressed as quantitatively as possible. Quantitative measurements have

three equally important parts: a numerical value, appropriate units, and a precision.

When recording data in your laboratory notebook and when reporting results in your

laboratory reports, always include all three of these parts.

Of these three parts, precision requires further discussion. Numerical value is

self-evident. Units are what allow us to scale a numerical value appropriately (20 miles

is quite different from 20 centimeters). Precision is the degree of certainty with which anumerical value is known: "about 20 miles" is a much less precise statement than "21.5

miles." Quantitative scientists have established a basic rule for stating the precision of

numerical values: the number of digits recorded for the numerical value expresses

the precision of the measurement.

As an example of how this rule works, consider measuring the length of a table.

You might look at it and estimate, "This is a 2-meter table." The length has been

expressed as a one-digit number. Scientifically speaking, this statement means, "This

table is more than 1.0, but less than 3.0 meters long." After a crude measurement, you

might be able to state the length more precisely as 1.8 meters, meaning that you know

the table to be longer than 1.7 but shorter than 1.9 meters. A measurement with a

better measuring device might give you a result of 1.83 meters. This means you are

stating that the table is greater than 1.82 meters long but less than 1.84 meters long. A

very careful measurement with a good tape measure might yield the result, 1.826

meters. Now you are asserting that the table is longer than l.825 but shorter than 1.827

meters.

The number of digits in a numerical result is called the number of significant

figures. Unless otherwise stated, it is understood that the measurement is precise to

within one unit in the last significant figure. Consider, for example, a length that is

reported as 1.826 meters. There are four significant figures and we assume, unless told

otherwise, that this result contains three certain figures and one doubtful (the last, "6")


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figure. This specific measurement is understood to be 1.826 0.001 meters (i.e. to lie

between 1.825 meters and 1.827 meters). Expressing the value in a different unit such

as centimeters, 182.6 cm, does not change the number of significant figures (still four).

The precision of a measurement depends on the quality of the measuring device

used to obtain the measurement. Very sensitive instruments yield measurements of

high precision, but less sensitive instruments yield results of lower precision. The

analytic balance is the most sensitive instrument that you will use in General Chemistry.

The precision of a measurement can also depend on variations in its value. In

our example of the table, the table top might be scalloped or fluted, in which case its

length would vary by a few centimeters, depending on whether it was measured at a

protrusion or an indentation. A scientific example of this kind of fluctuation is the

distance between the Earth and its moon. Our moon's orbit is not perfectly circular, so

this distance fluctuates with time, varying by about 48,000 kilometers in the course of a

month.

SCIENTIFIC NOTATION

Scientists commonly work with very large and small quantities. The diameter of

an atom, for instance, is 0.00000000014 meters, and the average distance of the moon

from the Earth is 384,000,000 meters. How many significant figures does each of these

distances contain? As the numbers are written, it is hard to tell, because all the extra

zeros are needed to locate the decimal points. They have nothing to do with the

precision of the number. To eliminate the ambiguity created by zeros needed to locate

the decimal point, and to shorten the writing of small and large numbers, scientists

commonly use a special format, scientific notation, to express these numbers.

Scientific notation is based on the fact that any number can be expressed as anumber between 1 and 10 multiplied or divided by ten an appropriate number of times.

The moon's distance from earth, 384,000,000 meters, can be written as 3.84 x 10 x 10 x

10 x 10 x 10 x 10 x 10 x 10. That looks cumbersome, but we can abbreviate the 8 " x

10" 's as 108 (meaning "multiply by 10, 8 times"): 3.84 x 108 meters. Similarly, an

atomic diameter of 0.00000000014 meters can be written as 1.4 10 10 10 10


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10 10 10 10 10 10, abbreviated as l.4 x 10-10 (meaning "divide by 10, 10

times"). (Although it is not needed for scientific notation, 100 has a specific meaning:

"multiply by 10, 0 times": 1 x 100=1).

The precision of a number that is written in scientific notation is unambiguous.

The number 3.84 x 108 meters means "not less than 3.83 x 108, nor more than 3.85 x

108 meters." Extra zeros now mean extra precision: 3.840 x 108 meters means "not

less than 3.839 x 108, nor more than 3.841 x 108 meters."

RELATIVE AND ABSOLUTE PRECISION

The degree of precision in a given experimental value can be viewed in twodifferent ways: as the absolute precision (how big or small is the uncertainty in the

value?) or as the relative precision (what is the fractional uncertainty in the value -- how

big is the uncertainty relative to the value itself). Each of these ways of looking at

precision is important.

To illustrate these concepts, we return to our example of the table length. If the

table has been measured to be 1.826 meters long, the absolute precision of the

measurement is 0.001 meters. The relative precision is 0.001/1.826, or 5 x 10-4. Note

that you only have single digit precision in 0.001 so the computed answer is rounded to

a single digit, 5 x 10-4, not 5.475 x 10-4. There are several different ways of expressing

relative precision: we can state it as 1/1826, or 5 x 10-4, or 0.05% (percent is relative

precision x 100), or 5 parts per 10,000. Notice that while absolute precision has the

same units as the measured quantity, relative precision is a ratio of two values having

the same units and is therefore dimensionless.

When you are reporting a measurement, either relative or absolute precision can

be used, but when measurements are combined to compute a result, the form of thecombination determines which type of precision is more useful. As an illustration,

consider the volume and perimeter of the table top whose length we measured earlier.

Suppose we find its width to be 0.320 meters (3.20 x 10-1 m). The absolute precision of

this width measurement is 0.001 meters, while its relative precision is 1/320, or 0.003

(3 x 10-3). If a measurement of the thickness gives 0.015 meters (1.5 x 10-2m), the


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absolute precision is 0.001 meters, and the relative precision is 1/15 or 0.067 (or 6.7 x

10-2).

Now combine these measurements to determine the perimeterPand the volumeV of the table top. Perimeter is P= L + L + W + W = 2(1.826) + 2(0.320) = 4.292

meters; volume is V= L x Wx T= 1.826 x 0.320 x 0.015 = 8.76 x 10-3 meters. How

precisely do we know each of these computed, or derived, values? The precision of

computed results can be found from the precision of individual measurements by

considering the largest possible change in each individual measurement.

First, consider the table's perimeter. According to the precision of the length

measurement, the length might be as large as 1.827 meters, or as small as 1.825

meters. The width might be 0.321 meters, or 0.319 meters. Some of the time, errors will

cancel -- the length may be a bit larger than measured, but the width is a bit smaller --

but we are interested in how precisely we know the perimeter, so we will assume the

worst case. In the worst case, both measurements are off by the maximum amount, in

the same direction. Then the perimeter could be as large as 2(1.827) + 2(0.321) =

4.296 meters, or as small as 2(1.825) + 2(0.319) = 4.288 meters. The absolute

precision in the perimeter is 0.004 meters. Notice that this is the sum of the

absoluteprecisions of the individual values: 0.001 + 0.001 + 0.001 + 0.001 = 0.004.

