CHEM-111CHEM-111General ChemistryGeneral Chemistry

Unit OneUnit One

Scientific MeasurementScientific MeasurementDepartment of ChemistryDepartment of Chemistry

February-2007February-2007

Contents

Scientific MeasurementsScientific Measurements

• Measurement and Units• System of Measurement• Scientific Notation• Significant figures in measurements• Length and Volume• Converting Units• Unit of Mass• Density and Specific Gravity• Units of Heat and Heat Capacity of

Matter

Metric Units Metric System is used by scientists and

health professionals

Type Name symbol

Mass Gram g

Length Meter m

Volume Liter L

Time Second s

Temperatue Celsius 0C

Systems of Measurements

International System of Units (SI Units)

Base Quantity Name Symbol

Length Meter m

Mass Kilogram kg

Time Second s

Electric current Ampere A

Temperature Kelvin K

Luminous intensity Candela cd

Amount of substance Mole mol

The seven SI base units

Name Symbol  Value in SI units

minute (time) min 1 min = 60 s

hour h 1 h = 60 min = 3600 s

day d 1 d = 24 h = 86 400 s

liter L 1 L = 1 dm3 = 10-1 m3

metric ton t 1 t = 1x103 kg

unified atomic mass unit u

1 u = 1.66054 x 10-27 kg, approximately

1 meter = 3.3 feet

.  Units Outside the SI That are Accepted for Use with the SI

Commonly-used metric prefixesPrefix Name Prefix Symbol Prefix Value

giga G 1 billion or 1 000 000 000 109

mega M 1 million or 1 000 000 106

kilo k 1 thousand or 1000 103

deci d 1 tenth or 1/10 or 0.1 10-1

centi c 1 hundredth or 1/100 or 0.01 10-2

milli m 1 thousandth or1/1000 or 0.001 10-3

micro µ 1/1 000 000 or 0.000 001 10-6

nano n 1/1 000 000 000 or 0.000 000 001 10-9

Prefixes that increase the size of the unit

Prefixes that decrease the size of the unit

Prefixes and equalities

Measuring length

1 meter10 dm

100 cm 1000 mm

Some Length Equalities 1 m = 100 cm 1 m = 1000 mm 1 cm = 10 mm

Measuring Volume 1 L = 10 dL 1 L = 1000 mL 1dL = 100 mL

1cm3 = 1 cc = 1 mL

Mass and Weight

In commercial and everyday use, and especially in common parlance, weight is usually used as a synonym for

mass.

How are weight and mass differ?1) Mass is a measurement of the amount of matter

something contains, while Weight is the measurement of the pull of gravity on an object.

2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale.

3) The Mass of an object does not change when an object's location changes. Weight, on the other hand does change with location .

Measuring mass

In metric system, the unit for mass is grams (g)

The SI unit of mass, the kilogram (kg), is used for larger masses.

1 kg = 2.20 lb

454 g = 1 lb

Some mass equality

1 kg = 1000g

1 g = 1000mg

1 mg = 1000µg

Scientific Notation Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10. The number 123,000,000,000 in scientific notation is written as 1.23 x 1011

Example93,000,000 = 9.3 X 107 miles

these two digits areretained 93,000,000 miles

7 digits

instruction: move decimal point

9.3 x 107 miles seven(7) digits to the right

exponent

9.3 x 107

decimal part exponential part

Scientific Notation for very large Numbers

The number 2,398,730,000,000 can be written in scientific notation as:

(the starred representation is most common) 0.239873 x 1013

****2.39873 x 1012**** 23.9873 x 1011

239.873 x 1010

A paper clip weighs a bit more than one thousandth of a pound (0.0011 Lb). This would be expressed in scientific notation as 1.1 x 10-3 lb. The negative sign indicates that the decimal point is moved to the left.

