The Numerical Side of
Chemistry
Chapter 2
Types of measurement
• Quantitative- use numbers to describe
– 4 feet
– 100 ْF
• Qualitative- use description without
numbers
– extra large
– Hot
Scientists prefer
• Quantitative- easy check
• Easy to agree upon, no personal bias
• The measuring instrument limits how good
the measurement is
How good are the
measurements?
• Scientists use two word to describe how
good the measurements are
• Accuracy- how close the measurement is to
the actual value
• Precision- how well can the measurement
be repeated
Differences
• Accuracy can be true of an individual
measurement or the average of several
• Precision requires several measurements
before anything can be said about it
• examples
Let’s use a golf analogy
Accurate?
Precise?
Accurate?
Precise?
Accurate?
Precise?
In terms of measurement
• Three students measure the
room to be 10.2 m, 10.3 m
and 10.4 m across.
• Were they precise?
• Were they accurate?
Summary of Precision Vs.
Accuracy
• Precision
– Grouping of
measurements
– Need to have several
measurements
• Repeatability
• Can have precision
without accuracy
• Accuracy
– How close to true
value
– Can use one
measurement or many
• Can have accuracy
without precision
Significant Figures
Significant figures (sig figs)
• How many numbers mean anything
• When we measure something, we can (and do)
always estimate between the smallest marks.
1
2
3
4
5
Significant figures (sig figs)
• The better marks, the better we can
estimate.
• Scientist always understand that the last
number measured is actually an estimate
1
2
3
4
5
Sig Figs
• What is the smallest mark on the ruler that
measures 142.15 cm?
– 142 cm?
– 140 cm?
• Here there’s a problem does the zero count or
not?
• They needed a set of rules to decide which
zeroes count.
• All other numbers count
Which zeros count?
• Those at the end of a number before the decimal
point don’t count
– 1000
– 1000000000
– 12400
• If the number is smaller than one, zeroes before
the first number don’t count
– 0.045
– 0.123
– 0.00006
Which zeros count?
• Zeros between other sig figs COUNT.
– 1002
– 1000000003
• zeroes at the end of a number after the decimal
point COUNT
– 45.8300
– 56.230000
• If they are holding places, they don’t.
• If they are measured (or estimated) they do
Sig Figs
• Only measurements have sig figs.
• Counted numbers are exact
• A dozen is exactly 12
• A a piece of paper is measured 11 inches tall.
• Being able to locate, and count significant figures is an
important skill.
• YOU MUST KNOW ALL THE SIG FIG RULES !!!!
Summary of Significant Figures
A number is not
significant if it is:
• A zero at the beginning of a
decimal number
ex. 0.0004lb, 0.075m
• A zero used as a
placeholder in a number
without a decimal point
ex. 992,000,or 450,000,000
A number is a S.F. if it is:
• Any real number ( 1 thru 9)
• A zero between nonzero
digits
ex. 2002g or 1.809g
• A zero at the end of a
number or decimal point
ex. 602.00ml or
0.0400g
Learning Check 2
• How many sig figs in the following
measurements?
•
•
•
•
•
•
458 g_____
4085 g_____
4850 g______
0.0485 g_____
0.004085 g_____
40.004085 g______
Learning Check 2 Con’t
•
•
•
•
•
405.0 g______
4050 g_______
0.450 g_______
4050.05 g______
0.0500060 g______
Scientific Notation
Problems
• 50 is only 1 significant figure
• if it really has two, how can I write it?
• A zero at the end only counts after the decimal
place
• Scientific notation
• 5.0 x 101
• now the zero counts.
Purposes of Scientific Notation
• Express very small and very large
numbers in a compact notation.
– 2.0 x 108 instead of 200,000,000
– 3.5 x 10-7 instead of 0.00000035
• Express numbers in a notation that also
indicates the precision of the number.
– What is meant if two cities are said to be
separated by a “distance of 3,000 miles”?
What Do We Mean by 3,000
miles?
• A distance between 2,999 and 3,001 miles?
• A distance between 2,990 and 3,010 miles?
• A distance between 2,900 and 3,100 miles?
• A distance between 2,000 and 4,000 miles?
What Do We Mean by 3,000
miles?
• Without a context, we don’t know what is meant. In
each case above, the colored digit is the largest
one that is uncertain. As you ascend from bottom
to top, the uncertainty decreases and the numbers
become increasingly precise.
• Scientific notation will allow us to express these
quantities (all are “three thousand”) with the
precision or uncertainty being explicit.
First Things First…
• Power-of-ten exponential notation is
central to scientific notation.
• To start, you should review powers of ten
and make sure that you understand the
exponential notation and can covert it to
standard notation.
How to Handle Significant
Figs and Scientific Notation
When Doing Math
Adding and subtracting
with sig figs
• The last sig fig in a measurement is an
estimate.
• Your answer when you add or subtract can
not be better than your worst estimate.
• You have to round it to the least place of
the measurement in the problem
For example
27.93 + 6.4