Applying the same logic to the volume computation, we find that it might be as

large as 1.827 x 0.321 x 0.016 = 9.38 x 10-3 cubic meters, or as small as 1.825 x 0.319 x

0.014 = 8.15 x 10-3 cubic meters. The volume is 8.76 x 10-3 0.62 x 10-3 cubic meters,

or there is a relative imprecision of 0.62 x 10-3/8.76 x 10-3 = 0.071. Notice that the

relative precision for the volume is the sum of the relative precisions of length

(5 x 10-4), width (3 x10-3) and thickness (6.7 x10-2): 0.0005 + 0.003 + 0.067 = 0.071

The precision of a composite result can always be determined by the type of

analysis described above, but this procedure is tedious. Fortunately the outcome is

always the same. For addition and subtraction, the absolute precision of the result is

the sum of the absolute precisions of the individual values. For multiplication and

division, the relative precision of the result is the sum of the relative precisions of the

individual values.


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Another example will illustrate the application of these rules for precision. A

student, asked to determine the density of a non-volatile unknown liquid, filled a 25-mL

graduate cylinder until it contained 25.0 mL of liquid. The full cylinder weighed 47.5764

g. Using an eye-dropper, the student carefully removed liquid until the cylindercontained 20.0 mL of liquid, whereupon it weighed 43.0464 g.

Consider the various quantities involved in this example. Table I-1 summarizes

the measurements, computations, and precisions. The absolute precision of each

measured quantity is found directly from the measurement, and the relative precision is

the absolute precision divided by the measured value. The precision of each computed

quantity is determined by adding the appropriate precisions (absolute or relative) of

quantities used in the calculation. The computed precision values in bold face are the

ones that we find directlyfrom the measured data, while the other computed precision

values are obtained from the bold face values and the value of the quantity.

TABLE I-1: MEASURED ANDDERIVED QUANTITIES AND

PRECISIONS

MEASURED QUANTITIES

QUANTITY VALUE ABS. PRECISION REL. PRECISION

initial Cyl. Vol 25.0 mL 0.1 mL 1/250

initial Cyl. mass 47.5764 g 0.0001 g 1/475,000

final Cyl. Vol 20.0 mL 0.1 mL 1/200

final Cyl. mass 43.0464 g 0.0001 g 1/430,000

COMPUTED QUANTITIES

QUANTITY VALUE ABS. PRECISION REL. PRECISION

vol. transferred 5.0 mL 0.2 mL 2/50 = 1/25

mass transferred 4.5300 g 0.0002 g 1/20,000

liquid density 0.9060 g/mL 0.04 g/mL 1/25 = 0.04


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Specifically, the volume transferred is obtained by subtracting two volumes, so its

absolute precision is the sum of absolute precisions of the volumes. The mass

transferred is obtained by subtracting two masses, so its absolute precision is the sum

of absolute precisions of the two masses. The relative precision for each of thesemeasurements is then obtained from the values of their absolute precision.

The density is obtained by dividing mass by volume, so its relative precision is

the sum of relative precisions of transferred mass and transferred volume. The sum of

1/25 and 1/20000 is 1/24.9687, which rounds to 1/25 or 0.04. After we find the relative

precision of the density, we use it to compute the absolute precision. The absolute

precision of the density is (1/25) x (0.9060 g/mL) = 0.04 g/mL.

The direct calculation of the maximum and minimum density values again shows

the validity of using the shortcut method to find the precision of the calculated result.

ROUNDING OFF

In the above example, the density might be as large as 0.944 g/mL or as small as0.871 g/mL. It is incorrect to write it as 0.9060 g/mL, which implies that it is known to

0.0001 g/mL. In such cases, the result is rounded off -- non-significant figures are

eliminated. Because the uncertainty in the density is in the second decimal place, this

result is rounded off to two decimals: 0.91 g/mL. We have still overstated the precision,

because 0.91 g/mL implies a precision of 0.01, while the actual precision is 0.04.


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Rounding off one more place and giving the density as 0.9 g/mL would imply an

uncertainty of 0.1, which is larger than the actual uncertainty. The convention is to

round off until dropping one more digit would result in an uncertainty larger than the

actual uncertainty.

When the digit following the last significant digit is 5 or greater, the remaining

digit is increased by one unit: 0.9060 becomes 0.91. If the digit following the last

significant digit is less than 5, the remaining digit remains unchanged: 0.9045 rounded

to 2 significant figures is 0.90.

Shortcuts to Precision

Chemists want to spend minimum time determining precision. Every time a

chemist makes a measurement, precision and significant figures are a concern, but

chemists are more interested in what experiments reveal than they are in significant

figures. The first question, then, is "How important is precision for this particular

experiment?" An analytical chemist, for example, might be interested in determining the

level of a particular carcinogen in a sample of ground water. If the carcinogen is

present at only about 1 part per billion, the precision of the measurement must be very

carefully stated. On the other hand, a synthetic chemist whose goal is to synthesize

new compounds is primarily interested in putting the substance in a bottle. The

quantitative yield is important (the higher the yield, the less expensive the product will

be), but precise values for this yield are not.

When quantitative values are being reported, but their exact values are less

important than the qualitative results, the detailed treatment of precision is not needed.

Instead, we can use a simple system to determine the appropriate number of significant

figures:

1. To determine the number of significant figures in an individual measurement,

read the number from left to right, counting all the digits starting with the first one that is

non-zero.

300. 3 sig. figs.


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1.00 3 sig. figs.

0.020 2 sig. figs.

2. When adding or subtracting, the number of decimal places in the answershould be equal to the number ofdecimal places in the number with the fewest places.

The number of significant figures is not relevant:

0.12 2 sig. figs. 2 decimal places

1.6 2 sig. figs. 1 decimal place

11.490 5 sig. figs. 3 decimal places

Sum: 13.2 3 sig. figs. 1 decimal place

3. When multiplying or dividing, the number ofsignificant figures in the answer

should be the same as that of the quantity with the fewest significant figures:. The

number of decimal places is not relevant:

1.365 x 2.63 / 3.0 = 1.2

significant figures: 4 3 2 2

The above example is one where the simplified procedure gives a different resultthan the more elaborate one. The divisor (3.0) has a relative precision of 1/30, so the

result could be stated more precisely than this: the result, 1.19665, could be rounded to

1.20 (1 part in 120) rather than to 1.2 (1 part in 12). If the importance of the result is its

quantitative value, 1.20 would be the more appropriate number to report; if its

importance is in its qualitative significance, report 1.2. (But don't spend a lot of time

worrying about it: either way of reporting is legitimate! What is not legitimate is to report

this result as 1.19665.)

