Problems: 1-64, 69-88, 91-120, 123-124
2.1 Measuring Global Temperatures measurement : a number with attached units
When scientists collect data, it is important that they record the measurements as accurately as possible, and the measurements must reflect the accuracy and precision of the instruments used to collect that data.
Consider the following plot of global land-ocean temperatures based on measurements taken from meteorological stations and ship and satellite temperature (SST) measurements:
Source: Hansen, J., Mki. Sato, R. Ruedy, K. Lo, D.W. Lea, and M. Medina-Elizade, 2006: Global temperature change. Proc. Natl. Acad. Sci.
, 103 , 14288-14293, doi:10.1073/pnas.0606291103.
( http://pubs.giss.nasa.gov/abstracts/2006/Hansen_etal_1.html
)
The plot above shows annual mean (average) temperatures in black, 5-year mean temperatures in red, and the uncertainty as green bars.
Ex. 1: Based on this plot how have global land-ocean temperatures changed since the 1950s?
CHEM 121: Chapter 2 v0912 page 1 of 17

2.3 SIGNIFICANT FIGURES (or SIG FIGS): Writing Numbers to Reflect Precision
To measure, one uses instruments = tools such as a ruler, balance, etc.
All instruments have one thing in common: UNCERTAINTY!
INSTRUMENTS CAN NEVER GIVE EXACT MEASUREMENTS!
When a measurement is recorded, all the given numbers are known with certainty (given the markings on the instrument), except the last number is estimated.
The digits
are significant
because removing them changes the measurement's uncertainty.
– Thus, when measurements are recorded,
– they are recorded to one more decimal place than the markings for analog instruments;
– they are recorded exactly as displayed on electronic (digital) instruments.
LENGTH
– generally reported in meters, centimeters, millimeters, kilometers, inches, feet, miles
– Know the following English-English conversions: 1 foot ≡ 12 inches 1 yard ≡ 3 feet
Example: Using Rulers A, B, and C below, indicate the measurement to the line indicated for each ruler. Assume these are centimeter rulers, so show the each measurement has units of cm . Circle the estimated digit for each measurement.
0 1 2 3 4 5
0 1 2 3 4 5
4.1
4.2
4.3
4.4
A B C
Measurement
Increment of the smallest markings on ruler
# of sig figs
Thus, a measurement is always recorded with one more digit than the smallest markings on the instrument used, and measurements with more sig figs are usually more accurate.
CHEM 121: Chapter 2 v0912 page 2 of 17

Guidelines for Sig Figs (if measurement is given) :
Count the number of digits in a measurement from left to right :
1. When there is a decimal point: measurements , count all the digits (even zeros).
–
62.4 cm
has
3
sig figs,
5.0 m
has
2
sig figs,
186.100 g has
6
s.f. measurements , start with the first nonzero digit and count all digits
(even zeros) after it.
– 0.011 mL and 0.00022 kg each have 2 sig figs
2. When there is no decimal point:
– Count all non-zero digits and zeros between non-zero digits
– e.g. 125 g has 3 sig figs, 1007 mL has 4 sig figs
– e.g. 1000 may have 1, 2, 3 or 4 sig figs
Example: Indicate the number of significant digits for the following: g _____ 90.40 m _____ e. 0.19600 g _____ cm _____ 100.00 L _____ f. 0.0050 cm _____
2.5 THE BASIC UNITS OF MEASUREMENT
VOLUME: Amount of space occupied by a solid, gas, or liquid.
– generally in units of liters (L), milliliters (mL), or cubic centimeters (cm 3 )
– Know the following:
1 L ≡ 1 dm 3 1 mL ≡ 1 cm 3 (These are both exact!)
Note: When the relationship between two units or items is exact, we use the “ ≡ ” to mean
“equals exactly” rather than the traditional “=” sign.
– also know the following equivalents in the English system
1 gallon ≡ 4 quart 1 pint ≡ 2 cups
MASS: a measure of the amount of matter an object possesses
– measured with a balance and NOT AFFECTED by gravity
– usually reported in grams or kilograms
WEIGHT: a measure of the force of gravity
– reported pounds (abbreviated lbs) mass ≠ weight = mass × acceleration due to gravity
CHEM 121: Chapter 2 v0912 page 3 of 17

