Chapter 2
Chemistry and Measurements
HW (no credit): 9,11,13,15, 23, 25, 27, 29,
55, 57, 67, 69, 77,105,117
2.1 Units of Measurement
Scientists use the metric system of measurement
and have adopted a modification of the metric
system called the International System of Units as
a worldwide standard.
The International System of Units (SI) is an official
system of measurement used throughout the world
for units of length, volume, mass, temperature, and
time.
Units of Measurement: Metric and SI
2.2 Measured Numbers and Significant
Figures
Measured numbers are the numbers obtained
when you measure a quantity such as your height,
weight, or temperature.
When reporting measured numbers:
1) find the smallest scale;
2) add one more digit to your measured number.
This is the estimated digit.
Smallest scale:
1 cm
Reported length:
____________________
Smallest scale:
____________________
Reported length:
____________________
Smallest scale:
____________________
Reported length:
____________________
Smallest scale:
____________________
Reported length:
____________________
Measured Numbers: Significant Figures
1. All nonzero digits are significant. Ex: 1.75
2. Interior zeros (zeros between two non-zero numbers)
are significant. Ex: 106
3. Trailing zeros (zeros to the right of a non-zero number)
that fall before or after a (visible) decimal point are
significant.
Ex:
90.0
40.
4. Leading zeros (zeros to the left of the first non-zero
number) that fall before or after a (visible) decimal point
are NOT significant. They only serve to locate the
decimal point.
Ex: 0.0700
5. Trailing zeros at the end of a number, but before an
implied (invisible) decimal point, are NOT signficant.
Ex: 3500
Measured Numbers: Significant Figures
Scientific Notation
A number written in scientific notation has two parts:
(i) decimal part – a number that is between 1 and 10.
(ii) exponential part – 10 raised to an exponent, n.
Scientific Notation and Significant Zeros
Zeros at the end of large standard numbers without a
decimal point are not significant.
► 400 000 g is written with one SF as 4 × 105 g.
► 850 000 m is written with two SFs as 8.5 × 105 m.
Scientific Notation and Significant Zeros
Zeros at the beginning of a decimal number are used as
placeholders and are not significant.
►
0.000 4 s is written with one SF as 4 × 10−4 s.
►
0.000 0046 g is written with two SFs as 4.6 × 10−6 g.
Exact Numbers
Exact numbers are not measured and have an
infinite number of significant figures. (DO NOT
COUNT SFs in exact numbers)
1) numbers obtained by counting
8 cookies
6 eggs
2) conversion factors
1 qt = 4 cups
1 kg = 1 000 g
Exact Numbers
Important Note:
► Conversion factors between two metric units or between two
U.S. system units are exact.
► Conversion factors between a metric unit AND a U.S. system unit
are measured (with the exception of 1 in =2.54 cm).
►
For Chem 120A, all conversion factors will be considered EXACT.
Conversion Factors
Practice:
How many significant figures are there on
the following measurements?
a) 3.45 m
b) 0.1400 kg
c) 10.003 L
d) 35 apples
e) 3.50 x 104 cm
f) 0.007 g
Rules for Rounding Off
RULE 1. If the digit to be dropped is 4 or less, drop
it and all the following digits.
Ex) 2.4271 becomes 2.4 (rounded to 2 SFs)
RULE 2. If the digit to be dropped is 5 or greater,
round up by adding 1 to the preceding digit.
Ex) 4.5832 becomes 4.6 (rounded to 2 SFs)
Practice:
Convert the following values to scientific notation with
2 SFs.
a) 58.5 g
b) 46,792 m
c) 0.0006720 cm
d) 345.3 kg
2.3 Significant Figures in Calculations
A calculator is helpful in
working problems and
doing calculations faster.
Multiplication and Division:
Measured Numbers
RULE: In multiplication or division, the final answer is written so
that it has the same number of significant figures (SFs) as the
measurement with the fewest significant figures.
Example 1: Multiply the following measured numbers:
24.66 cm × 0.35 cm
= 8.631 (calculator display)
= 8.6 cm2 (two significant figures)
Multiplication and Division:
Measured Numbers
Example 2: Multiply and divide the following measured
numbers:
Multiplication and Division:
Measured Numbers
Example 3: Multiply and divide the following measured
numbers:
Practice:
Perform the following calculation of measured numbers. Give
the answer in the correct number of significant figures.
×
Measured Numbers: Addition and
Subtraction
RULE: In addition or subtraction, the final answer is
written so that it has the same number of decimal places
as the measurement with the fewest decimal places.
