Chapter 1
Units of Measurement for Physical and Chemical Change
Dr. Peter Warburton
[email protected]
http://www.chem.mun.ca/zcourses/1010.php
What is chemistry?
Chemistry is the study of the
composition, structure, and properties
of matter and energy, and of the changes
that they undergo.
Matter is anything that occupies space
and has mass.
Energy is the ability to do work.
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Physical change
To understand how matter is classified by its
chemical constitution we must first look at physical
and chemical changes.
A physical change is a change in the form of
matter but not in its chemical identity.
Physical changes are usually reversible.
No new compounds are formed during a physical
change.
Melting ice and dissolving sugar in water are
examples of a physical changes.
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Elements, compounds, and mixtures
A chemical change, or chemical reaction, is a
change in which one or more kinds of matter are
TRANSFORMED into one or more NEW kinds of
matter.
Chemical changes often result in a lowering of
the potential (stored) energy of a chemical
system.
Chemical changes are usually irreversible
Vinegar, CH3COOH, reacting with baking soda
NaHCO3 is an example of a chemical change…
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Elements, compounds, and mixtures
A physical property is a characteristic that can
be observed for material without changing its
chemical identity.
Examples are physical states (solid, liquid, or
gas), melting point, and color.
A chemical property is a characteristic of a
material involving its chemical change.
A chemical property of iron is its ability to react
with oxygen to produce rust. Fe can be oxidized
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Physical vs chemical properties
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Which of the following represents a
chemical change?
a. freezing water to make ice cubes
b. dry ice evaporating at room
temperature
c. toasting a piece of bread
d. dissolving sugar in hot coffee
e. crushing an aluminum can
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Measurement and significant figures
Measurement is the comparison of a physical quantity to
be measured with a unit of measurement—that is, with a
fixed standard of measurement.
The term precision refers to the closeness of the set of
values obtained from identical measurements of a
quantity. Measurements such as 23.3 cm, 23.4 cm,
23.2 cm of the same object are precise.
Accuracy is a related term; it refers to the closeness of
a single measurement to its true value. If the true
value is 18.3 cm and the measurement was 23.4 cm,
then the measurement is not accurate.
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Problem
A student measures the mass of a penny
4 times and records the following data.
What can be said about the data if the
actual mass of the penny is 2.2987 g?
a.
The data is both accurate and
precise.
b.
The data is neither accurate nor
precise.
c.
The data is accurate but not
precise.
d.
The data is not accurate but it is
precise.
Trial
Number
Mass,
g
1
2.5104
2
2.5106
3
2.5102
4
2.5109
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Measurement and significant figures
To indicate the precision of a measured
number (or result of calculations on
measured numbers), we often use the
concept of significant figures (or digits).
Significant figures (or sigfigs or sf) are those
digits in a measured number (or result of
calculations using measured numbers) that
include all certain digits plus a final one
having some uncertainty.
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Uncertainty due to estimation
“Better” equipment
provides more accurate
measurements!
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Measurement and significant figures
To count the number of significant figures in a
measurement, observe the following rules:
Count the first non-zero digit as the first significant
figure.
Zeros at the end of the number are only
significant if there is a decimal point shown.
0.0009870 (four sf)
254000 (ONLY three sf since ambiguous)
4050.00 (six sf)
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Scientific notation
We saw the number 254000 only has three
significant figures since there is no decimal
place to tell us if the zeros are significant.
We can use scientific notation as a
better means to show numbers like this.
254000 = 2.54 x 100000 = 2.54 x 105
254000 = 2.540 x 100000 = 2.540 x 105
254000 = 2.5400 x 100000 = 2.5400 x 105
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Scientific notation
Scientific notation can also be used even if the
sigfigs are obvious to make a number easier to
express.
0.0009870 = 9.870 x 0.0001 = 9.870 x 10-4
59.8 = 5.98 x 10 = 5.98 x 101
4050.00 = 4.05000 x 1000 = 4.05000 x 103
Notice the sigfigs are all given in the decimal
part. The power of 10 (exponent part) only tells
you where the decimal place is in the original
number).