Mass is not affected by gravity!
2.2 SCIENTIFIC NOTATION
Some numbers are very large or very small
→
difficult to express. number 602,000,000,000,000,000,000,000 an electron’s mass = 0.000 000 000 000 000 000 000 000 000 91 kg
To handle such numbers, we use a system called scientific notation . Regardless of their magnitude, all numbers can be expressed in the form
N
× 10 n
where N = digit term = a number between 1 and 10 , so there can only be number the #.#### n = an exponent = a positive or a negative integer (whole #).
To express a number in scientific notation:
– Count the number of places you must move the decimal point to get N between 1 and 10.
Moving decimal point to the right ( if # < 1 ) →
negative exponent.
Moving decimal point to the left ( if # > 1 )
→ positive exponent.
Example: Express the following numbers in scientific notation (to 3 sig figs ):
555,000
→
__________________
→
__________________
602,000,000,000,000,000,000,000
→
___________________________
CHEM 121: Chapter 2 v0912 page 4 of 17

Some measurements may be rounded to a number of sig figs requiring scientific notation.
Express 100.0 g to 3 sig figs: ___________
→
______________
Express 100.0 g to 2 sig figs: ___________
→
______________
Express 100.0 g to 1 sig fig: ___________ → ______________
UNBIASED ROUNDING (or ROUND-TO-EVEN METHOD )
How do we eliminate nonsignificant digits ?
• If first nonsignificant digit < 5 , just drop the nonsignificant digits
• If first nonsignificant digit ≥ 5 , raise the last sig digit by 1 and drop nonsignificant digits
– e.g. ⎯ ⎯ 3 ⎯ ⎯ → 3.15 (since the nonsig figs are 501 in 3.14
501 )
Express each of the following with the number of sig figs indicated: a. 648.75 ⎯ ⎯ ⎯ ⎯ ⎯ _______________________
⎯ ⎯ ⎯ ⎯ figs
→ _______________________
⎯ ⎯ ⎯ ⎯ figs
→ _______________________
⎯ ⎯ ⎯ ⎯ figs
→ _______________________
⎯ ⎯ ⎯ ⎯ ⎯ _______________________
⎯ ⎯ ⎯ ⎯ figs
→ _______________________
When necessary express measurements in scientific notation to clarify the number of sig figs.
2.4 SIGNIFICANT FIGURES IN CALCULATIONS
ADDING/SUBTRACTING MEASUREMENTS
When adding and subtracting measurements, your final value is limited by the measurement with the largest uncertainty—i.e. the measurement with the fewest decimal places.
MULTIPLYING/DIVIDING MEASUREMENTS
When multiplying or dividing measurements, the final value is limited by the measurement with the least number of significant figures.
CHEM 121: Chapter 2 v0912 page 5 of 17

Ex. 1: 7.4333 g + 8.25 g + 10.781 g = _________________________
Ex. 2: 13.50 cm × 7.95 cm × 4.00 cm = _________________________
Ex. 3: 9.75 mL − 7.35 mL = _________________________
Ex. 4:
101.755
g
25.75
cm × 10.25
cm × 8.50
cm
= _________________________
MULTIPLYING/DIVIDING WITH EXPONENTIAL NUMBERS:
When multiplying or dividing measurements with exponents, use the digit term (N in
“N
× 10 n to determine number of sig figs.
”)
Ex. 1: (6.02
× 10 23 )(4.155
× 10 9 ) = 2.50131
× 10 33
How do you calculate this using your scientific calculator?
Step 1. Enter “6.02
×
10
23
” by pressing:
6.02
then EE or EXP (which corresponds to “ × 10”) then 23
→
Your calculator should look similar to:
Step 2. Multiply by pressing:
×
Step 3. Enter “4.155
×
10
9
” by pressing:
6.02 x10
4.155
then EE or EXP (which corresponds to “ × 10”) then 9
→
Your calculator should look similar to: 4.155 x10
9
23
Step 4. Get the answer by pressing: =
→
Your calculator should now read
2.50131 x10
33
Be sure you can do exponential calculations with your calculator. Many calculations we do in chemistry involve numbers in scientific notation.
Ex. 2: (3.25
× 10 12 ) (8.6
× 10 4 ) = 2.795 × 10 17 ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ → _________________
Ex. 3:
3.75
8.605
× 10
15
× 10
4
= 4.357931435
× 10 10 ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ → __________________
CHEM 121: Chapter 2 v0912 page 6 of 17

