in
Chemistry
Study Guides
Big Picture
Math and measurements are essential parts of chemistry, allowing scientists to make hypotheses, calculate and record
data, and interpret and display results. In order to communicate with and understand other chemists and scientists,
it is important to understand conventions, signs, abbreviations, and other math and measurement concepts that are
used in chemistry.
Key Terms
Chemistry
Math
Qualitative (observation): A descriptive, non-numerical observation.
Quantitative (observation): A numerical result involving both a number and a unit.
Precision: How close the values in a set of measurements are to one another.
Accuracy: How close a measurement is to the true value of the quantity being measured.
Error: The difference between a measured or computed value and a value that is accepted to be true.
SI (abbreviated from International System of Units): The standard metric system of measurement units used in
science.
Derived Unit: A unit based on other SI units.
Measurement
A qualitative observation cannot be substantiated
with numbers.
• Example: The ball is red.
A quantitative observation, also called a measurement, is substantiated with numbers.
• Example: The ball weighs 25.3 grams.
Quantitative observations are usually more helpful
than qualitative observations.
Precision vs. Accuracy
Precision and accuracy are two different terms used to
describe a set of data for the same measurements repeated
several times.
• Precision:
A data point that is close to other data
points is precise. All these points might be “wrong,” but
if they are very close to each other, there is a high degree of precision.
• Accuracy: A data point that is close to the true value is
accurate. The “correct” answer is usually considered to
be the average of all the other pieces of data.
While we often think of precision and accuracy as
synonyms, in the context of chemistry, the two
terms are very different.
Error
There are two common sources of error:
• Random
error - caused by human or equipment error,
such as contamination of materials, inaccurate readings, or poor timing.
• Systematic
error - occurs in every trial, such as a scale
that always measured 0.50 grams too heavy, or a
thermometer that is always 1 °C too low.
Image Credit: Rory Runser, CC-BY-SA 3.0
To express error as a percentage:
Notes
This guide was created by Steven Lai, Rory Runser, and Jin Yu. To learn more
about the student authors, visit http://www.ck12.org/about/about-us/team/
interns.
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v1.1.12.2012
Disclaimer: this study guide was not created to replace
your textbook and is for classroom or individual use only.
Figure. This image shows the differences between
accurate and precise data.
The equation for error is:
Chemistry
Math
in
Chemistry
cont .
SI Units
The SI (International System of Units, from the French Système international d'unités) is a standardized method of
measuring and collecting data used by scientists around the world.
SI Base Units
The SI uses seven base units:
• meter (m): length
• kilogram (kg): mass
• second (s): time
• kelvin (K): temperature
• mole (mol): quantity
• candela (cd): luminous intensity
• ampere (A): electric current
The meter, kilogram, kelvin, second, and mole
are the five commonly used base units used in
chemistry.
The mole is a unit that tells us how much stuff we have. It is equal to a number called Avogadro's number, which is just
a number (a very big number). Avogadro's number is equivalent to 6.022 x 1023.
• Just like you can have a dozen (12) eggs, you can have a mole (6.022 x 1023) of eggs (that would be a lot of eggs!)
• A mole of popcorn kernels could be spread over the entire USA and be 14 kilometers deep!
As for temperature, many scientists also use the Celsius scale when dealing with day-to-day calculations. To convert
between Celsius (°C) and Kelvin (K) scales:
• K = °C + 273
• °C = K - 273
Derived Units
SI Prefixes
There are many other properties of substances that can
be measured, and they often require more than just the
base units defined above. That is where derived units
come in. Two examples are volume and density.
Prefixes can be used to alter the decimal value of
a quantity and are a way to express large and small
numbers. These prefixes are attached to the unit (either
base or derived) and represent the exponents in the
table below.
Volume: A measure of the amount of space an object
takes up.
• SI unit: cubic meter (m3)
• Another commonly used
unit is the liter (L). The
liter is used in all calculations involving volume,
such as the volume of water and gas.
• 1 L = 1 dmc3= 1000 cm3
• Also, 1 milliliter (mL) of water weighs exactly 1 gram
— that is how the gram is defined!
Density: A measure of the mass per unit volume.
• SI unit: kilograms per cubic meter (kg/m3)
• Substances with greater densities feel
heavier
compared to an equal volume of something with a
lighter density.