4. Calculators do not necessarily give results with the correct number of

significant figures. They automatically drop trailing zeroes even when they are

significant (try multiplying or adding 3.00 and 5.00 on your calculator) and they may

carry extra decimal places even when they are not significant (try dividing 5.00 by 3.00

on your calculator). Even when a calculator is programmed to report a particular


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number of digits, that number of digits may not be the correct number of significant

figures. Never believe the number of significant figures on your calculator!


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Precision in Volume Measurements

Volume measurements illustrate both absolute and relative precision. As

examples, consider the three volume measurements illustrated in Figure I-1. A liquid inany cylindrical container has a curved surface, as the figure shows. The lowest point on

the curved surface, called the meniscus, is the position that we read. We can never

read that position exactly but must always estimate it as closely as possible.

Figure I1: Examples of volume measurements. The buret reading is 33.34 mL, the

gradiated cylinder contains 30.0 mL, and the beaker contains 37 2 mL

The absolute precision of our measurement depends on the diameter and

markings on the container. A reading always is more precise than the scale markings,

because we can estimate the distance of the meniscus from the nearest mark. In the

figure, the buret has a line for every 0.1 mL, and we can estimate with an absolute

precision of 0.01 mL. The buret reading in Figure I1 is 33.34 mL. The graduated

cylinder in the figure has a larger diameter than the buret, and its markings are every 1

mL. This graduated cylinder is filled to the 30 mL line, but we can estimate that it is not

more than 30.1 or less than 29.9 mL, so the absolute precision is 0.1 mL and we record

a volume of 30.0 mL. We can estimate the volume of liquid in the 50 mL beaker to the

nearest1 mL, 37 mL, but notice that the beaker is marked 5%. This indicates that


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the lines marked on the beaker are only reliable by this amount. Because 5% of 37 mL

is 2 mL, we should report this volume as 37 2 mL.

The absolute precision of a volume measurement in the graduated cylinder

shown in the figure is 0.1 mL, whether the volume is 30.0 mL or 100.0 mL. Therelative precision changes, however, as the amount of liquid in the cylinder changes.

The relative precision of a 30.0 mL volume is 0.1/30.0 or 0.003. If the graduated

cylinder were filled, on the other hand, the relative precision would be 0.1/100.0 or

0001.

Precision in Mass Measurements

The most precise mass measuring device in the introductory chemistry

laboratories is the electronic analytic balance. This balance reads mass digitally with an

absolute precision of 0.0001 gram (0.1 mg). However, when a digitally reporting

instrument displays a particular number of digits, the uncertainty may be larger than 1

in the last digit to the right. To be sure of the precision of a digital readout, we must

measure the same object several times, preferably using different instruments. For

example, two balances may read 35.8252 g and 35.8255 g for the mass of the same

beaker. In this case, we conclude that the precision of the balances is 0.0003 g,

because the "true" mass may have any value between these two measurements.

Mass measurements using an analytic balance are more precise than volume

measurements using burets. You can measure the volume of 35 mL of water to 0.01

mL using a buret, a relative precision of 3 x 10-4, but you can measure the mass of the

same amount of water (about 35 g) to 0.0001 g using an analytic balance. This is a

relative precision of 3 x 10-6 , 100 times more precise than the volume measurement.

ACCURACY AND ERROR

Our discussion so far has concentrated on the precision of numerical results,

which is the uncertainty in the numerical value. Although precision is very important in

quantitative scientific work, the accuracy of a result is even more important because

the accuracy indicates how close the result is to the actual ortrue value.


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Absolute error (E) is defined to be the difference between the measured (M)

and the true (T) values.

E= M- T

Absolute error can be either positive or negative. Like precision, error can be

expressed either as absolute or relative. Relative error(RE) is the ratio of the absolute

error to the correct value.

RE=MT( )T

Think about how scientists can be sure of the true value of any quantity. It's not

easy, because every experimental measurement is subject to error, and the usual way

of discovering errors is by comparison with a "better" or "truer" value. Although it isalmost always necessary to measure with great precision in order to achieve accuracy,

precise measurements may not be accurate, particularly if what is actually measured

differs for some reason from what it is intended to measure.

An everyday example will illustrate this point. A farmer, concerned about

whether his crops were receiving enough rainfall, bought 3 precise rain gauges, each

capable of registering rainfall to 0.01 mm. He installed two on different sides of his

house and one on a fence post beside his fields. After the next rainfall, he read each

gauge. Gauge 1, outside his bedroom, registered 55.65 mm; Gauge 2, outside his

kitchen, registered 7.45 mm; and Gauge 3, on the fence post, registered 17.78 mm.

Although each of these readings was precise to 0.01 mm, they cannot all be accurate.

On closer inspection, the farmer found that Gauge l was just at the edge of his roof and

had been collecting a significant amount of roof runoff. Gauge 2 was on the downwind

side of the house and therefore had been protected from the rain. Only Gauge 3, on the

fence post in the open, was both precise and accurate: the true rainfall was 17.78 mm.

In chemistry experiments, mistakes in what is measured can cause precisemeasurements to be in error. A supposedly dry sample that contains some water will

have an erroneously high mass. A sample, some of which has been accidentally lost,

will have an erroneously low mass. A pressure reading thought to be of only one gas

may actually be the total pressure of more than one gas. You should always be alert to

the possibility of such errors and do your best to avoid or minimize them.


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AVERAGING

One way to avoid accidental mistakes in measurement is to repeat an

experiment several times and then report the average of several measurements as the

most reliable result. In such replications of experiments, in addition to precision and

error we can also define the average or mean value and the deviation of individual

values from this average value. The average value (A) is the sum of all individual

values divided by the number of values (N):

A =M

N

(The symbol - the Greek capital letter sigma - means "add up all the individual values

of"). The deviation (D) of each individual value is the absolute value (i.e. always

positive) of the difference between the value and the average.

D = |M-A|

This is the absolute deviation. If we divide an absolute deviation by the measured

value, we obtain the relative deviation, Drel:

Drel =D

M

We can average a set of deviations to obtain an average deviation (Dav

):

Dav =D

N

The average of the relative deviations is the Relative Average Deviation, RAD, which

you will be asked to calculate in several of the reports for Chemistry 120A:

RAD =Drel

N

The average deviation and relative average deviation are good measures of

precision, because they reflect the uncertainty in a whole set of measurements.

We return to our (now wiser) farmer friend for an example of these concepts.

The farmer has bought a fourth rain gauge (being skeptical of all of them) and has

installed one at each corner of his field. After the next storm, he checks all four gauges,


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finding readings of 60.52, 60.48, 60.78, and 60.54 mm. Table I-2 summarizes the

measurements and their deviations from the average.