SIGNIFICANT DIGITS AND EXACT NUMBERS
Although measurements can never be exact, we can
count an exact number of items. For example, we can count exactly how many students are present in a classroom, how many
M&Ms are in a bowl, how many apples in a barrel. We say that exact numbers of objects have an infinite number of significant figures
.
2.6 CONVERTING FROM ONE UNIT TO ANOTHER ( or DIMENSIONAL ANALYSIS)
UNIT EQUATIONS AND UNIT FACTORS
Unit Simple statement of two equivalent values
Conversion factor = unit factor = equivalents:
- Ratio of two equivalent quantities
Unit equation
1 dollar ≡ 10 dimes
1 dollar
10 dimes or
10 dimes
1 dollar
Unit factors are exact if we can count the number of units equal to another.
For example, the following unit factors and unit equations are exact:
7 days
1 week
24 hours
1 day
1 gallon
4 quarts
100 cm
1 m and 1 yard ≡ 3 feet
Exact equivalents have an infinite number of sig figs
→ never limit the number of sig figs in calculations!
Other equivalents are inexact or approximate because they are measurements or approximate relationships, such as
1.61 km 55 miles 454 g
1 mile 1 hour lb
Approximate equivalents do limit the sig figs for the final answer .
2.7 SOLVING MULTSTEP CONVERSION PROBLEMS
( or DIMENSIONAL ANALYSIS PROBLEM SOLVING)
1. Write the units for the answer.
2. Determine what information to start with.
3. Arrange all unit factors (showing them as fractions with units), so all of the units cancel except those needed for the final answer.
4. Check for the correct units and the correct number of sig figs in the final answer.
CHEM 121: Chapter 2 v0912 page 7 of 17

Example 1: If a marathon is 26.2 miles, then a marathon is how many yards?
(1 5280 feet, 1 yard ≡ 3 feet)
Example 2: You and a friend decide to drive to Portland, which is about 175 miles from
Seattle. If you average 99 kilometers per hour with no stops, how many hours does it take to get there? (1 mile = 1.609 km)
Example 3: The speed of light is about 2.998
× 10 8 meters per second.
Express this speed in miles per hour. (1 mile=1.609 km, 1000 m ≡ 1 km)
2.5 Basic Units of Measurement
International System or SI Units (from French "le S ystème I nternational d’Unités")
– standard units for scientific measurement
Metric system : A decimal system of measurement
with a basic unit for each type of
measurement quantity basic (symbol) length mass volume meter (m) gram (g) liter (L) length mass time meter (m) kilogram (kg) second (s)
CHEM 121: Chapter 2 v0912 page 8 of 17

Metric Prefixes
− Multiples or fractions of a basic unit are expressed as a prefix
→
Each prefix = power of 10
→
The prefix increases or decreases the base unit by a power of 10.
Prefix Symbol Multiple/Fraction kilo k 1000 deci d 0.1 ≡
1
10 centi c milli m micro μ (Greek “mu”)
0.01 ≡
1
100
0.001 ≡
1
1000
0.000 001 ≡
1
1,000,000
KNOW the metric units above!
a. ≡ __________ cents
Metric Conversion Factors
Ex. 1 Complete the following unit equations:
→
1
b. ≡ __________ dimes
→
1
Note: To help remember the number of centimeters or decimeters in a meter, just think of the number of cents or dimes in a dollar!
Ex. Complete the following unit equations: kg c. 1 L ≡ ________ mL e. 1 m ≡ ________ mm
1 ≡ ________ ds f. 1 g ≡ ________
μ g
Note: Although scientists use
μ g to abbreviate microgram , hospitals avoid using the
Greek letter
μ
in handwritten orders since it might be mistaken for an m for milli
— i.e., an order for 200
μ g might be mistaken to be 200 mg which would lead to an that’s .
Instead, hospitals use the abbreviation mcg to indicate micrograms .
CHEM 121: Chapter 2 v0912 page 9 of 17

