Chapter 1
Matter, Energy and Measurement
Scientific Method
The Scientific Method is the systematic
investigation of natural phenomena where:
 Observations are explained in terms of general



scientific principles
Principles are formulated from hypotheses
Hypotheses are tested by further experimentation
Sufficient empirical support elevates hypothesis to
theory or natural law
In Science is there ALWAYS
a “Right” answer?
• Most of the calculations you will encounter in this
course (i.e., the homework problems no known
answer- they propose a “best” explanation and
exams) have “right” answers
• In “real life”, researchers investigate questions for
which there is
Scientific Notation
• Scientific notation is a method of conveniently
expressing extremely large or extremely small
numbers. We will use scientific notation
whenever dealing with large or small numbers.
Scientific Notation
• How to write numbers in scientific notation:




Find the decimal point.
Find the first non-zero digit (reading left to right).
Move the decimal point to the right of the first non-zero
digit. Count the number of spaces moved. If the decimal
point was moved to the left, the number of spaces moved is
the positive exponent. If the decimal was moved right, it is
the negative exponent.
Re-write the number with the decimal point in the new
position. Drop all zeros to the left of the first non-zero digit.
Drop all zeros to the right of the last non-zero digit only if
the original number did not show the decimal.
Scientific Notation
•
•
•
•
Distance to the moon = 380,000 km = 3.8 x 105 km
Distance to the sun = 150,000,000 km = 1.5 x 108 km
Diameter of a neuron = 0.00005 m = 5 x 10-5 m
Diameter of plutonium atom = 0.0000000003 m =
3 x 10-10 m
• Number of water molecules in an drop =
1000000000000000000000 = 1 x 1021
Scientific Notation
•
•
•
•
•
•
180,000,000 g
0.00006 m
750,000 g
0.15 m
0.024 s
1,500 m3
Scientific Notation to
Standard Numbers
• How to take numbers out of scientific notation:
 Write the number portion of the scientific notation
expression, including the decimal point. (Do not include
“times ten to the power of…”)
 If the exponent is positive, move the decimal point to the
right and move the number of spaces indicated by the
exponent. If the exponent is negative, move the decimal
point to the left. You will need to add zeros as you are
moving the decimal point.
Scientific Notation to
Standard Numbers: Examples
•
•
•
•
3.6 x 10-5
8.75 x 104
3 x 10-2
2.12 x 105
Scientific Notation to
Standard Numbers: Problems
• Write the following as standard numbers:




7.2 x 10-3 m
2.4 x 105 g
3.6 x 10-5 ml
8.75 x 104 m
Scientific Notation:
Calculator Practice
• (7.2 x 103) x (8.2 x 102) = 5904000 = 5.904 x 106
• (4.5 x 10-4) x (3.2 x 10-2) = 0.0000144 = 1.44 x 10-5
• (1 x 104) x (1 x 104) = 100000000 = 1 x 108
• (5.2 x 10-4) x (6.8 x 10-2) = 0.0000354 = 3.54 x 10-5
Measured vs Exact Numbers
• Measured numbers are those obtained from some
type of measuring device, like a thermometer (which
measures temperature) or a scale (which measures
mass) or a ruler (which measures length).
• Exact numbers are obtained from counting, like 12
eggs or 3 feet in a yard (conversions)
Measured vs Exact Numbers
• The difference between a measured number and an exact
number is the certainty or uncertainty of the number.
• Exact numbers are known with certainty. We are certain
that there are exactly 12 eggs in a dozen. We do not
wonder if there might really be 12.5 eggs, or 12.1 eggs.
• Measured numbers have a certain amount of uncertainty.
When we take a measurement, we always are limited by
the sensitivity of our measuring device. Typically, the last
digit expressed in a measured number is approximated and
therefore uncertain.
Measured vs Exact Numbers
• Identify the following numbers as measured
or exact and give the number of sig figs in
each measured number:
42.2 g
3 eggs
450 000 km
0.0005 cm
3.500 x 105s
Measured vs Exact Numbers
• Identify the numbers in each of the following
statements as measured or exact:




There are 31 students in the laboratory
The oldest known flower lived 120 000 000 years ago
The largest gem ever found has a mass of 104 kg
A laboratory test shows a blood cholesterol level of 184
mg/dL
Measured vs Exact Numbers
• In each of the sets of numbers, identify the
exact number(s) if any:




