Measurements and Calculations Chapter 2. Quantitative Observation Comparison Based on an Accepted...
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Transcript of Measurements and Calculations Chapter 2. Quantitative Observation Comparison Based on an Accepted...
Measurements and
Calculations
Chapter 2
Quantitative Observation Comparison Based on an Accepted Scale
◦ e.g. Meter Stick Has 2 Parts – the Number and the Unit
◦ Number Tells Comparison◦ Unit Tells Scale
Technique Used to Express Very Large or Very Small Numbers
Based on Powers of 10
1. Move the decimal point so there is only one non-zero number to the left of it. The new number is now between 1 and 9
2. Multiply the new number by 10n
◦ where n is the number of places you moved the decimal point
3. Determine the sign on the exponent n◦ If the decimal point was moved left, n is +◦ If the decimal point was moved right, n is –◦ If the decimal point was not moved, n is 0
1 Determine the sign of n of 10n
◦ If n is + the decimal point will move to the right◦ If n is – the decimal point will move to the left
2 Determine the value of the exponent of 10◦ Tells the number of places to move the decimal
point3 Move the decimal point and rewrite the
number
75,000,000
0.0005710
0.0000000011
8,031,000,000
2.75 x 10-7
5.22 x 104
7.10 x 10-5
9.38 x 1012
Change to scientific notation
41080.642
1.8732
Change to standard notation
0.00065 x 106
391 x 10-2
All units in the metric system are related to the fundamental unit by a power of 10
The power of 10 is indicated by a prefix
The prefixes are always the same, regardless of the fundamental or basic unit
SI unit = meter (m)◦ About 3½ inches longer than a yard
1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light
Commonly use centimeters (cm)
◦ 1 m = 100 cm◦ 1 cm = 0.01 m = 10 mm◦ 1 inch = 2.54 cm (exactly)
Measure of the amount of three-dimensional space occupied by a substance
SI unit = cubic meter (m3) Commonly measure solid volume in cubic
centimeters (cm3 (cm x cm x cm))◦ 1 m3 = 106 cm3 ◦ 1 cm3 = 10-6 m3 = 0.000001 m3
Commonly measure liquid or gas volume in milliliters (mL)◦ 1 L is slightly larger than 1 quart◦ 1 L = 1 dL3 = 1000 mL = 103 mL ◦ 1 mL = 0.001 L = 10-3 L◦ 1 mL = 1 cm3
Measure of the amount of matter present in an object
SI unit = kilogram (kg) Commonly measure mass in grams (g) or
milligrams (mg)◦ 1 kg = 2.2046 pounds, 1 lbs.. = 453.59 g◦ 1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg◦ 1 g = 0.001 kg = 10-3 kg, 1 mg = 0.001 g = 10-3
g
250 mL to Liters
1.75 kg to grams
88 daL to mL
475 cg to g
328 hm to Mm
0.00075 nL to cL
A measurement always has some amount of uncertainty
Uncertainty comes from limitations of the techniques used for comparison
To understand how reliable a measurement is, we need to understand the limitations of the measurement
To indicate the uncertainty of a single measurement scientists use a system called significant figures
The last digit written in a measurement is the number that is considered to be uncertain
Unless stated otherwise, the uncertainty in the last digit is ±1
Nonzero integers are always significant
◦ How many significant figures are in the following examples: 2753
89.659
0.281
Zeros ◦ Captive zeros are always significant◦ How many significant figures are in the
following examples: 1001.4
55.0702
0.4900008
Zeros ◦ Leading zeros never count as significant figures◦ How many significant figures are in the
following examples: 0.00048
0.0037009
0.0000000802
Zeros ◦ Trailing zeros are significant if the number has a
decimal point◦ How many significant figures are in the
following examples: 22,000 63,850. 0.00630100 2.70900 100,000
Scientific Notation◦ All numbers before the “x” are significant. Don’t
worry about any other rules.◦ 7.0 x 10-4 g has 2 significant figures◦ 2.010 x 108 m has 4 significant figures
If the digit to be removed• is less than 5, the preceding digit stays the
same Round 87.482 to 4 sig figs.
• is equal to or greater than 5, the preceding digit is increased by 1 Round 0.00649710 to 3 sig figs.