Writing Unit Factors
Example: Complete the following unit equations then write two unit factors for each equation: a. 1 km ≡ __________ m b. 1 g ≡ ___________ mg
Metric-Metric Conversions : Solve the following using dimensional analysis.
Ex. 1 Convert 175 ms into units of seconds.
Ex. 2 Convert 0.120 kilograms into milligrams.
Ex. 3 Convert 3.00
× 10 8 m/s into kilometers per hour.
Ex. 4 Convert 3.50
× 10 7 cm to units of kilometers.
CHEM 121: Chapter 2 v0912 page 10 of 17

Metric-English Conversions
English system: Our general system of measurement.
Scientific measurements are exclusively metric. However, most Americans are more familiar with inches, pounds, quarts, and other English units.
→ Conversions between the two systems are often necessary.
These conversions will be given to you on quizzes and exams.
Quantity English unit
length 1 inch (in) 1 cm 1 in. ≡ 2.54 cm (exact)
mass 1 pound (lb) 1 g 1 lb = 453.6 g (approximate)
volume 1 quart (qt) 1 mL 1 qt = 946 mL (approximate)
Ex. 1 What is the mass in kilograms of a person weighing 155 lbs?
Ex. 2 A 2.0-L bottle can hold how many cups of liquid? (1 qt. ≡ 2 pints, 1 pint ≡ 2 cups)
Ex. 3 A light-year (about 5.88
× 10 12 miles) is the distance light travels in one year.
Calculate the speed of light in meters per second. (1 mile=1.609 km)
CHEM 121: Chapter 2 v0912 page 11 of 17

Temperature:
– A measure of the average energy of a single particle in a system.
The instrument for measuring temperature is a thermometer
.
Temperature is generally measured with these units:
References freezing point for water boiling point for water
Fahrenheit scale (°F)
English system
32°F
212°F
Celsius scale (°C)
Metric system
0°C
100°C
Nice summer day in Seattle 77°F 25°C
Conversion between Fahrenheit and Celsius scales:
° C = (
° F - 32)
1.8
° F = ( ° C × 1.8) + 32
Kelvin Temperature Scale
– There is a third scale for measuring temperature: the Kelvin scale .
– The unit for temperature in the Kelvin scale is Kelvin ( K, NOT ° K!
).
– The Kelvin scale assigns a value of zero kelvins (0 K) to the lowest possible temperature, which we call absolute zero and corresponds to –273.15°C.
– The term absolute zero is used to indicate the theoretical lowest temperature.
Conversion between °C and K:
K = ˚ C + 273 ˚ C = K – 273
Ex. 1 Liquid nitrogen is so cold, it can be used to make a banana hammer. If liquid nitrogen’s temperature is 77 K, calculate the equivalent temperature in ˚ C and in ˚ F?
CHEM 121: Chapter 2 v0912 page 12 of 17

Determining Volume
– Volume is determined in three principal ways:
1. of any liquid can be measured directly using calibrated glassware in the laboratory (e.g. graduated cylinder, pipets, burets, etc.)
The of a solid with a regular shape (rectangular, cylindrical, uniformly spherical or cubic, etc.) can be determined by calculation .
3. Volume of solid with an irregular shape can be found indirectly by the amount of liquid it displaces. This technique is called volume by displacement .
VOLUME BY CALCULATION
The can be calculated as follows: volume = length × width × thickness
Ex. 1 What is the volume of a gold bar that is 5.25 cm long, 3.50 cm wide, and 2.75 cm thick?
Ex. 2 A rectangular bar of gold with a volume of 35.5 cm 3 is 7.50 cm long and 3.50 cm wide.
How thick is the bar?
VOLUME BY DISPLACEMENT a. Fill a graduated cylinder halfway with water, and record the initial volume. b. Carefully place the object into the graduated cylinder so as not to splash or lose any water. c. Record the final volume. d. Volume of object = final volume – initial volume
CHEM 121: Chapter 2 v0912 page 13 of 17