Scientific notation for very small numbers

0.0011 kg = 1.1 x 10-3 kg

0.0 0 11 kg0 1 2 3 4

1.1 x 10 -3 kg

these two digits areretained

instruction: move decimal pointthree digits to the left

The number 0.003,483 can be written in scientific notation as

(the starred representation is most common): 0.3483x 10-2

****3.483 x 10-3**** 34.83x 10-4

348.3x 10-5

3483.x 10-6

Scientific notation for very small numbers

Conventional Notation Scientific Notation 0.012 1.2 x 10-2

0.000541 5.41 x 10-4

0.000007 7 x 10-6

0.0010 1.0 x 10-3

value significant figures rule

16.74 g 4 sig. figs non zero digits are significant

0.003 m 1 sig. fig a zero at the beginning of a decimal number is not significant

2500 km 2 sig. figs a zero at the end of a large number withouta decimal point after is not significant

25.0 ml50. L

3 sig. figs2 sig. figs

a zero at the end of a decimal number is significant

405 3 sig. figs zeros between non zero digits are significant

Number of Significant Figures

Number of Significant Figures • According to these rules, all of these

numbers have three significant digits:123123,0000.000123

• 12.31.23 x 106

0.00012367 .2 units = three significant figures

uncertain digit

certaindigit

Remember- Rules for zeros

1. Leading zeros are not significant.

0.523– three significant figuresLeading zeros

2. Captive zeros are significant. 5016 – four significant figures

Captive zeros

3 .Trailing zeros are significant.

315.60 – five significant figuresTrailing zeros

4. A zero at the beginning of a decimal number is not significant

0.008 - one significant figure

Zero at the beginning of a decimal number

Scientific notation can be used to clearly express significant figures.

A properly written number in scientific notationalways has the proper number of significant

figures.

0.00524 = 5.24 x 10-3

Three significant figures

378 000 3.78 x 10 5 Three8931.5 8.9315 x 10 3 Five

0.000 593 5.93 x 10 -4 Three

0.000 000 4 4 x 10 -7 One

Conventional Notation Scientific Notation significant figures

Scientific notation and significant figures

Temperature The temperature of an object tells us how hot or cold an object is (intensity

of heat).

In metric system temperature is measured on the Celsius temperature scale.

On Celsius thermometer, freezing point of water is 0 0C and boiling point of water is 100 0C.

On a Fahrenheit scale, freezing point of water is 320F and boiling point of water is 212 0F.

• 0F = 1.8 (0C) + 32

Kelvin Temperature scale

In SI system, temperature is based on Kelvin (K) temperature scale.

• K = 0C + 273

180Fahrenheitdegrees

100Celsiusdegrees

100Kelvinsdegrees

FahrenheitCelsiusKelvin

Normal bodytemperature

Freezing pointof water

Boilingwater

373 K 100 0C 212 0F

310 K 37 0C 98.6 0F

273 K 0 0C 32 0F

Boiling pointof water

Comparison of the Fahrenheit, Celsius,and Kelvin Temperature

Accuracy

Accuracy indicates how close a measurement is to the accepted value.  For example, we'd expect a balance to read 100 grams if we placed a standard 100 g weight on the balance.  If it does not, then the balance is inaccurate.

Accuracy

100 g

100.00

100 g

98.89

InaccurateAccurate

Measurements and Units

Which Factors effect on Accuracy & Precision

Predict the effect on accuracy and precision: 1. Instrument not “zeroed” properly

2. Reagents made at wrong concentration

3. Temperature in room varies “widely”

4. Lab partner is not properly trained

Precision• Precision indicates how close together or how

repeatable the results are.  A precise measuring instrument will give very nearly the same result each time it is used.

Precision More precise

Trial # Mass (g)

1 100.00

2 100.01

3 99.99

4 99.99

Average 100.00

Range 0.01

Std. Dev. 0.05

Less precise

Trial # Mass (g)

1 100.10

2 100.00

3 99.88

4 100.02

Average 100.00

Range 0.11

Std. Dev.

0.09

Measurements and Units

Accuracy with PrecisionPrecision with mistake Accuracy with mistake

Accuracy and Precision of Measurements

The box that has more balls has more mass per unit of volume. This property of matter is called

density

Each box has the same volume If each ball has the same mass, which box would weigh more? Why?