Table I-2Deviations in Measured Rainfall

Gauge Reading Absolute Deviation Relative Deviation

|M-A| 103(|M-A|)/A

Units: mm mm Parts per 1000 (ppt)

1 60.52 0.06 1.0

2 60.48 0.10 1.6

3 60.78 0.20 3.3

4 60.54 0.04 0.7

Sum 242.32 0.40 6.6

Average 60.58 0.10 1.6

The average absolute deviation is 0.10 mm, and the average relative deviation is

0.0016 or 1.6 ppt (parts per thousand), or 0.16%. Because the absolute deviations are

only precise to about 1 part in 10 (0.01 mm out of about 0.1 mm), each relative

deviation is rounded off to 2 significant figures.

STATISTICAL ANALYSIS:THE RULE OF FOUR

Sometimes, in a set of measurements, one result deviates greatly from the other

results. If the large deviation is due to known experimental error, exclude the result

(Remember the farmer's first placement of his rain gauges.) Many times, however, the

cause of a large deviation is not known. In such a case, a statistical test can be applied

to find out whether the result should be retained or rejected. The easiest test is the

"Rule of Four".

For the Rule of Four to be valid, the set must include at least four values. The

average (mean) value is calculated without including the value which deviates the most,

and the average deviation is computed for the set without this value. Then the deviation


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of the excluded value is evaluated; if it is greater than four times the average deviation,

its exclusion is statistically valid. Conversely, if its deviation is less than four times the

average deviation, the result must be included in the set as a valid measurement, and

the mean value and average deviations must be obtained for the entire set.

Applying the Rule of Four to the data in Table I-2, we temporarily exclude the

reading with the highest deviation, that from Gauge 3. This gives the results shown in

Table I-3:

Table I-3

Adjusted Rainfall Deviations

Gauge Reading Absolute Deviation

Units mm mm

1 60.52 0.01

2 60.48 0.03

4 60.54 0.03

Sum 181.54 0.07

Average 60.51 0.02

3 60.78 0.27

The average deviation of the three remaining values is only 0.02 mm, and the

deviation of the Gauge 3 reading, 0.27 mm, is more than four times that. On statistical

grounds, we are justified in rejecting the Gauge 3 reading and reporting the rainfall as

60.51 0.02 mm.


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EXPLORATION A1IS VOLUME CONSERVED?

OBJECTIVES

Science is built on sets of general laws. Some of these laws involve

conservation. Energy is conserved. Usually, mass is conserved. How about volume?

Your objective in this exploration is to determine whether volume is conserved. To

determine this, you will learn how to make quantitative measurements of both mass and

volume.

INTRODUCTION

Consult your textbook, Sections 1.5 and 1.6, for more details about measurements and

density.

Is volume conserved? This question must be answered by experiments. We can

theorize all we like, but no theory will tell us what actually exists in nature. Chemistry

textbooks describe theories that predict behavior, but all the concepts described in a

textbook are based on observations and experiments done by generations of chemists.

You probably already know one of the fundamental laws of nature having to do

with mass: mass is neither created nor destroyed in physical or chemical processes.

This is an example of a conservation law. We say that mass is conserved. You will

explore whether volume is also conserved. In other words, when two liquids are mixed

together, is the new volume always equal to the sum of the volumes of the individual

samples?

In order to study any property like mass or volume, we must have techniques formaking quantitative measurements. Because mass and volume are everyday

properties, you already know something about how to measure them. Bathroom scales

measure mass, and measuring cups measure volume. To explore volume

conservation, however, you need to measure masses and volumes with higher

accuracy than everyday measuring devices allow. In this exploration, you will learn to


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use precision scientific tools for measuring mass and volume. An analytic balance

measures masses with high accuracy, while volumetric glassware measures volumes

accurately.

Bathroom scales and analytic balances both work by weighing - that is, by

measuring the amount of gravitational force that a mass exerts. Force is directly

proportional to mass (f = ma), so force measurements can be converted to masses,

provided we know the proportionality. Whereas a bathroom scale measures mass only

to the nearest half-pound, a quality analytic balance can measure to 0.0001 g (0.1 mg).

Using the conversions, 1 pound = 454 g and 1 mg = 0.001 g (10 -3 g), we can see that an

analytic balance is over 2 million times more precise than a bathroom scale.

Volumetric glassware and measuring cups both work by measuring height. Each

has been carefully manufactured so that when full, it contains a known volume of liquid.

In the case of measuring cups, we fill "to the brim" or to a mark etched on the cup. In

the case of volumetric glassware, we always fill to some prescribed mark. You will use

two types of such glassware: volumetric flasks, which contain known volumes of liquid,

and volumetric pipets, which deliver known volumes of liquid. Each of these is very

simple: it is nothing more than a piece of glassware with a line scribed on it.

Nonetheless, they allow the measurement of volumes with high precision and accuracy.

Analytic balances are more versatile than volumetric glassware, because the

analytic balance measures masses over a continuous range with high precision and

accuracy. Each volumetric flask and volumetric pipet, in contrast, can accurately and

precisely measure just one fixed volume. For volumes other than the fixed volume, it is

more convenient to measure mass and find a way to convert to volume.

Density provides a connection between mass and volume. Experiments have

shown that the ratio of mass to volume of any pure liquid or solid is a constant, provided

that temperature does not change. This ratio is defined to be the density d, given by the

equation,

d=m

V Equation A1-1

Density commonly is expressed in units of g/mL or g/cm3 (1 mL = 1 cm3), so it

will be convenient to measure masses in grams and volumes in milliliters.


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Equation A1-1 links three quantities. If you know any two of these three quantities, you

can calculate the third. To determine density, you can weigh a sample of known volume, then

calculate density using Equation A1-1. If you weigh a container filled with a liquid of known

density, you can use a rearranged version of Equation A1-1 to calculate the volume:

V=m

d Equation A1-2

Accurate mass determinations actually involve two mass measurements. When you

weigh an object, you compare the gravitational force on the balance pan plus the object to the

force on the balance pan alone. To obtain the mass of a liquid sample, you compare the mass of

a container filled with liquid to the mass of the empty container.

mobject = m2 - m1

Many analytic balances permit the mass reading to be pre-set to read zero for

the comparison mass. This is called taring the balance. When this is done, the second

mass reading gives the mass of the object directly (When you zero a bathroom scale

before stepping on it, you are taring the scale). Taring sets m1 = 0, giving

mobject = m2 - m1 = m2 - 0 = m2

Equation A1-2 provides a way of determining volume to high precision. If

the density of a liquid is accurately known, you can use mass

measurements and Equation A1-2 to determine the volume of any

particular container. Water is the most convenient liquid to use for such

measurements. It is inexpensive, non-toxic, and its density has been very

accurately measured. To apply Equation A1-2, however, we must

measure the temperature as well as the mass, because the density of

water varies slightly with temperature, as Figure A1-1 (next page) shows.


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Figure A1-1: Density of water as a function of temperature

SEQUENCEOFEXPERIMENTS

Part A: Estimate whether liquid volumes are conserved.