5 pizzas and 50.0 g of cheese
6 nickels and 16 g of nickel
3 onions and 3 lb of potatoes
5 miles and 5 cars
Significant Figures
• Significant figures (“Sig Figs”) are all the
certain digits in a measured number as well as
the first uncertain digit. It is important for us
to be able to recognize the significant figures
of a number. When we multiply or divide
numbers, there are rules that dictate how many
digits in the answer are “Certain”
Significant Figures
Significant Figures
• Significant figures:
 All non-zero digits are significant.
 All zeros in the middle of non-zero digits are significant.
 All zeros at the end of a number with a written decimal
point.
 All digits written in scientific notation
• Not significant figures:
 All zeros at the beginning of any number.
 All zeros at the end of a number written without a decimal
point. The zero is used as a placeholder
Significant Figures:
Examples
•
•
•
•
20.60 g
1036.48 mL
4.00 mg
60,800,000 years
Significant Figures:
Problems
• For each measurement, indicate if the zeros
are significant:





20.05 g
5.00 m
0.000 02 L
120 000 years
8.05 x 102 g
Significant Figures:
Problems
• How many sig figs are in each of the following
measured quantities:
– 20.60 L
– 1036.48 g
– 4.00 m
– 60 8000 000 g
– 20.8 °C
– 5.0 x 10-3 L
Significant Figures:
Problems
• Write each of the following in scientific
notation with 2 sig figs
– 5 100 000 g
– 26 000 s
– 40 000 m
– 0.000 820 kg
– 0.000 004 5 m
Rounding Numbers
• When rounding a number, look to the digit
immediately to the right of the last significant
digit.
 If that number (the number to the right) is 0, 1, 2,
3, or 4, simply drop all insignificant digits.
 If that number (the number to the right) is 5, 6, 7,
8, or 9, round the last significant figure up and
drop all significant digits.
Significant Zeros
• When a number needs to be expressed to more
significant figures, add “significant zeros” to the right
of the number.
 If the number is a decimal, simply add more zeros to the
right of the number.
 If the number does not have a decimal, it is easiest to write
the number in scientific notation (which requires you to
write a decimal point) and then add zeros to the right of the
number.
Rounding-Examples
• Re-write the following numbers to three
significant digits.




1.854
184.2038
0.004738265
8800
Sig Figs in Calculations
• Rule for multiplying and dividing:
 Express the final answer to the lowest number of
significant figures.
• Rule for adding and subtracting:
 Express the final answer to the lowest number of decimal
places
Sig Figs in Calculations:
Examples
• Perform the following calculations and express
the answer to the proper number of sig figs:




45.7 x 0.034
0.00278 x 5
34.56 x 1.25
(0.2465 x 25) x 1.78
Sig Figs in Calculations:
Examples
• Perform the following calculations and express
the answer to the proper number of sig figs:




45.48 + 8.057
23.45 + 104.1 + 0.025
145.675 – 24.2
1.08 – 0.585
Sig Figs in Calculations:
Problems
• Round off each of the following numbers to
three sig figs:




35.7823 m
0.002627 L
3826.8 g
1.2836 kg
Sig Figs in Calculations:
Problems
• Perform the following calculations of
measured numbers. Give the answers with
the correct number of sig figs:




56.8 x 0.37
71.4/11
(2.075 x 0.585)/(8.42 x 0.00450)
25.0/5.00
Sig Figs in Calculations:
Problems
• Perform the following calculations and give
the answers with the correct number of
decimal places:
 27.8 cm + 0.235 cm
 104.45 mL + 46 mL + 0.838 mL
 153.247 g - 14.82 g
Sig Figs in Calculations:
Problems
• Round off each of the following numbers to
three sig figs:





1.854
184.2038
0.004738265
8807
1.832149
• Round the numbers above to 2 sig figs:
Sig Figs in Calculations:
Problems
• For the following calculations, give answers
with the correct number of significant figures:




400 x 185
2.40/(4 x 125)
0.825 x 3.6 x 5.1
(3.5 x 0.261)/(8.24 x 20.0)
Sig Figs in Calculations:
Problems
• For the following calculations, give answers
with the correct decimal places:




5.08 cm + 25.1 cm
85.66 cm + 104.10 cm + 0.025 cm
24.568 mL - 14.25 mL
0.2654 L - 0.2585 L
Practice
Problems
• Problem 1.1 page 9
The Metric System of
Measurement
DIMENSION
Mass
Length
Time
Temperature
Volume
COMMON UNIT SYMBOL
gram
g
meter
m
second
s
kelvin
K
deg Celsius
ºC
liter
L
The Metric System
•
Three nations have not officially adopted the International System of Units as their
primary or sole system of measurement: Burma, Liberia and the United States
Length
• Distance from one point to another
– US Customary Units: Inch, foot, yard, mile
– Metric Units: Meter, centimeter, millimeter,
kilometer, etc.
– SI Unit: Meter
Volume
Amount of space an object occupies
 US Customary Units: Pint, quart, gallon, etc.
 Metric Units: Liter, milliliter, cubic centimeter, etc.
 SI Unit: Cubic meter
Mass
• Quantity of an object (note that mass and
weight are not the same!)
– US Customary Units: Pound, ounce, ton, etc.
– Metric Units: Gram, kilogram, etc.
– SI (International System of Units) Unit: Kilogram
Time
• US Customary Unit: Second, minute, hour,
day, etc.
• Metric Unit: Second, millisecond, etc.
• SI Unit: Second
Temperature
• Measurement of the heat of an object
– US Customary Unit: Degrees Fahrenheit
– Metric Unit: Degrees Celsius
– SI Unit: Kelvin
Three Temperature Scales
The Metric System:
Metric prefixes
Prefix Symbol
Multiple
nano
n
10-9
micro
milli
centi
kilo
mega
giga
m
m
c
k
M
G
10-6
10-3
10-2
103
106
109
Example
nm (molecule
size)
mm (cell size)
mL (flu shot)
cm (ski length)
kg (weights)
MW (power)
GB (memory)
Prefixes
• Prefixes are added to metric base units to increase
or decrease the metric unit by some factor of ten.
• Liter is the base unit of volume.
• Gram is the base unit of mass.
• Meter is the base unit of length.
• Table 1.2 Page 9: All prefixes must be
memorized, including the symbol and numerical
value.
Equalities
• Equalities are set of numbers which are
mathematically equal, but expressed in
different units. For example, 12 inches = 1
foot.




1 m = ____ cm
1 km = ____ m
1 mm = ____ m
1 L = ____ mL
Prefixes and Equalities:
Problems
• Fill in the blanks with the correct numerical
value:
 Kilogram = _____ grams
 Millisecond = _____ second
 Deciliter = _____ Liter
Prefixes and Equalities:
Problems
• Complete the following list of metric
equlaities:




1 L = _____ dL
1 km = _____ m
1 m = _____ cm
1 cm3 = _____ mL
Prefixes and Equalities:
Problems
• Write the abbreviation for each of the
following units:





Milligram
Deciliter
Kilometer
Kilogram
microliter
Prefixes and Equalities:
Problems
• Write the complete name for each of the
following units:





cm
kg
dL
Gm
mg
Prefixes and Equalities:
Problems
• Write the complete name (prefix + unit) for
the following numerical values:





0.10 g
0.000 001 g
1000 g
1/100 g
0.001 g
Prefixes and Equalities:
Problems
• Complete the following relationships




1 kg = _____ g
1 mL = _____ L
1 g = _____ kg
1 g = _____ mg
Prefixes and Equalities:
Problems
• Which is the smaller unit?
– mg or g
– Centimeter or millimeter
– mm or km
– mL or µL
Writing Conversion Factors
• I have a half-dozen eggs, how many is that?
• We’ve been in here for about X hours, how many
minutes is that?
• We are going to learn how to convert between the
metric and US customary units, and also converting
within the metric system. The process is the same as
converting between hours and minutes
Writing Conversion Factors
• For any conversion, we use a conversion factor
which relates the current units to the desired
units.
• The conversion factor comes from the
equalities that you just practiced writing.
Common Conversion Factors
Length
2.54 cm = 1 in (exact)
1 mi = 1609 m
1 yd = 0.9144 m = 3 ft (exact)
1 mi = 5280 ft (exact)
Mass
1 kg = 2.2046 lb
1 lb = 453.6 g
1 lb = 16 oz (exact)
1 oz = 28.35 g
Volume
1 mL = 1 cm3 (exact)
1 qt = 0.9464 L
1 gal = 3.786 L
4 qt = 1 gal (exact)
1 BTU = 1055 J
1 cal = 4.184 J
Energy
Temperature
T(K) = T(°C)+ 273.15
T(°F) = 1.8 x T(°C) + 32
Writing Conversion Factors
1 dozen
1 dozen  12 units
12 units

1000 mL  1 L
1 lb  454 g

5% acid by mass

1000 mL
1L
1 lb
454 g
5 g acid
100 g solution
12 units
1 dozen
1L
1000 mL
454 g
1 lb
100 g solution
5 g acid
Writing Conversion Factors: Problems
• Write conversion factors for the relationship
for the following pairs of units:
 milligrams and grams
 quarts and milliliters
Writing Conversion Factors: Problems
• Write the conversion factors for each of the
following statements:




There are 325 mg of asprin in 1 tablet
One kilogram of bananas costs $1.25
A cyclist rides at the average speed of 62.2 km/hr
A 100 g sample of silver has a volume of 9.48 cm3
Writing Conversion Factors:
Problems
• Write a numerical relationship and conversion factors
for each of the following statements:





One gallon is 4 quarts
At the store, oranges are $1.29 per 1b
There are 7 days in a week
One dollar has four quarters
A ring contains 58% by mass gold
Writing Conversion Factors: Problems
• Write the numerical relationship and
conversion factors for the following pairs of
units:




centimeters and meters
milligrams and grams
liters and milliliters
Deciliters and milliliters
Writing Conversion Factors: Problems
• Write the numerical relationship and
conversion factors for the following pairs of
units:




Centimeters and inches
Pounds and kilograms
Pounds and grams
Quarts and milliliters
Problem Solving Strategies
•
•
•
•
Given/Need
Plan
Equalities/Conversion Factors
Set Up Problem
Example with Multiple Unit Factors
The density of ethanol is 0.789 g/mL. What is it in lb/gal?
Step 1: Collect unit factors
1 lb = 453.6 g & 1 gal = 3.786 L & 1000 mL = 1 L
Step 2: Write desired quantity on left & known on right
lb 0.789 g
d

 ...
gal
1 mL
Step 3: Set up unit factors to cancel unwanted units
lb 0.789 g
1lb
1000 mL 3.786 L
d




gal
1 mL
453.6 g
1L
1 gal
Step 4: Complete calculation
(0.789  1000  3.786)
lb
 6.59
453.6
gal
Conversion Factors: Examples
• A container holds 0.750 qt of liquid. How many
milliliters of lemonade will it hold?
• In England, a person is weighed in stones. If one
stone has a weight of 14.0 lb, what is the mass in
kilograms of a person who weighs 11.8 stones?
Conversion Factors: Examples
• How many inches thick is an arterial wall that
measures 0.50 μm?
• The femur, or thighbone, is the longest bone in
the body. In a 6-foot tall person, the femur
is19.5 inches long. What is the length of that
femur in millimeters?
Solve Problems without Formulas
My crazy in-laws drove their camper and boat from Bellingham to
Fairbanks (5100 mile round trip) to fish for salmon. Their rig gets 7.0
miles per gallon, with most of their fuel purchased in Canada at
1.20$Cdn per liter (the exchange rate was 1$US = 1.10$Cdn).
 How much did they spend on fuel in $US?
 If they caught 9 salmon with an average
weight of 11 lb, what was the fuel cost
per lb of salmon?
Solve Problems without
Formulas
If Marmota Monax can move 17.0 lb of
wood in a day, how many cords of wood
could it move in a year?
1 cord = 128 ft3
density of stacked wood = 45.0 lb/ft3
 Find the answer to the question.
Solve Problems without
Formulas
The sun is 93 million miles
from earth.
The speed of light is 2.998
x 108 m/s.
How many years does it take for sunlight to reach
earth from the sun?
Thickness of Aluminum Foil
A sample of aluminum foil has the
following characteristics.
Dimensions: 10. cm x 10. cm
Mass: 0.4405 g
 If the density of aluminum is 2.70 g/cm3, find
the thickness of the foil in µm.
 How many atoms thick is the foil? (X-ray
crystallography shows the distance between Al
atoms in a solid is 250 pm.)

Suppose you dump a 5-lb sack of sugar into
Bellingham Bay.

Assume the sugar disperses uniformly throughout
all of the world’s oceans.
Estimate how many molecules of sucrose would be
found in each liter of sea water.
Earth’s surface is 70.8%
ocean