Example 1: Add the following measured numbers:
2.012
61.09
+ 3.0
Thousandths place
Hundredths place
Tenths place
66.102
Calculator display
66.1
Answer rounded to the tenths place
Measured Numbers: Addition and
Subtraction
Example 2: Subtract the following measured numbers:
65.09
Hundredths place
− 3.0
Tenths place
62.09
Calculator display
62.1
Answer rounded to the tenths place
Practice:
Add the following measured numbers:
82.409 mg
+ 22.0
mg
Subtract the following numbers:
845 mL
- 215 mL
2.4 Prefixes and Equalities
A special feature of the SI as well as the metric
system is that a prefix can be placed in front of
any unit to increase or decrease its size by some
factor of ten.
Metric and SI Prefixes
The Cubic Centimeter
The cubic centimeter (abbreviated as cm3 or cc) is the
volume of a cube whose dimensions are 1 cm on each side.
A cubic centimeter has the same volume as a milliliter, and
the units are often used interchangeably.
1 cm3 = 1 cc = 1 mL
A plastic intravenous fluid
container contains 1000 mL.
The Cubic Centimeter
A cube measuring 10 cm on each side has a volume of
1000 cm3.
10 cm × 10 cm × 10 cm = 1000 cm3 = 1000 mL = 1 L
2.5 Writing Conversion Factors
Any equality can be written as conversion factors (fraction).
Conversion Factors for the Equality 60 min = 1 h
Conversion Factors for the Metric Equality 1 m = 100 cm
Some Common Equalities
Conversion Factors
Equalities and Conversion Factors Within a
Problem
An equality may also be stated within a problem that applies
only to that problem.
The car was traveling at a speed of 85 km/h.
One tablet contains 500 mg of vitamin C.
Conversion Factors: Percentage, ppm, ppb
A percentage (%) is written as a conversion factor by choosing
a unit and expressing the numerical relationship of the parts of
this unit to 100 parts of the whole.
A person might have 18% body fat by mass.
To indicate very small ratios, we use parts per million (ppm)
and parts per billion (ppb).
2.6 Problem Solving Using Unit Conversion
►Dimensional Analysis Method: A quantity in one
unit (starting unit) is converted to an equivalent
quantity in a different unit (target unit) by using a
conversion factor (fraction) that expresses the
relationship between units.
(Starting quantity) x (Conversion factor) = Equivalent quantity
Example 1
A rattlesnake is 2.44-m long. How many centimeters
long is the snake?
1) Solution Map
2) Choose your conversion factor
3) Dimensional analysis set up
Example 2:
A doctor’s order prescribed a dosage of 0.150 mg of
Synthroid. If tablets contain 75 micrograms (mcg) of
Synthroid, how many tablets are required to provide
the prescribed medication?
1) Solution Map
2) Choose your conversion factor
3) Dimensional analysis set up
Note: The number of tablets should not be reported as
a measurement. It should not be 2.0 or 2.1 tablets.
2.7 Density
Objects that sink in water are more dense than water; objects
that float are less dense.
Densities of Common Substances
Calculating Density
Density of Solids
The density of a solid can be determined by dividing the mass
of an object by its volume.
Density Using Volume Displacement
To determine its displaced volume, submerge the solid in
water so that it displaces water that is equal to its own
volume.
45.0 mL − 35.5 mL = 9.5 mL = 9.5 cm3
Density calculation:
Example:
What is the density (g/cm3) of a 48.0–g sample of a metal if
the level of water in a graduated cylinder rises from 25.0 mL
to 33.0 mL after the metal is added?
25.0 mL
33.0 mL
object
Problem Solving Using Density
Practice 1: Ken, a 195-lb patient, has a blood volume
of 7.5 qt. If the density of blood is 1.06 g/mL, what is
the mass (in grams) of Ken’s blood?
Problem Solving Using Density
Practice 2: An unknown liquid has a density of 1.32
g/mL. What is the volume (mL) of a 14.7-g sample of
the liquid?
Specific Gravity
Specific gravity (sp. gr.)
►is a relationship between the density of a substance
and the density of water.
►is calculated by dividing the density of a sample by
the density of water, which is 1.00 g/mL.
►is a unit less quantity.
A hydrometer is used to measure the specific
gravity of urine, which, for adults, is 1.012 to
1.030.
<1.012
>1.030
- approaches density of water; maybe very
hydrated or may have type 2 diabetes or
kidney disease
- more dense than water; maybe dehydrated
or may have kidney infection or liver
disease
Example:
What is the volume (mL) of a solution that has a
specific gravity of 1.2 and a mass of the 185g?