Part B: Calibrate a 10-mL Volumetric Flask to determine its precise volume.Part C: Calibrate a 5-mL Transfer Pipet to determine the precise volume it delivers.

Part D: Determine precisely the density of an Unknown liquid.

Part E: Quantitatively determine whether liquid volumes are conserved.

0.995

0.996

0.997

0.998

0.999

1

5 10 15 20 25 30 35

Dty(gmL

Temperature (C)


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PROCEDURE

Precaution: no open flames are permitted during this experiment!

Cleaning: The first time you use a piece of glassware, clean it by washing with

soap and water, then rinsing thoroughly with tap water, and finally rinsing with about 5

mL of deionized water from your wash bottle. Once you have clean glassware, you

need not clean it again during this exploration, because none of the liquids

contaminates glassware.

Drying: When the procedure calls for dryglassware, add 2-3 mL of acetone to

the clean glassware, swirl to wet all surfaces, and then discard the acetone in the

acetone waste bottle. Dry the outside of the glassware with a paper towel. Dry the

inside by inserting a Pasteur pipet attached to the house vacuum and drawing air

through until the glassware is dry. Do not blow air through the glassware, because

compressed air contains oil droplets that will contaminate the glassware!

PartA:PreliminaryStudyofVolumeConservation

1.) Clean your 10-mL graduated cylinder and one test tube. Invert them in a 250-

mL beaker containing a paper towel and allow them to drain. Rinse your metal spatula

with deionized water.

2.) Using your wash bottle, add 5.0 mL of deionized water to your 10-mL

graduated cylinder. Pour this liquid into the clean test tube. Again using your wash

bottle, add another 5.0 mL of deionized water to your 10-mL graduated cylinder. Pour

the water from the test tube back into your 10-mL graduated cylinder, stir thoroughly

with your metal spatula, and then read and record the total volume. Discard the water

in the graduated cylinder.

3.) Again, add 5.0 mL of deionized water to your 10-mL graduated cylinder, and

then pour it into the clean test tube.


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4.) Obtain an acetone wash bottle. Rinse your 10-mL graduated cylinder with

about 3 mL of acetone, swirl to wet all the surfaces, then discard the liquid in the

acetone waste bottle.

5.) Now add 5.0 mL of acetone to your 10-mL graduated cylinder. Add the water

from the test tube to the acetone in the graduated cylinder, stir the liquid mixture

thoroughly with your metal spatula, and then read and record the total volume. Discard

this liquid in the waste bottle marked "acetone waste."

Answer the following questions as comments in your notebook, and give your

reasoning. Note: Comments should appear on both the original and the carbon

copy of your notebook pages. A.) When you mixed two volumes of the same liquid

(water) was the resulting volume close to or equal to the sum of the two volumes? B.)

Is the sum of the two volumes within the range of uncertainty with which you can read

volume using the 10 mL graduated cylinder? C.) Answer the same questions when two

different liquids (water and acetone) are mixed. D.) Does it appear to you that volume is

conserved when the same liquids are mixed? When differentliquids are mixed?

Part B: Volumetric Flask Calibration

The quantitative determination of whether volume changes when two different

liquids are mixed requires the calibration of a volumetric flask (Part B) and a pipet (Part

C).

1.) Place about 11 mL of deionized water in your clean 10-mL graduated

cylinder. Let it stand so that its temperature will equilibrate with that of the lab.

2.) Clean and dry a 10-mL volumetric flask and stopper. After drying, handle

them only with a paper towel or Kimwipe, because oil from your hands can change themass of the flask. Do not handle the flask any more than is necessary.

3.) Zero an electronic analytic balance, and then weigh the stoppered flask to the

nearest 0.0001 g (0.1 mg). Record this mass.


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5.) Using a Pasteur pipet and rubber bulb, fill the flask with deionized water until

the bottom of the meniscus is exactly even with the mark. (See Figure A1-2).

Adjust the water level with the Pasteur pipet, being careful that no water

droplets adhere to the walls of the flask above the mark

Figure A1-2: Proper location of liquid level when a

volumetric container has been correctly filled to the mark.

5.) Stopper the flask and reweigh to the nearest 0.1 mg, using the same balance

as for the weighing in step 2. Handle the flask with a paper towel or Kimwipe to prevent

fingerprints.

6.) Return the sample to the graduated cylinder. Measure and record the

temperature of the water to the nearest 0.5 oC.

7.) Repeat steps 1-6 four more times to obtain five sets of data. Note: It is

essential that you dry your volumetric flask for each trial. Rinse with acetone and

draw a vacuum through it using a Pasteur pipet. DO NOT BLOW HOUSE AIR INTO

THE FLASK.

PartC:PipetCalibration

Note: The upper limit of electronic balances is 105 g.

1.) Clean a 50-mL Erlenmeyer flask, wipe the outside dry, and invert it on a paper

towel to allow it to drain. Fill a 250-mL beaker with about 200 mL of deionized water.


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2.) Clean your 5-mL pipet. Fill it about 1/2 full with soapy water, seal it with your

fingers at both ends, and shake. After a minute, drain the pipet (do notblow). Repeat

the process. Then rinse the pipet with tap water (3 times), deionized water (3 times),

acetone (once), and deionized water (3 times). The water should drain without leavingdrops on the pipet walls. If drops still adhere, Consult your instructor to determine

how to clean your pipet with NOCHROMIX.

3.) You can deliver very precisely the same volume each time if you master

pipetting, but reproducibly delivering the same volume requires practice, otherwise your

data will be neither accurate nor precise. Use a pipet bulb to draw water from the 250-

mL beaker into the pipet until the level is above the pipet mark. Use your fingertip to

control the pipet as you drain it to the mark while holding it vertical. Once the pipet is at

the mark, let it drain by gravity (do not shake or blow out the liquid).

4.) Weigh your clean 50-mL Erlenmeyer flask to the nearest 0.1 mg. Measure

and record the temperature of the water in the 250-mL beaker. Using your 5-mL

transfer pipet, transfer a 5 mL sample of deionized water to this flask. Weigh it again to

the nearest 0.1 mg, using the same balance for this and subsequent weighings. This is

the first calibration of the pipet.

5.) Measure and record the temperature of the water in the 250-mL beaker.Using the same pipet, add another 5 mL of deionized water to the Erlenmeyer flask and

then weigh it. Repeat with three additional samples of deionized water, recording the

water temperature and weighing after each addition. This gives a total of five additions,

so the flask should contain 25 mL of deionized water.

PartD:DensityofanUnknownLiquid

1.) Obtain from the solutions stockroom (SLC-242) a yellow box containing yourunknowns for the semester. It will include an unknown liquid for Experiment A1. Use

this liquid in the following procedure and in Part E.