What is Density

More Dense Less Dense

Density is a measure of mass per unit of volume. The higher an object's density, the higher its mass per

volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less dense substance (such as water).

Common units are : g/ mL or g/ cm3 or kg/L (kg/m3) ( cm3 = ml)

DensityDensity

Density = mass

volume

d = mv

or

Density is a characteristic property of a substance.

Air 0.0013 g/L Bone 1.7-2.0 g/mlWater 1.0 g/ml Urine 1.01-1.03 g/mlGold 19.3 g/ml Gasoline 0.66-0.69 g/ml

DensitySubstance Substance

Density of some common substance

Density

1. An Iron ball was weight and found to have a mass of 42.6 g. Its volume was measured to be10.00 mL. What is the density of Fe? SOLUTION: Density is the ratio of mass to volume. Using the symbol d for density, therefore, we obtain

d = mass

volume

42.6g10.00mL

4.26g/mL

=

=

Density Calculation

Mass

Volume = Density

15.69g

1 5mL = 1.046g/mL=

2.What is the density of 15.00 mLof urine if it has a mass of 15.69 grams?

Density calculation

What would be the mass of 3.00 liters of this milk sample?The density was 3.02 g/mL

Mass

Volume = Density

mass = 9.06x 103 g

mass = volume x density

Specific gravity

The density of a substance compared to a reference substance is known as specific gravity.

Specific Gravity = density of substancedensity of reference

Specific gravity is unit less.

Reference material is commonly water at 40C.At 40C, density = specific gravity.

Specific gravity measurement

Hydrometer

Float height will be based on Specific Gravity.Hydrometer is used to know density of urine by health care workers.

The specific gravity of a liquid can be determined with a hydrometer, a hollow, sealed, calibrated glass tube. The depth to which the hydrometer sinks is inversely proportional to the specific gravity of the liquid.

Units of Heat

• Heat is the energy associated with the motion of particles in a substance.

• Heat is commonly measured in calories.

• A Calorie (cal): is the amount of heat needed to raise the temperature of exactly 1 g of water by exactly 10 C.

• 1 Kcal = 1000 calories

• 1 cal = 4.18 j ( Joule, pronounced jewel)

• 1 kJ = 1000 J

Specific Heat

• All substances absorb energy.

• Some need less amount of heat to become hot and others need more.

• The amount of heat that raises the temperature of 1 g of a substance by 10C is known as its specific heat.

Specific heat =Amount of heat (Cal)

1 gm x 1 0C

Specific Heats of some Substances

. All substances absorb energy, but some need only small amount of heat to become hot and others need more

Substances Specific Heat (cal/g0C)

Water 1.00

Ethanol 0.58

Sand 0.19

Iron 0.11

Copper 0.093

Silver 0.057

Gold 0.031

Some Relationships to findThe Mass

Heat ChangeTemperature Changeand Specific Gravity

Specific heatAmount of heat ( cal )

=1 g x 1 0C

Heat gain or loss = (mass) x ( temperaturechange(ΔT)

) X (specific heat)

Heat (calories) = g x 0C x g 0C

cal

1.

2.

3.g 0C

calg 0C

Exercise

1. Write the following measurements in scientific notation.

a. 350 g b. 0.00016 L

c. 5220000 m d. 0.0086

2. What is the name of the unit and the type of measurement

( mass, volume, length, or temperature) indicated for each of the following quantities.

a. 4.8 m b. 325 g

c. 1.5mL d. 373K

3. How many significant figure are in each of the following numbers

a. 4.5 b. 205 c. 5.082 d. 0.0004

4. Complete the following metric relationship:

a. 1m = cm b. 1 km = m

c. 1mm = m d. 1L = mL

e. 1 kg = g f. 1mL = L

g. 1 g = kg h. 1 g = mg

5. For each of the following pairs, which is the smaller unit

a. mg or kg b. mL or µL

c. cm or km d. kL or dL

6. Choose the larger unit

a. mg or g b. cm or m

c. ml or dL d. mm or µm