Chapter 2
Measurements and Calculations
Chapter 2 Section 1
Section 2-1 Objectives
Describe the purpose of the scientific method.
Distinguish between qualitative and quantitative observations.
Describe the differences between hypotheses, theories, and models.
Scientific Method: a logical approach to
understanding or solving problems that needs solved.
The goal is to solve a problem or to better understand an observed event.
The scientific method is a set of processes and scientists may
repeat stages many times before there is sufficient evidence
to formulate a theory. You can see in the diagram above that
each stage represents a number of different activities.
• Aspects of the Scientific Method
Observation is information that you obtain through your
senses. Repeatable observations become known as facts.
Generalizing/ Hypothesis: A hypothesis is a testable statement that
serves as the basis for predictions and further experiments.
Your hypothesis addresses questions raised by your
observations. Your hypothesis states that one variable
causes a change in another variable.
Testing / Experimenting – Controlled Experiment: an
experiment in which only one variable, the manipulated
variable, is deliberately changed; the responding variable is
observed for changes, all other variables are kept constant
(controlled).
Theorizing: A theory is a broad generalization that explains
believed facts or phenomena.
Integrated Chemistry
Chapter 2
Measurements and Calculations
A scientific theory is a well-tested explanation for a set of
observations or experimental results, supported in repeated
experiments by scientists.
Integrated Chemistry
Theories are never proved; they become stronger if the
facts continue to support them. However, if an existing
theory fails to explain new facts and discoveries, the
theory must be revised or a new theory will replace it.
A scientific law is a statement that summarizes a pattern found in
nature.
A scientific law describes an observed pattern in nature
without attempting to explain it.
Model: representation, of an object or event. Scientific models are
used to make it easier to understand things that might be
too difficult to observe directly.
HW: Section Review Page 31 #1-5; Chapter Review: Page 59 #1-3
SECTION REVIEW Page 31
1. What is the scientific method?
2. Which of the following are quantitative?
a. the liquid floats on water
b. the metal is malleable
c. the liquid has a temperature of 55.6°C
3. How do hypotheses and theories differ?
4. How are models related to theories and hypotheses?
5. What are the components of the system in the graduated
cylinder shown on page 38?
FIGURE 2-7 (from page 38 in your text) Density
is the ratio of mass to volume. Both water and
copper shot float on mercury because mercury
is more dense.
Chapter 2
Measurements and Calculations
Integrated Chemistry
Chapter 2 Section 2
Chapter 2-2 Objectives
1. Distinguish between a quantity, a unit, and a measurement
standard.
2. Name SI units for length, mass, time, volume, and density.
3. Distinguish between mass and weight.
4. Perform density calculations.
5. Transform a statement of equality to a conversion
factor.
Measurements are quantitative information.
Measurements represent quantities (how much, how
big etc.).
However; they are not the same thing,
Measurements use specific units
Quantity states what the unit means.
For example, the quantity represented by a teaspoon is volume. The
teaspoon is a unit of measurement, while volume is a quantity.
Scientists have agreed on a single measurement system:
The SI (Le Système International d’Unités).
SI units are defined in terms of standards of measurement.
SI has seven base units; other units are derived from these
seven.
Numbers are written in a form that is agreed upon internationally.
The number seventy-five thousand is written 75 000, not 75,000,
because the comma is used in other countries to represent a decimal
point. In place of the comma a space is used to avoid confusion
Some non-SI units are still commonly used by chemists and
are also used in this class.
The standards are objects or natural phenomena that are of constant value,
easy to preserve and reproduce, and practical in size. In the United States,
the National Institute of Standards and Technology plays the main role in
maintaining standards and setting style conventions.
Select Base Units – See Table 2-1 page 34 for the entire list
Quantity Unit
Length
Mass
Time
Temperature
Amount of matter
Quantity symbol Unit name
l
m
t
T
n
meter
kilogram
second
Kelvin
mole
abbreviation
m
kg
s
K
mol
Chapter 2
Measurements and Calculations
Integrated Chemistry
Mass & Weight Mass is often confused with weight because people
often express the weight of an object in grams, this is incorrect – weight is
measured in newtons a derived unit.
Mass is determined by comparing the object to a set of
standards that are part of the balance.
Weight is a measure of the gravitational pull on mass, and
depends on gravity.
Mass is measured on instruments such as a balance and
weight is typically measured on a spring scale.
Length: The standard unit for length is the meter.
To express long distances, the kilometer (km) is used. To express shorter
distances, the centimeter is often used.
