The Tools of
Quantitative
Chemistry
Let’s Review
Units of Measurement
• Metric System
(International
System of Units –
SI)
• All units are
derived from base
units; quantities
expressed using
prefixes
Unit
Mass
kilogram kg
Length meter
m
Time
second s
Temp
kelvin
K
Amount
mole
mol
Current ampere A
SI units
kilo-
k
103
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-
μ
10-6
nano-
n
10-9
Temperature Scales
• Celsius
– zero is the freezing point of pure water
– 100 is the boiling point of pure water
• Kelvin
– same size unit as Celsius
– zero is the lowest temp that can be
achieved (absolute zero)
– no degree symbol is used with kelvin
Length, Volume, and Mass
• SI unit for length is the meter, but
usually in chemistry it is necessary to
use smaller divisions, such as
micrometer or nanometer.
• SI unit for volume is m3, but liters
are commonly used in chemistry.
1 mL = 1 cm3
1 L = 1000 mL = 1000 cm3
Length, Volume, and Mass
• SI unit for mass it the kilogram, but
smaller masses in chemistry are
often used such as grams or
milligrams.
Making Measurements
• Precision indicates how well several
determinations of the same quantity
agree.
– often expressed as standard deviation
• Accuracy is the agreement of a
measurement with the accepted
value of the quantity.
– often expressed as percent error
Making Measurements
• Experimental Error
Error = experimental value – accepted value
% Error = (Error/accepted value) x 100%
• Standard Deviation = the square
root of the sum of the squares of the
deviations for each measurement
from the average divided by one less
than the number of measurements.
Practice Problem
• Two students measured the freezing point
of water. Student A used an ordinary
thermometer calibrated in 0.1oC units.
Student B used a thermometer certified by
NIST and calibrated in 0.01oC.
• A: -0.3oC; 0.2oC; 0.0oC; -0.3oC
• B: -0.02oC; 0.02oC, 0.00oC; 0.04oC
• Calculate the average value, the percent
error, and standard deviation for each
student. Which is more precise? Which
has a smaller error?
Exponential or Scientific
Notation
• Scientific (or exponential) notation is
a way of presenting very large or
very small numbers in a compact
and consistent form that simplifies
calculations.
N x 10n
exponent is positive if the number is
greater than 1 and negative if the
number is less than 1
Significant Figures
• A result calculated from experimental
data can be no more precise than the
least precise piece of information
that went into the calculation.
• Significant figures are the digits in a
measured quantity that were
observed with the measuring device.
Determining Significant
Figures
• Rules on page 36
• Arrow Method
• Addition/Subtraction
– The number of decimal places in the answer is
equal to the number of decimal places in the
number with the fewest digits after the
decimal.
• Multiplication/Division
– Number of sig figs in answer is equal to the
quantity with the fewest sig figs.
Dimensional Analysis
• Uses the dimensions of each unit to
guide you through calculations.
Conversion factors are used to
change measured quantities to
chemically useful information.
Graphing
• Goal is to obtain an equation that
may help us obtain new results.
y = mx + b
• “y” is the dependent variable; “x” is
the independent variable; “m” is the
slope of the line (Δy/Δx); “b” is yintercept
Practice Problem
• To find the mass of 50 jelly beans,
we weighed several samples of
beans. (see Exercise 8 on page 41)
Plot these data with the number of
beans as independent variable and
mass as dependent. What is the
slope of the line? Use your equation
of a straight line to calculate the
mass of exactly 50 jelly beans.
Homework
• After reading the “Let’s Review”
section, you should be able to do the
following problems…
• pp. 43-44 (3-6, 15-18, 21-24)