First line up the decimal places
27.93
+ 6.4
34.33
Then do the adding
Find the estimated
numbers in the problem.
This answer must be
rounded to the tenths place
What About Rounding?
• look at the number behind the one you’re rounding.
– If it is 0 to 4 don’t change it
– If it is 5 to 9 make it one bigger
• round 45.462 to four sig figs
• to three sig figs
• to two sig figs
• to one sig fig
Practice
•
•
•
•
•
•
•
•
4.8 + 6.8765
520 + 94.98
0.0045 + 2.113
6.0 x 102 - 3.8 x 103
5.4 - 3.28
6.7 - .542
500 -126
6.0 x 10-2 - 3.8 x 10-3
Multiplication and Division
• Rule is simpler
• Same number of sig figs in the answer as
the least in the question
• 3.6 x 653
• 2350.8
• 3.6 has 2 s.f. 653 has 3 s.f.
• answer can only have 2 s.f.
• 2400
Multiplication and Division
•
•
•
•
•
•
•
Same rules for division
practice
4.5 / 6.245
4.5 x 6.245
9.8764 x .043
3.876 / 1983
16547 / 714
The Metric System
An easy way to measure
Measuring
• The numbers are only half of a
measurement
– It is 10 long
– 10 what.
• Numbers without units are meaningless.
The Metric System
• Easier to use because it is a decimal system
• Every conversion is by some power of 10.
• A metric unit has two parts
• A prefix and a base unit.
• prefix tells you how many times to divide or
multiply by 10.
The SI System
Physical
Quantities
Name of Unit
Abbreviation
Mass
Kilogram
kg
Length
Meter
m
Time
Second
s
Temperature
Kelvin
K
Amount of
Substance
Mole
mol
• The SI system has seven
base units from which all
others are derived. Five
of them are showed here
SI Units (Con’t)
Prefix
Abbreviation
Meaning
Mega-
M
106
Kilo-
k
103
Deci-
d
10-1
Centi-
c
10-2
Milli-
m
10-3
Micro-

10-6
Nano-
n
10-9
Pico-
p
10-12
Femto-
f
10-15
•
These prefixes indicate
decimal fractions or
multiples of various units
Derived Units
Derived Units
• SI units are used to derive the units of
other quantities.
• Some of these units express speed,
velocity, area and volume….
• They are either base units squared or
cubed, or they define different base units
Volume
• calculated by multiplying
– L x W x H (for a square)
– π x r2 x H (for a cylinder)
–
(for a sphere)
• Basic SI unit of volume is the cubic meter (m3 ).
• Smaller units are sometimes employed ex. cm3, dm3 ….
• Volume is more commonly defined by liter (L).
Mass
• weight is a force, is the amount of matter.
• 1gram is defined as the mass of 1 cm3 of
water at 4 ºC.
• 1000 g = 1000 cm3 of water
• 1 kg = 1 L of water
Temperature Scales
0ºC
Measuring Temperature
• Celsius scale.
• water freezes at 0ºC
• water boils at 100ºC
• body temperature 37ºC
• room temperature 20 - 25ºC
273 K
Measuring Temperature
• Kelvin starts at absolute zero (-273 º C)
• degrees are the same size
• C = K -273.15
• K = C + 273.15
• Kelvin is always bigger.
• Kelvin can never be negative.
Temperature Conversions
•
°C = 5/9 ( °F-32)
• °F = 9/5 (°C ) +32
•
K = °C + 273.15
At home you like to keep
the thermostat at 72 F. While
traveling in Canada, you find
the room thermostat calibrated
in degrees Celsius. To what
Celsius temperature would
you
need to set the thermostat to
get the same temperature you
enjoy at home ?
Which is heavier?
it depends
Density
• how heavy something is for its size
• the ratio of mass to volume for a
substance
• D=M/V
• Independent of how much of it you have
• gold - high density
• air low density.
Calculating
• The formula tells you how
• units will be g/mL or g/cm3
• A piece of wood has a mass of 11.2 g and
a volume of 23 mL what is the density?
• A piece of wood has a density of 0.93
g/mL and a volume of 23 mL what is the
mass?
Calculating
• A piece of wood has a density of 0.93
g/mL and a mass of 23 g what is the
volume?
• The units must always work out.
• Algebra 1
• Get the thing you want by itself, on the
top.
• What ever you do to onside, do to the
other
Floating
•
•
•
•
•
Lower density floats on higher density.
Ice is less dense than water.
Most wood is less dense than water
Helium is less dense than air.
A ship is less dense than water
Density of water
•
•
•
•
1 g of water is 1 mL of water.
density of water is 1 g/mL
at 4ºC
otherwise it is less
Problem Solving
Word Problems
• The laboratory does not give you numbers
already plugged into a formula.
• You have to decide how to get the answer.
• Like word problems in math.
• The chemistry book gives you word
problems.
Problem solving
 Identify the unknown.