Example: What is the volume of the piece of green jade in the figure below?
2.9 DENSITY: The amount of mass in a unit volume of matter density = mass volume or d = m
V generally in units of g/cm 3 or g/mL
For water, 1.00 g of water occupies a volume of 1.00 cm 3 : d = m
V
=
1.00
g
1.00
cm
3
= 1.00
g/cm 3
Density also expresses the concentration of mass
– i.e., the more concentrated the mass in an object
→ the heavier the object → the higher its density
Sink or Float
Some objects float on water (e.g. a cork), but others sink (e.g. a penny). Thus, objects with a higher density than a liquid will sink in the liquid, but those with a lower density than the liquid will float.
Since water's density is about 1.00 g/cm 3 , a cork's density must be less than 1.00 g/cm 3 , and a penny's density must be greater.
Ex.: Consider the figure at the right and the following solids and liquids and their densities: ice (d=0.917 g/cm 3 ) iron cube (7.87 g/cm 3
honey (d=1.50 g/cm 3
) hexane (d=0.65 g/cm
)
3 ) rubber cube (d=1.19 g/cm 3 )
Identify L
1
, L
2
, S
1
, and S
2
by filling in the blanks below:
L
1
= _______________ and L
2
= _______________
S
1
= _______________, S
2
= _______________, and S
3
= _______________
CHEM 121: Chapter 2 v0912 page 14 of 17

Applying Density as a Unit Factor
Given the density for any matter, you can always write two unit factors. For example, the density of ice is 0.917 g/cm 3 .
Two unit factors would be:
0.917g
cm
3 or cm
3
0.917g
Ex. 1 Give 2 unit factors for each of the following: a. density of lead = 11.3 g/cm 3 b. density of chloroform = 1.48 g/mL
Ex. 2 Aluminum has a density of 2.70 g/cm 3 . What is the volume (in mL) of a piece of aluminum with a mass of 0.125 kg?
Ex. 3 Ethanol is used in alcoholic beverages and has a density of 0.789 g/mL. What is the mass of ethanol that has a volume of 1.50 L?
Ex. 4 A chunk of silver metal weighing 168 g is placed in a graduated cylinder with 21.0 mL of water. The volume of water now reads 37.0 mL. Calculate the density of silver.
CHEM 121: Chapter 2 v0912 page 15 of 17

CALCULATING PERCENTAGES
Percent: Ratio of parts per 100 parts
→
10% is
10
, 25% is
25
, etc.
100 100
To calculate percent, divide one quantity by the total of all quantities in sample:
Percentage = one part
× 100% total sample
Ex. 1 In a chemistry class with 25 women and 20 men, what percentage of the class is female? What percentage is male? (Express your answers to 3 sig figs.)
Writing out Percentage as Unit Factors
Ex. 1: Water is 88.8% oxygen by mass. Write two unit factors using this info.
Ex. 2: Pennies cast between 1963 and 1982 are a mixture of 95.0% copper and 5.0% zinc by mass. Write four unit factors using this information.
CHEM 121: Chapter 2 v0912 page 16 of 17

Percentage Practice Problems
Ex. 1 An antacid sample was analyzed and found to be 10.0% aspirin by mass. What mass of aspirin is present in a 3.50 g tablet of antacid?
Ex. 2 Water is 88.8% oxygen and 11.2% hydrogen by mass. How many grams of hydrogen are present in 250.0 g (about a cup) of water?
Ex. 3: Pennies cast between 1963 and 1982 are a mixture of 95.0% copper and 5.0% zinc.
Calculate the mass of copper present in a 2.495 g penny cast in 1968.
Ex. 4: Calculate the mass of pennies cast in the 1970s that contains 1.00 lbs. of copper.
(1 lb. = 453.6 g)
CHEM 121: Chapter 2 v0912 page 17 of 17