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Math using scientific notation
See Appendix I A. of the textbook (pages
A-1 to A-3)
𝐴 𝑥 10𝑚 𝐵 𝑥 10𝑛 = 𝐴 𝑥 𝐵 𝑥10 𝑚+𝑛
𝐴 𝑥 10𝑚 𝐴
𝑚−𝑛
=
𝑥10
𝐵 𝑥 10𝑛 𝐵
Addition and subtraction needs both
numbers to be expressed to the same power
of 10!
𝐴 𝑥 10𝑚 ± 𝐵 𝑥 10𝑚 = 𝐴 ± 𝐵 𝑥10𝑚
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Math using scientific notation
See Appendix I A. of the textbook (pages
A-1 to A-3)
Powers and roots require the decimal part
to be raised to the power or root and the
exponent part to be multiplied by the power
or root
𝐴 𝑥 10𝑚 𝑛 = 𝐴𝑛 𝑥 10 𝑚 𝑥 𝑛
𝑚
1
𝑚 1𝑛
𝑛
𝐴 𝑥 10
= 𝐴 𝑥 10 𝑛
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Be careful with trailing zeros!
0.0009870 or 9.870 x 10-4 (four sf)
IS NOT the same as
0.000987 or 9.87 x 10-4 (three sf)
4050.00 or 4.05000 x 103 (six sf)
IS NOT the same as
4050. or 4.050 x 103 (four sf)
Remember that sigfigs give an idea of how certain
you are in the measurement. Always show the
number of sigfigs the data is entitled to. This means
paying special attention to how many trailing zeros
you have is VERY IMPORTANT!
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Measurement and significant figures
In math calculations…
When multiplying and dividing measured
quantities, give as many significant figures as
the least found in the measurements used in
the calculation.
When adding or subtracting measured
quantities, give the same number of decimal
places (dp) as the least found in the
measurements used.
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Quick examples
14.0 g / 102.4 mL = 0.137 g mL-1
3 sf
4 sf
can only have 3 sf
1.03 g + 0.013 g + 10.2 g = 11.2 g
2 dp
3 dp
1 dp only 1 dp here
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Guard digits
If you use a calculated value in a later
calculation, to avoid rounding errors it
makes sense to keep an extra NONSIGNIFICANT digit.
14.0 g / 102.4 mL = 0.1367 g mL-1
Subscript number is guard digit
1.03 g + 0.013 g + 10.2 g = 11.24 g
Underlined number is last significant digit
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Calculate the following with the correct
number of significant figures.
a.
1.428 − 1.08
+ 2.83 𝑥 0.360 = b.
0.288
c.
Application of sigfig rules follows the d.
same order of operations rules for
e.
mathematics.
2
2.227
2.2
2.2271
2.23
Do calculations in parentheses first.
Powers and roots from left to right.
Multiplication and division from left to right
Addition and subtraction from left to right
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Measurement and significant figures
An exact number is a number that has an
infinite number of significant digits.
When you say there are twelve inches in a
foot, you mean exactly twelve
or 1.609344 km = 1 mile (exactly)
In calculations any exact numbers will
never have the least number of sf, so they
don’t determine the number of sigfigs in
the answer.
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Problem
How many significant digits in each
number? Where appropriate, use scientific
notation to better express the number.
1.03
0.013
1.000420
0.000420
900
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Problem
Convert 295 miles to km
given 1.609344 km = 1 mile (exactly)
WARNING!
Reporting measurements and results of
calculations to the correct significant
figures is an IMPORTANT aspect of this
course. You will lose marks if you don’t do
it!
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SI Units and SI Prefixes
In 1960, the General Conference of
Weights and Measures adopted the
International System of Units (or SI),
which is a particular choice of metric
units.
This system has seven SI base
units, the SI units from which all
others can be derived.
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SI base units
The last 2 are not used in Chem 1010
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SI units and prefixes
The advantage of the metric system is that
it is a decimal system.
A larger or smaller unit is indicated by a SI
prefix — that is, a prefix used in the
International System to indicate a power of
10.
The next slide lists the SI prefixes most
commonly used.