Both in words and what units it will be measured in.

May need to read the question several times.
 Identify what is given
 Write it down if necessary.
 Unnecessary information may also be given
Problem solving
 Plan a solution
 The “heart” of problem solving
 Break it down into steps.
 Look up needed information.




Tables
Formulas
Constants
Equations
Problem solving
 Do the calculations – algebra
 Finish up
Sig Figs
Units
Check your work
Reread the question, did you answer it
Is it reasonable?
Estimate
Conversion factors
• “A ratio of equivalent measurements.”
• Start with two things that are the same.
One meter is one hundred centimeters
• Write it as an equation.
1 m = 100 cm
• Can divide by each side to come up with
two ways of writing the number 1.
Conversion factors
• A unique way of writing the number 1.
• In the same system they are defined
quantities so they have unlimited
significant figures.
• Equivalence statements always have this
relationship.
• 1000 mm = 1 m
Write the conversion factors
for the following
• kilograms to grams
• feet to inches
• 1.096 qt. = 1.00 L
What are they good for?
• We can multiply by one creatively to
change the units .
• 13 inches is how many yards?
• 36 inches = 1 yard.
• 1 yard = 1
36 inches
• 13 inches x
1 yard
=
36 inches
What are they good for?
We can multiply by one creatively to
change the units .
 13 inches is how many yards?
 36 inches = 1 yard.
 1 yard
=1
36 inches
 13 inches x
1 yard
=
36 inches

Dimensional Analysis
•
•
•
•
Dimension = unit
Analyze = solve
Using the units to solve the problems.
If the units of your answer are right,
chances are you did the math right.
Dimensional Analysis
• A ruler is 12.0 inches long. How long is it
in cm? ( 1 inch is 2.54 cm)
• in meters?
• A race is 10.0 km long. How far is this in
miles?
– 1 mile = 1760 yds
– 1 meter = 1.094 yds
• Pikes peak is 14,110 ft above sea level.
What is this in meters?
Multiple units
• The speed limit is 65 mi/hr. What is this in
m/s?
– 1 mile = 1760 yds
– 1 meter = 1.094 yds
65 mi
hr
1760 yd
1m
1 hr 1 min
1 mi
1.094 yd 60 min 60 s
Units to a Power
• How many m3 is 1500 cm3?
1500 cm3
1500
1m
1m
1m
100 cm 100 cm 100 cm
cm3
1m
100 cm
3
Dimensional Analysis
• Another measuring system has different
units of measure.
6 ft = 1 fathom
100 fathoms = 1 cable length
10 cable lengths = 1 nautical mile
3 nautical miles = 1 league
• Jules Verne wrote a book 20,000 leagues
under the sea. How far is this in feet?
Quantifying Energy
Recall
Energy
• Capacity to do work
• Work causes an object to move (F x d)
• Potential Energy: Energy due to position
• Kinetic Energy: Energy due to the motion
of the object
Energy
A
C
B
Kinetic Energy – energy of motion
KE = ½ m v 2
mass
velocity (speed)
Potential Energy – stored energy
Batteries (chemical potential energy)
Spring in a watch (mechanical potential energy)
Water trapped above a dam (gravitational potential energy)
The Joule
The unit of heat used in modern thermochemistry is
the Joule
1 kg  m
1 joule 
2
s
Non SI unit calorie
1Cal=1000cal
4.184J =1cal or 4.184kJ=Cal
2
Calorimetry
The amount of heat absorbed or released
during a physical or chemical change can be
measured…
…usually by the change in temperature of a
known quantity of water
1 calorie is the heat required to raise the
temperature of 1 gram of water by 1 C
Coffee Cup Calorimeter
Bomb Calorimeter
Specific heat
• Amount of heat energy needed to warm 1
g of that substance by 1oC
• Units are J/goC or cal/goC
Specific heats of some common
substances
Substance
Water
Iron
Aluminum
Ethanol
(cal/g° C)
• 1.000
• 0.107
• 0.215
• 0.581
(J/g ° C)
4.184
0.449
0.901
2.43
Calculations Involving
Specific Heat
q  s  m  T
s = Specific Heat Capacity
q = Heat lost or gained
T = Temperature change
(Tfinal-Tinital)
Example
Example
Calculate the energy required to raise the temperature
of a 387.0g bar of iron metal from 25oC to 40oC. The
specific heat of iron is 0.449 J/goC