In a series of calculations, carry the extra digits to the final result and then round off◦ Ex: Convert 80,150,000 seconds to years
Don’t forget to add place-holding zeros if necessary to keep value the same!!◦ Round 80,150,000 to 3 sig figs.
Count the number of significant figures in each measurement
Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures
14.593 cm x 0.200 cm =
3.7 x 103 x 0.00340 =
Calculators/computers do not know about significant figures!!!
Exact numbers do not affect the number of significant figures in an answer
Answers to calculations must be rounded to the proper number of significant figures◦ round at the end of the calculation
Exact Numbers are numbers known with certainty
Unlimited number of significant figures They are either
◦ counting numbers number of sides on a square
◦ or defined 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm 1 kg = 1000 g, 1 LB = 16 oz 1000 mL = 1 L; 1 gal = 4 qts. 1 minute = 60 seconds
Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another
Conversion factors are relationships between two units
Conversion factors generated from equivalence statements◦ e.g. 1 inch = 2.54 cm can give or
Arrange conversion factor so starting unit is on the bottom of the conversion factor
You may string conversion factors together for problems that involve more than one conversion factor.
Find the relationship(s) between the starting and final units.
Write an equivalence statement and a conversion factor for each relationship.
Arrange the conversion factor(s) to cancel starting unit and result in goal unit.
Check that the units cancel properly
Multiply all the numbers across the top and divide by each number on the bottom to give the answer with the proper unit.
Round your answer to the correct number of significant figures.
Check that your answer makes sense!
28.5 inches to feet
4.0 gallons to quarts
48.39 minutes to hours
155.0 pounds to grams
2.00 x 108 seconds to hours
682 mg to pounds
3.5 x 10-4 L to cm3
0.091 ft2 to inches2
47.1 mm3 to kL
25 miles per hour to feet per second
4.70 gallons per minute to mL per year
5.6 x 10-6 centiliters per square meter (cL/m2) to cubic meters per square foot (m3/ft2)
Fahrenheit Scale, °F◦ Water’s freezing point = 32°F, boiling point = 212°F
Celsius Scale, °C◦ Temperature unit larger than the Fahrenheit◦ Water’s freezing point = 0°C, boiling point = 100°C
Kelvin Scale, K◦ Temperature unit same size as Celsius◦ Water’s freezing point = 273 K, boiling point = 373
K
Fahrenheit to Celsius oC = 5/9(oF -32)
Celsius to Fahrenheit oF = 1.8(oC) +32
Celsius to Kelvin K = oC + 273
Kelvin to Celsius oC = K – 273
86oF to oC
-5.0oC to oF
352 K to oC
12oC to K
248 K to oF
98.6oF to K
Density is a property of matter representing the mass per unit volume
For equal volumes, denser object has larger mass For equal masses, denser object has small
volume Solids = g/cm3
◦ 1 cm3 = 1 mL Liquids = g/mL Gases = g/L Volume of a solid can be determined by water
displacement Density : solids > liquids >>> gases In a heterogeneous mixture, denser object sinks
Volume
MassDensity
Volume
MassDensity
Density
Mass Volume
Volume Density Mass
What is the density of a metal with a mass of 11.76 g whose volume occupies 6.30 cm3?
What volume, in mL, of ethanol (density = 0.785 g/mL) has a mass of 2.04 lbs?
What is the mass (in mg) of a gas that has a density of 0.0125 g/L in a 500. mL container?
To determine the volume to insert into the density equation, you must find out the difference between the initial volume and the final volume.
A student attempting to find the density of copper records a mass of 75.2 g. When the copper is inserted into a graduated cylinder, the volume of the cylinder increases from 50.0 mL to 58.5 mL. What is the density of the copper in g/mL?
Percent error – absolute value of the error divided by the accepted value, multiplied by 100%.
% error = measured value – accepted value x 100%
accepted value Accepted value – correct value based on
reliable sources. Experimental (measured) value – value
physically measured in the lab.
In the lab, you determined the density of ethanol to be 1.04 g/mL. The accepted density of ethanol is 0.785 g/mL. What is the percent error?
The accepted value for the density of lead is 11.34 g/cm3. When you experimentally determined the density of a sample of lead, you found that a 85.2 gram sample of lead displaced 7.35 mL of water. What is the percent error in this experiment?