2.) Dry your 10-mL graduated cylinder. Carry out steps 1-6 of procedure B using your

unknown liquid instead of deionized water. Return the liquid to the graduated cylinder after each


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trial. It is essential to dry your volumetric flask at the start of each trial. Repeat the procedure

three times. From the mass differences and the calibrated volume of your 10-mL volumetric

flask, calculate the density of the unknown liquid, to four significant figures. If your three

results do not agree to within 1%, repeat the procedure once more.3.) Discard the liquid in your volumetric flask and any liquid remaining in the 10-

mL graduated cylinder in the Organic Liquid Waste container. The liquids used in this

procedure are organic materials that are injurious to the biosphere. Do not pour

them down the sink!

Part E: Additivity of Volumes

1.) Clean and dry your 10-mL graduated cylinder and 10-mL volumetric flask. Fillyour 50-mL beaker about half full of deionized water. Using your 5-mL transfer pipet,

add a 5 mL sample of deionized water to the volumetric flask. Stopper and weigh to the

nearest 0.1 mg.

2.) Transfer about 11 mL of your unknown liquid into your 10-mL graduated

cylinder. Using a Pasteur pipet and rubber bulb, add the unknown liquid to the

volumetric flask until the meniscus coincides with the line.

3.) Stopper the flask, invert it several times to mix thoroughly, allow it to stand for

2-3 minutes and then observe the liquid level in the flask. Using a Pasteur pipet and

rubber bulb, add additional unknown liquid until the liquid level is again at the line.

4.) Repeat step 3 until the liquid level remains at the line after mixing and

standing. Then reweigh the flask and record the mass.

5.) Discard this liquid mixture in the waste bottle labeled "Non-Halogenated

Liquid Waste".

Repeat Part E to obtain a second set of data. If the results from the two sets of

data do not agree, repeat again to obtain a third set of data.


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CALCULATIONSCalculations for Part B: Compute the mass of water in the flask for each trial

as follows:

mwater= mfull flask - mempty flask

Use the water temperature and Figure A1-1 to find the density of water at this

temperature. Read the density from the graph to the correct number of significant

figures. Use the mass of the water and its density to compute the volume of the flask.

Vflask =mwater

dwater

Record this result with the correct number of significant figures. You measured

the mass of water with an accuracy of 0.1 mg out of 10 g (1 part in 10

5

), and you canread the density of water to 0.0001 g/mL (1 part in 104), so each calculated volume

should be reported with a precision of 1 part in 104.

Calculate the average volume of your experimental values.

Vflask, average =Vtrial 1+Vtrial 2 + .....( )

Number of trials

Determine and report the absolute deviation and relative deviation of each

measurement.Absolute Deviation = Vflask - Vflask, average

Relative Deviation =Absolute Deviation

Average Volume

Also, calculate the average deviation and relative average deviation (RAD).

These deviations are a measure of the uncertainty of the volume determinations.

Average Deviation =Deviationtrial 1+Deviationtrial 2 + .....( )

Number of trials

Relative Average Deviation =Rel. Dev.trial 1 +Rel. Dev.trial 2 + .....( )

Number of trials

Use the rule of four (pp. 23-24) to discard any volume that is not statistically valid.

Calculate the average volume from the statistically valid data. Use this average value in all

calculations that call for the volume of your volumetric flask.


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Calculations for Procedure C: Calculate the pipet volume for each trial. You

will have five separate values. Compute the average volume delivered and the

deviation of each individual value from this average. Use the rule of four (pp. 23-24) to

discard any statistically invalid measurements. Calculate the average volume of yourpipet using all statistically valid data. Use this statistically valid average value in all

calculations that call for the volume of your 5-mL transfer pipet.

For each addition of water in part C, compute the mass of water delivered by the

pipet.

mwater= mflask,with5mL added - mflask, prior to adding5mL

Use the water temperature and Figure A1-1 to find the density of the water at this

temperature. Read the graph to the correct number of significant figures and record the

density reading in your notebook.

Use the mass and density to calculate the volume delivered by the pipet:

Vpipet =mwater

dwater

Calculate the pipet volume to the correct number of significant figures. Take the

average of your experimental values.

Vpipet, average =

Vtrial 1+Vtrial 2 + .....( )Number of trials

Also determine and report the absolute deviation and the relative deviation of

each measurement as well as the relative average deviation (see p. 34).

Calculations for Procedure D: Compute the density of your liquid from the

mass data and the average flask volume from calculation B:

mliquid = mfull flask - mempty flask

dliquid =mliquid

V

flask, average

Calculate and report the average of your determinations, the absolute and

relative deviations of the individual results, the average deviation, and the RAD.

Calculations for Procedure E: The calculation of volume change on mixing

uses the results of earlier calculations. The volume of water is equal to the calibrated


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volume of your transfer pipet. The volume of your unknown liquid is found from the

mass difference between step E1 and E4 and the density of your liquid, which you

calculated in part D:

Vliquid =mE4

mE1

dliquid

The initial volume is the sum of these two volumes: Vinitial = Vpipet + Vliquid

The final volume is the volume of your volumetric flask. Thus, the volume

change Vmix is the volume of the flask minus the initial volume:

Vmix = Vflask, average - Vinitial

After computing Vmix, convert your result to percent change:

% change = 100%

Vmix

Vflask, average

Report Vmix and the percentage change with the correct number of significant

figures.

REPORT

RESULTS REPORTING FORM: Attach a completed copy of the form in the

Appendix.

WRITTEN NARRATIVE: In no more than one typewritten page, state your

conclusions concerning the conservation of volume, describe the evidence that leads

you to these conclusions, and state how reliable you think your conclusion is. (Could

your experiments be in error? By how much?)

DATA AND CALCULATIONS: Construct and print out an Excel spreadsheet

organized according to the data sheets that appear on the following pages.

QUALITY OF RESULTS: There are 20 results points in this experiment:

calibration of the volumetric flask, 4 points; calibration of the pipet, 4 points; density of

the unknown liquid, 6 points; and volume change on mixing, 6 points.