Derived SI Units
Many SI units are combinations of the Base units
Combinations of SI base units form derived units.
See Table 2-3 page 36.
Volume is the amount of space occupied by an object.
3
The derived SI unit of volume is cubic meters, m .
Such a large unit is inconvenient for expressing the volume of materials in
a chemistry laboratory.
A smaller unit, the cubic centimeter, cm3, is used. There are one
hundred centimeters in a meter, so a cubic meter contains one
million cm3. Here is the math:
100 cm 100 cm
100 cm
1m3 X
X
X
=1 000 000 cm3
1m
1m
1m
Density is the ratio of mass to volume, or density equals
D=
m
V
mass divided by volume.
Conversion Factors A conversion factor is a ratio derived from the
equality between two different units that can be used to convert from one
unit to the other. By multiplying by the conversion factor, you do not
change the overall meaning of the quantity. A conversion factor is a
ratio made from an equality – which means the ratio is
equal to one. Example: 1 m = 100 cm which means
and we can Substitute this in the equation for
100 cm
= 1 volume in 1 m3 . . . = ? cm3
1m
After substituting into
100 cm 100 cm 100 cm
X
X
1m3 X
=1 000 000 cm3
1m
1m
1m
you get 1m3 X 1 X 1 X 1 =1 000 000 cm3 = 106 cm3
Chapter 2
Measurements and Calculations
Then
106 cm3
1=
=
is
m3
now
conversion factor to use
1m3
106 cm3
Integrated Chemistry
your final answer
1m3 =106 cm3 and
we have a new
Note: quantity sought = quantity given multiplied by the
conversion factor
Examples: page 39 sample problem (sp) 2-1; page 41 sp 2-2
HW:
Practice Problems: Page 40 #1-3(AT THE TOP OF THE PAGE; page 42 #1-5
Chapter Review: Page 59 #12 -15; 27-29; 32-34
Chapter 2
Measurements and Calculations
Chapter 2 SECTION 3
Section 2-3 Objectives
Distinguish between accuracy and precision.
Determine the number of significant figures in measurements.
Perform mathematical operations involving significant figures.
Convert measurements into scientific notation.
Distinguish between inversely and directly proportional relationships.
Accuracy refers to the closeness of measurements to the
correct or accepted value of the quantity measured.
Precision refers to the closeness of a set of measurements of
the same quantity made in the same way.
% Error
Significant Figures
Determining Whether Zeros Are Significant Figures
Rule (Examples)
1. Zeros between other nonzero digits are significant.
a. 50.3 m has three significant figures.
b. 3.0025 s has five significant figures.
2. Zeros in front of nonzero digits are not significant.
a. 0.892 kg has three significant figures.
b. 0.0008 ms has one significant figure.
3. Zeros that are at the end of a number and also to the right of
the decimal are significant.
a. 57.00 g has four significant figures.
b. 2.000 000 kg has seven significant figures.
Integrated Chemistry
Chapter 2
Measurements and Calculations
Integrated Chemistry
4. Zeros at the end of a number but to the left of a decimal are
significant if they have been measured (the decimal point is
shown); otherwise, they are not significant. In this class,
they will be treated as not significant if no decimal point is
used.
a. 1000 m; in this book it will be assumed that
measurements like this have one significant figure, and so
shall we.
b. 20. m may contain one or two significant figures, but it
will be assumed to have two significant figures, because of
the decimal point at the end of the number.
Calculating with Significant Figures
Rule (Examples)
Addition (subtraction) The final
answer should have the same
number of digits to the right of the
decimal as the measurement with the
smallest number of digits to the right
of the decimal.
In this case 1 digit to the right of the decimal.
In the case of addition the decimal point is the boss.
Multiplication (division) The final
answer has the same number of
significant figures as the measurement
having the smallest number of
significant figures.
In the case of multiplication the decimal point is not in charge.
Exact conversion factors are completely certain and do not
limit the number of digits in a calculation.