1 lb = 453.6 g

1 m3 = 1000 L

Earth’s diameter is 12,750 km

1 km = 1000 m

Average depth of ocean is
3790 m

Surface area of sphere = 
(diameter)2

Molecular weight of sucrose
= 342 g/mole

1 mole = 6.023 x 1023
molecules

States of Matter
• Matter can exist in different states
• In this class we will discuss 3 different states
matter can exist in
– Gas
– Liquid
– Solid
Gas
•
•
•
•
•
No definite shape
No definite volume
Expand to fill whatever container they are in
Highly compressible
Essentially no attractive forces between gas
particles
• Particles move very, very quickly
Liquids
•
•
•
•
•
No definite shape
Have definite volume
Slightly compressible
Particles move slowly
Some attractive forces between particles
Solids
•
•
•
•
Have definite shape and volume
Essentially incompressible
Move very, very slowly
Strong attractive forces between particles
Properties of Matter
• “Physical” properties: what is the physical
nature of the matter? For example: color,
odor, physical state (liquid, gas, solid),
melting/boiling point, tensile strength,
density...
• “Chemical” properties: what is the
“reactivity” of the matter (e.g. flammability,
oxidizing agent, etc.)
Density
• Density is the relationship between mass and
volume of an object:
mass
Density 
volume
• What does it mean to have a high density?
– Examples are bricks, lead, fishing weights.
• Whatdoes it mean to have a low density?
– Examples are sponges, feathers, balsa wood.
• Density is usually expressed in g/mL or g/cm3.
Density
• Density is a conversion factor.
• It is an equality or relationship between mass
and volume, so it can be used to convert from
mass to volume or vice versa.
• The only way to convert between mass and
volume
Density of Water

The density of liquid water is defined as
exactly 1 g/mL at 4 ºC.

At other temperatures between 0 and
100 ºC the density of liquid water is very
close to 1 g/mL.
Density
Matter with lesser
density than water
will float
Matter with greater
density than water
will sink,
Density Calculations
• How many liters of ethanol contain 1.5 kg of
alcohol?
• How many grams of mercury are present in a
barometer that holds 6.5 mL of mercury?
Density Calculations
• A sculptor has prepared a mold for casting a bronze
figure. The figure has a volume of 225 mL. If
bronze has a density of 7.8 g/mL, how many ounces
of bronze are needed in the preparation of the bronze
figure?
• How many kilograms of gasoline fill as 12.0 gallon
gas tank? (1 gallon = 4 qt)
Density Calculations
• Determine the denisty (g/mL) for each of the
following:
 A plastic material that weighs 2.68 lb and has a
volume of 2.5 L
 A 10.00 L sample of oxygen gas that has a mass of
0.014 kg.
Density Calculations
• A graduated cylinder contains 28.0 mL of water.
What is the new water level after 35.6 g of silver
metal is submerged in the water?
• A cannon ball made of iron has a volume of 115 cm3.
If iron has a density of 7.86 g/cm3, what is the mass
in kilograms of the cannon ball?
Density Calculations
• The mass of an empty container is 88.25 g.
The mass of the container and a liquid with
a density of 0.758 g/mL is 150.50 g. What
is the volume (mL) of the liquid in the
container?
Specific Gravity
• Specific gravity is related to density and is used in the health fields
to test urine. Specific gravity is calculated by dividing the density
of an object by the density of water, which is 1.00 g/mL. Make
sure the sample density is expressed in the same units as the
density of water (g/mL).
• What are the units for specific gravity?
density of sample
sp gr 
density of wat er
Energy
• Energy is defined as the ability to do _____.
Examples of work:
– Walking
– Talking
– Running
– Metabolizing
Energy
• We will discuss two types of energy in this
class
– Potential Energy
– Kinetic Energy
Potential Energy
• Stored Energy
• Examples include:
– Water at the top of a dam
– Food
Kinetic Energy
The energy of motion
Examples:
◦
◦
◦
◦

Running
Walking
Water falling over a dam
Food in your body
Problem 2.4 page 59
Heat
• Heat is a specific type of energy associated
with molecular/atomic motion.
• Atoms are constantly in motion. ________
motion is associated with a greater amount of
heat.
• Putting heat into a system causes the
molecules to move ________.
Heat
• Energy used in Chemistry
• Heat will always flow from a warmer object to
a cooler one
• 2 units of heat
– Joule
– calorie
– 1 cal = 4.184 J
Energy and Nutrition
• The nutritional Calorie (Cal) is equal to 1 kcal.
• (Calorimeter is used to measure calories in
food.)
Specific Heat (SH)
• Specific heat is the amount of heat necessary to raise
the temperature of 1 gram of an object by 1C. Every
type of substance has a characteristic specific heat.
• Specific heat has units of J/gC or cal/gC. It can be
calculated.
• Table 1.4 page 22 (note the high specific heat of
water.)
• Problem 1.9 page 24
• Problem 1.10 page 24
• Problem 1.11 page 25
Specific Heat
• Specific heat is used to perform calculations
on how hot an object will get if it is exposed to
a certain amount of heat, or how much heat is
necessary to raise the temperature of an object
by a certain amount.