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EXPLORATION A1 IS VOLUME CONSERVED?DATA AND RESULTS SHEETS

PARTBCALIBRATIONOFTHEVOLUMETRICFLASK

Trial 1 2 3 4 5

mass (flask empty) ____ ____ ____ ____ ____

mass (flask & water) ____ ____ ____ ____ ____

mass (water) ____ ____ ____ ____ ____

water temperature (oC) ____ ____ ____ ____ ____

water density (from graph) ____ ____ ____ ____ ____

flask volume ____ ____ ____ ____ ____

average flask volume ____

absolute deviation ____ ____ ____ ____ ____

average absolute deviation ____

relative deviation ____ ____ ____ ____ ____

relative average deviation (RAD) ____

average flask volume from statistically valid data ____


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PART C CALIBRATION OF THE PIPET

Trial 1 2 3 4 5

mass (before addition) ____ ____ ____ ____ ____

mass (after addition) ____ ____ ____ ____ ____

mass (water added) ____ ____ ____ ____ ____

water temperature (oC) ____ ____ ____ ____ ____

water density (from graph) ____ ____ ____ ____ ____

pipet volume ____ ____ ____ ____ ____

average pipet volume ____





average pipet volume from statistically valid data ____


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PART D DENSITY OF AN UNKNOWN LIQUID

Trial 1 2 3 4 5

mass (flask empty) ____ ____ ____ ____ ____

mass (flask + unknown) ____ ____ ____ ____ ____

mass (unknown liquid) ____ ____ ____ ____ ____

average flask volume from part B ____

density of unknown liquid ____ ____ ____ ____ ____

average density of unknown liquid ____





average density of unknown liquid from statistically valid data ____


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PART E DETERMINING IF VOLUME IS CONSERVED

Trial 1 2 3

mass (flask + 5 mL water) _____ ______ ______

mass (flask + water + unknown liquid) _____ ______ ______

mass (unknown liquid) _____ ______ ______

average density of unknown liquid (from D) _____

volume of unknown liquid _____ ______ ______

average pipet volume (from C) _____

initial volume (water + unknown liquid) _____ ______ ______

final volume (average Vof flask, from B) _____

Vmix _____ ______ ______

average Vmix ______

percent change ______ ______ ______

average percent change ______


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EXPLORATION A4

EQUIVALENT MASS OF AN ACIDOBJECTIVES

The mole is the currency of chemistry, and chemists often have to analyze substances using molecalculations. One important way to do this uses chemical reactions that proceed quantitatively.In this exploration, you will make use of acid-base neutralization and its quantitativemeasurement by means of titration. The objectives are to learn how to make accuratequantitative chemical measurements and carry out acid-base analysis with an accuracy of betterthan 0.5%. You will standardize a solution and use that solution to analyze an unknownsubstance.

INTRODUCTION

Refer to your textbook, Section 4.6, for more details about acid-base reactions and the

technique of titration.

In titration, the amount of a substance in a sample is determined by measuring the volume of asolution of known concentration (the standard solution) required to react completely with thesubstance. A buret is used to deliver and measure the standard solution. The point of a titrationat which exactly enough titrant has been added is the stoichiometric point. The end point of a

titration is the point when there is an abrupt change in some property of the reaction system, suchas a change in the color of an indicator. In a good titration, the end point is also thestoichiometric point.

A standard solution may be prepared directly, by preparing a precisely known volume of solutioncontaining a precisely weighed amount of a compound of known purity. When this is notconvenient, standardization can be done by titrating a precisely weighed amount of a compoundof known purity with the solution that is to be standardized.

In the titration of an acid by a strong base, hydroxide ions (OH-) react with acidic hydrogenatoms. At the stoichiometric point, the moles n of hydroxide added exactly equals the moles n of

acidic hydrogen atoms initially present.nhydroxide ion = nacidic hydrogen

We do not measure amounts of moles (n) directly. Instead, we measure mass (m) and volume(V). The molar mass (MM) and concentration (M) provide connections between these measuredquantitites and the amount in moles:


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n =m

MM and n = M V

One mole of a substance may generate one or more moles of hydronium ions or hydroxide ions.Whereas one mole of HCl will consume one mole of hydroxide ions, one mole of sulfuric acid,H2SO4, will consume two moles of hydroxide ions. We define a new quantity, the equivalentmass (EM) of an acid, to be the mass in grams that reacts with one mole of strong base. Theunits of equivalent mass are g/eq. The equivalent mass of an acid is related to the molar massthrough the number of acidic hydrogen atoms that the acid contains:

EM =MM

# of acidic H

Here are two examples illustrating the concept of equivalent mass.

1) reaction of acetic acid with hydroxide ions:

CH3CO2H (aq) + OH-(aq)CH3CO2

-

(aq) + H2O (l)

Each acetic acid molecule contains one acidic hydrogen atom, so one mole of this acid reactswith one mole of hydroxide ion. The equivalent mass of CH

3CO

2H

is numerically the same as its

molar mass:

EM =MM

# of acidic H=

60 g/ mol

1 eq/ mol= 60 g/eq

2) reaction of oxalic acid with hydroxide ions:

H2C2O4(aq) + 2 OH-

(aq)C2O42-(aq) + 2 H2O (l)

Each oxalic acid molecule contains two acidic hydrogen atoms, so one

mole of oxalic acid reacts with two moles of hydroxide ions. In this case,

the equivalent mass is one-half the molar mass:

EM =MM

# of acidic H=

90 g/ mol

2 eq /mol= 45 g/eq

The usefulness of equivalent mass is that we can calculate it from the results of a titration,without knowing how many acidic hydrogen atoms an unknown substance contains. Supposethat titration of a known mass (macid) of an acidic substance with a solution of strong base ofknown concentration (Mbase) requires volume Vbase to reach the stoichiometric point. The number

of moles of acidic hydrogen atoms is the mass of acid divided by the equivalent mass, so theequality at the stoichiometric point is:

nhydroxide ion = nacidic hydrogen

MbaseVbase =macid

EMacid

Equation A4-1

Rearranging gives an expression for the equivalent mass in terms of measured quantities:


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EMacid =macid

MbaseVbase

Equation A4-2

In this exploration, you will use acid-base titrations to determine the equivalent mass of an

unknown acid. You will first standardize a solution of NaOH to determine its molarity, titratingit against a known mass of an acid that is a primary standard. A primary standard is a purecompound that can be weighed accurately and then titrated. The primary standard reactscompletely and in only one way with the titrating reagent. Your primary standard is potassiumhydrogenphthalate (KHC8H4O4). This salt dissolves in water to yield potassium ion (K

+) and thehydrogenphthalate ion (HC8H4O4

-). The hydrogenphthalate anion has only one acidic hydrogenatom, and it reacts completely and cleanly with OH-:

HC8H4O4-(aq)+ OH

-(aq) H2O(l) + C8H4O4

2-(aq)

The equivalent mass of KHC8H4O4 is therefore numerically the same as its molar mass, 204.23g/mol.

After standardizing your NaOH solution, you will use it to titrate a known mass of unknown butpure acid. After titration, the mass of the acid, the volume of the titrant (NaOH), and themolarity of the titrant will all be known, so you can calculate the equivalent mass of theunknown acid.

PROCEDURE

Solution disposal: The solutions used in this exploration are not toxic. Dispose of them in the

sink with a tap water rinse.

I. Preliminary Procedures:

1.) At the beginning of the laboratory period, fill your 500-mL plastic

storage bottle with deionized water. Transfer this water to your largest

beaker and heat until the water boils. As soon as it boils vigorously,

discontinue heating, cover loosely with Al foil, and allow the water to cool

until the beaker can be handled without discomfort.

While the water cools, carry out steps 2-7.

2.) Clean and dry a weighing bottle.