• Density allows the conversion of volume to mass.
A table of common SI prefixes
Prefix
Scientific
Notation
Abbreviation
tera-
1012
T
giga-
9
10
G
mega-
106
M
kilo-
10
k
deci-
10
d
centi-
10
c
milli-
10-3
m
micro-
10
μ (Greek mu)
nano-
10
n
pico-
10
p
3
-1
-2
-6
-9
Adding these prefixes
describe quantity.
-12
often
makes
it
easier
to
Scientific Notation
In science, we often deal with very large or very small numbers. For example, the mass of the earth is approximately
5,972,000,000,000,000,000,000,000 kg. That's a lot of zeroes! In order to save time and minimize error, use scientific
notation. The mass of the earth can be rewritten as:
The exponent on the 10 is equal to the number of places the decimal point is shifted. The decimal point is moved so
that it is to the right of the first nonzero digit. The mass of the earth has 25 digits, so it is raised to the 24th power.
• If the exponent is positive, the decimal point was shifted to the left.
• If the exponent is negative, the decimal point was shifted to the right.
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Chemistry
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Significant Figures
In chemistry, there is always a bit of uncertainty when
reporting data. For instance, it is impossible to have
exactly 1 liter of water; there might be a few drops too
many or too few. It might be 1.01 liters, 0.98 liters, or
1.000000001 liters. When making measurements, use
significant figures.
• Depending
on the accuracy of the measurement
equipment, more or fewer significant figures (called
sig figs for short) can be reported.
• Report
one estimated digit past the final level of
marking on an instrument.
Image Credit: CK-12 Foundation,
CC-BY-NC-SA 3.0
• Zeroes sandwiched in between nonzero numbers are
significant. For example, 4005 has four significant
figures.
• Exact
numbers have infinite significant figures.
For instance, a dozen (12) eggs does not limit
computations to 2 significant figures.
• Some conversion factors have infinite significant figures. For instance, 1 foot has exactly 12 inches, so
converting from feet to inches does not reduce a
number to 2 sig figs. However, a conversion factor
between centimeters and inches (1 in ≈ 2.54 cm) is
not exact, so a conversion would limit an answer to
3 sig figs.
In order to reduce the ambiguity over the number of
insignificant zeroes, numbers can, and often should, be
written in scientific notation.
In science, calculations cannot be more precise than the
least precise measurement. Rules for calculations with
significant figures:
• When
Figure: Significant figures in measurement.
Here are some rules on significant figures:
• All nonzero numbers are significant.
• Zeroes
after a number and before a decimal point
may or may not count as significant figures. For
example, 2100 could have two, three, or four significant figures. However, an exception is when the
decimal point is written out. So 2100. would have
four significant figures.
• Numbers
after a decimal point are significant. For
example, 100.0000 has seven significant figures.
adding or subtracting, the sum or difference
has the same number of decimal places as the number with the least number of decimal places. So
30.62+54.3=84.9 (one decimal point).
• When multiplying or dividing, the product or quotient
has the same number of significant figures as the
number with the least number of significant figures.
For instance, 25.1 has three sig figs and 67 has two.
Even though 25.1 × 67=1681.7 (5 sig figs), it must
be rounded to 1700 (which has only two significant
figures).
If the calculations involve multiple steps, keep all
the figures (significant or not). When you reach
the final answer, round off the answer to the
correct number of significant figures.
Dimensional Analyses
Dimensional analysis is used to convert quantities in one unit of measure to another unit of measure. It involves
multiplying a quantity by one or more conversion factors. Conversion factors are ratios of equivalent measurements.
• Units
are treated like numbers and can be multiplied and divided. Order the factors so that the units cancel and
that the final answer is in the correct unit.
Example:
How many gallons of water would fit in a swimming pool that is 500 cubic feet large? Conversion factors: 4 quarts/
gallon, 2 pints/quart, 16 ounces/pint, 29.6 mL/ounce, 3.3 ft/meter, 2.54 cm/inch
Solution:
PITFALL PREVENTION: Make sure to cube both 12 in and 2.54 cm, as those units are for 1 dimension. Cubing
the unit (cm to cm3) requires cubing the conversion factor.
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Chemistry
Math