Integrated Chemistry - Chapter 2
Page 7 of 10
Chapter 2
Measurements and Calculations
Integrated Chemistry
Rounding
What
When to do it
to do
• whenever the digit following the last significant figure
is a 0, 1, 2, 3, or 4: 30.24 becomes 30.2
round
• if the last significant figure is an even number and the
down
next digit is a 5, with no other nonzero digits: 32.25
becomes 32.2 and 32.65 becomes 32.6 (Bankers rule)
• whenever the digit following the last significant figure
is a 6, 7, 8, or 9: 22.49 becomes 22.5
• if the digit following the last significant figure is a 5
round followed by a nonzero digit: 54.7501 becomes 54.8
up
• if the last significant figure is an odd number and the
next digit is a 5, with no other nonzero digits: 54.75
becomes 54.8 and 79.35 becomes 79.4 (Bankers rule)
Scientific Notation: A number written in scientific notation is
of the form M × 10n, where M is greater than or equal to 1 but
less than 10 and the n is an integer. This is a way to write a very
large or vary small number easily. Sometimes scientific
notation is used to specify exact Significant Figures
The x 10n is used to save from writing zeros.
Examples:
A large number: 7.25 trillion dollars = 7.25 x 1012 dollars
A small number: one 4 trillionth of a meter
1
of a meter = 0.000 000 000 000 25 m
4 000 000 000 000
= 2.5 x 10 – 13 m
Additionally scientist will also use prefixes; the two values
above could be expressed
7.25 x 1012 dollars = 7.25 teradollars;
2.5 x 10 – 13 m = 25 picometers (prefixes are on page 35)
Scientific Notation used to specify exact Significant Figures
6.2 x 102 m = 620 m (by the rules both have 2 sig figs)
But 6.00 x 102 m = 600 m do not have the same # of sig figs
6.00 x 102 m has 3; 600 has only 1
Integrated Chemistry - Chapter 2
Page 8 of 10
Chapter 2
Measurements and Calculations
Integrated Chemistry
When adding in scientific notation the power of ten must be the
same for each number before lining up the decimal.
1.5 x 1015m + 5.2 x 1014m  15 x 1014m + 5.2 x 1014m to add
the 15 x 1014m + 5.2 x 1014m = 20.2 x 1014mStill need to fix 2
things: 20.2 is not ≥ 1 & < 10 and by the Significant Figure
addition rule the 15 has nothing after the decimal. Fix the sig
fig first: 20. x 1014m
Final step change the number to 2.0 x 1015m
Proportionality
Two quantities are directly proportional to each other if
dividing one by the other gives a constant value.
When two variables like x and y are directly proportional to
each other, the relationship is expressed as y  x, which is read
as “y is proportional to x.” The line equation is expressed as k
= y/x; k is a constant value.
In the example, it is the density of aluminum (k=D; x=m; y=V).
Note, by averaging, the k value is 2.71 g/cm3 Rewrite the
expression as the line equation y = kx This may look familiar to you; it
is the equation for a special case of a straight line, with the y intercept = 0. The y
intercept is not always zero; for example: temperature comparisons.
We can use the direct proportionality of temperature readings in
both oC and oF to create a conversion factor for temperature
between the two.
Temperature 0oC = 32oF so the y intercept = 32;
Water freezes at 0oC = 32oF; water boils at 100oC = 212oF
Recall x is oC and y is oF, then slope is (y2 – y1) /(x2 – x1)
o
o
o
212
F
–
32
F
180
F = 1.8 oF/oC
slope =
=
o
o
o
100 C – 0 C
100 C
Integrated Chemistry - Chapter 2
Page 9 of 10
Chapter 2
Measurements and Calculations
Integrated Chemistry
To use the conversion equation you must let x be the Celsius
reading; and y is Fahrenheit then  y= (1.8 oF/ oC)*x + 32 oF
 If you rearrange this you will get
x=
(y - 32 oF)
(y - 32 oF)(oC)
which
means:
x
=
(1.8 oF/ oC)
(1.8 oF)
and y = (1.8 oF/ oC)(x) + 32 oF
Examples: Convert 37oC to oF
Use y = (1.8 oF/ oC)(x) + 32 oF and let x = 37oC
y = (1.8 oF/ oC)(37oC) + 32 oF = 66.6 oF + 32 oF = 98.6 oF
Convert 68 oF to oC
Let y = 68 oF
o
o
o
(y - 32 oF)(oC) = (68 F - 32 F)( C)
Use x =
(1.8 oF)
(1.8 oF)
(36 oF)(oC)
= 20 oC
=
o
(1.8 F)
Two quantities are inversely proportional to each other if their
product is constant. y  1/x;
the line equation has the form k = yx
In this example k = PV
HW:
All Practice problems: Pages 45; 48; 50; & 54 (Yes I know they have the answers, show
step by step how to get the answers for credit); and Section Review page 57 # 1 – # 9
Integrated Chemistry - Chapter 2
Page 10 of 10