3.) Check the color of the solid drying agent in your desiccator. It should be blue. If it appearspink, take the desiccator to the solutions stock room and exchange the drying agent for a freshsupply.

4.) You should have vials of unknown acid and potassium hydrogenphthalate in your box ofunknowns. Transfer the KHC8H4O4 into the clean, dry weighing bottle, put the uncovered bottle


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and its stopper (do notstopper the weighing bottle) inside a 250-mL beaker labelled with your

name and section number, cover loosely with Al foil, and dry it in the oven at 110 oC for at leastan hour.

5.) Store the vial of unknown acid, capped, in your desiccator. NOTE: DO NOT DRY YOURUNKNOWN. Record your unknown number in your lab notebook.

6.) Mount your buret in a buret clamp, so it is in fully vertical position. Check the buret forcleanliness by filling with deionized water and allowing it to drain. If droplets adhere on thewalls, consult your instructor for the appropriate cleaning procedure. When your buret is clean,fill it about halfway with deionized water. Read and record the buret reading. Then open thestopcock slowly and allow ten drops to fall from the buret. Close the stopcock, read and recordthe new buret reading. From the volume difference, calculate the size of one drop for your buret.7.) Calculate the approximate molarity of the NaOH solution that you are going to prepare. Thestock solution is about50% by mass NaOH (MM= 40 g/mol), and the density of this solution is

about1.5 g/mL. You will dilute 5 mL of this solution to about500 mL. Also calculate the massof potassium hydrogenphthalate, KHC8H4O4, (MM= 204.23 g/mol) that will be neutralized by 20mL of this NaOH solution. What is the correct number of significant figures for these results?Show your calculations to your laboratory instructor and verify that they are correct beforeproceeding further. The approximations calculated for the NaOH stock solution concentration,give the estimated amount of KHP that you will use in the first titrations. The KHP mass thatyou weigh out, and the molar mass of KHP, are known precisely, so the titrations against KHPwill allow you to calculate exact NaOH concentration in the stock solution instead ofapproximate values. Once the exact value of the NaOH concentration in stock solution isknown, then the NaOH stock solution will be used to titrate your unknown acid to allowcalculations of its equivalent mass.

8.) When the beaker of boiled water from step 1 is cool enough to handle without discomfort,pour about half the water into your 500-mL storage bottle. Add approximately 5 mL (graduatedcylinder accuracy) of the NaOH stock solution, then add the remaining water and cap the bottle.Mix this solution thoroughly by inverting the storage bottle and shaking many times(approximately thirty) so that the solution is perfectly homogeneous. Thorough mixing isessential for good results. This is your standard base solution. Keep it capped except when youare transferring it to your buret (this prevents absorption of carbon dioxide from the atmosphere).

9.) Remove your weighing bottle containing potassium hydrogenphthalate from the oven and letit cool (lid still off) in your closed desiccator. Once it is cool, cap the weighing bottle and keep it

in your desiccator with its cap on except when actually weighing (this prevents absorption ofwater by the potassium hydrogenphthalate).

II. Weighing and Titration Procedures:

Weighing: Each solid sample must be weighed on weighing paper to the nearest 0.1 mg. Tarethe balance and weighing paper, add solid KHC8H4O4 until you have the appropriate masscalculated in Part 1, Step 7, then record that mass. Transfer the solid quantitatively to a clean


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125-mL Erlenmeyer flask, then return the weighing paper to the balance, reweigh, and record thenew mass. The mass of solid in the Erlenmeyer flask is the difference between these tworecorded masses. Add to the Erlenmeyer flask about 30 mL of deionized water and 2-4 drops ofphenolphthalein indicator.

Titration: To avoid spillage, always transfer standard NaOH solution from your storage bottleto a clean, dry 50-mL beaker and use this to fill and refill your buret. Do this transferimmediately before filling, as base solution that stands in contact with air becomes contaminatedwith carbon dioxide. Transfer no more than 25 mL of solution at a time, in order to conserveyour solution.

Before beginning titrations, rinse your buret with a few mL of standard base. Then fill it so thevolume of titrant is more than 25 mL. Allow about 1 mL to drain out. Make sure no bubblesappear in the tip; consult your instructor if you see bubbles. Read and record this volume tothe nearest 0.01 mL.

Titrate each sample to the first, pale pinkcolor that persists upon thorough mixing. Caution:Dark pink means you overtitrated! When you get near the endpoint (pink color disappearsslowly), add base dropwise with swirling. If you believe that one additional drop will exceedthe endpoint, you can add a partial drop by opening the stopcock just long enough for a dropletto form on the buret tip. Touch the tip to the side of the titration flask to transfer the partial drop,and swirl the flask to mix the partial drop with the solution. After the endpoint is reached, rinsethe sides of the flask using a squeeze bottle filled with deionized water (to be sure that none ofthe sample was splashed on the sides). If the color disappears, you have not yet reached the trueendpoint.

At the end of the titration, record the buret reading to the nearest 0.01 mL.

Standardization: Titrate at least four KHC8H4O4 samples. The first sample mass should bewithin 10% of your calculated amount for 20 mL of base. Subsequent samples should have amass that you expect to require 22-24 mL of base, based on your calculated molarity from your

initial titration. After each titration, calculate the molarity of your NaOH solution. If the resultsof the first two titrations disagree by more than 5 ppt (parts per thousand: 5 ppt is 0.5%), consultyour instructor before proceeding with the third titration. Continue doing standardizations untilyou have 3 results that agree within 5 ppt. Use these three to compute the molarity of yourstandard base and label your storage bottle accordingly.

Equivalent Mass: Titrate at least four samples of unknown acid. For the first titration, use amass within 10% of 0.15 g (0.135-0.165) (Do not waste time by attempting to have a mass ofexactly 0.1500 g.) From the result of this "pilot" titration, calculate the mass that will require 22mL of titrant. (You can use simple proportions to get this result!). For subsequent titrations, usea sample mass within 10% of this value. To get full points for results, you must have at leastthree "good" titrations that agree within 5 ppt!

Solid disposal: Any unused solid can be disposed of by washing down the sink with tap water.


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REPORT

RESULTS REPORTING FORM: Attach a completed copy of the form in the Appendix.

WRITTEN NARRATIVE: In no more than one typewritten page, describe how each part of theprocedure in this exploration is important for obtaining accurate results. Comment on whether ornot the equivalent mass that you obtained for your acid is a reasonable one (The unknowns areorganic acids; you may wish to consult reference sources such as the Handbook of Chemistryand Physics).

DATA AND CALCULATIONS: This consists of three parts:

1.) Complete an Excel spreadsheet that is constructed according to the layout on the

following page.

2.) Provide a clear and organized set of sample calculations. Provide a sample

calculation for each unique type of calculation, but do notshow allcalculations. For example, if

you carried out four trials of one type, show only the calculations for the first trial. Organize the

sample calculatio

CHEM120A Traditional LabManual S2012

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