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SI prefixes
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Units in Chem 1010
The SI base unit of length is the metre (m)
though we might use centimetres (cm),
millimetres (mm), micrometres (mm),
nanometres (nm), picometres (pm).
A non-SI unit of length we might encounter
in the course is the angstrom
1 Å = 1 x 10-10 m = 0.1 nm = 100 pm
(exactly)
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Units in Chem 1010
The SI base unit of mass is the kilogram
(kg) though we might use grams (g),
milligrams (mg), and micrograms (mg)
The SI base unit of time is the second (s)
though we might use the non-SI units of
minutes (min) or hours (hr)
1 hr = 60 min = 3600 s (exactly)
1 min = 60 s (exactly)
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Problem
The distance between atoms is sometimes
given in picometers, where 1 pm is
equivalent to 1 x 10-12 m. If the distance
between two carbon atoms in a diamond is
1.54 x 10-8 cm, then what is this distance
given in picometres?
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Moles
The SI unit for the amount of a substance
is the mole (mol). We will see what a mole
is in much greater detail later, but you can
start thinking of it like a “chemist’s dozen”
(though it’s really really big!)
1 dozen = 12
1 baker’s dozen = 13
1 gross = 1 dozen dozen = 144
1 mole = 6.022 x 1023
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Temperature
The Celsius scale (formerly the centigrade
scale) is the temperature scale in general
scientific use.
However, the SI base unit of temperature is
the kelvin (K), a unit based on the absolute
temperature scale.
The conversion from Celsius to kelvin is
simple since the two scales are simply offset
by 273.15
TK/K = TC/oC + 273.15
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Problem
The maximum temperature on the surface of mercury is 420 oC and
the minimum surface temperature is -220 oC. What is the “difference”
in this range of temperatures, in kelvin, on the surface of Mercury?
A.
913 K
B.
640 K
C.
473 K
D.
367 K
E.
200 K
©NASA
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Derived units
The SI unit for speed is meters per second, or m s-1.
This is an example of an SI derived unit, created by
combining SI base units.
Volume is defined as length cubed and has an SI
unit of cubic meters (m3).
Traditionally, chemists have used the liter (L), which
is a unit of volume equal to one cubic decimeter.
1 m3 = 1000 L (exactly)
1 dm3 = 1 L (exactly)
1 cm3 = 1 mL (exactly)
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Derived units
The density of an object is its mass
per unit volume
d = m/V
We may see units for density such as
g mL-1 (liquids)
g L-1 (gases)
g cm-3 (solids)
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Density example
A sample of the mineral galena (lead
sulfide) weighs 12.4 g and has a volume of
1.64 cm3. What is the density of galena?
mass
Density =
12.4 g
= 7.5609 = 7.56 g/cm3
=
volume
1.64 cm3
3 sig. fig.
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Problem
A piece of germanium (mass = 18.258 g) is
placed in 12.05 mL of chloroform in a 25
mL graduated cylinder. The chloroform
level increases to 15.46 mL. What is the
density of germanium?
Ge
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Units: Dimensional analysis
In performing numerical calculations, it is
very good practice to associate units with
each quantity.
The advantage of this approach is that the
units for the answer will come out of the
calculation.
If you make an error in arranging factors in
the calculation, it will be apparent because
the final units will be nonsense.
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Units matter! Always track them!
I’m considering giving one of you five.
Five?
Five bonus marks?
Five dollars?
Five kicks to the seat of the pants?
Five sandwiches?
Five screaming babies beside you in a
plane?
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Units: Dimensional analysis
Dimensional analysis (or the factor-label
method) is the method of calculation in which
one carries along the units for quantities.
Suppose you simply wish to convert 20 yards to
feet (1 yard = 3 feet)
 3 feet 
20 yards 
 = 60 feet
1 yard 
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Units: Dimensional analysis
The ratio (3 feet / 1 yard) is called a conversion
factor.
The conversion-factor method may be used to
convert any unit to another, provided a
conversion equation exists.
In Chapter 3 we will be extensively using the
concept of dimensional analysis and the
Conversation factor
NOTE: marks will be taken off if units are absent
or wrong
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Unit conversion example
Sodium hydrogen carbonate (baking soda)
reacts with acidic materials such as
vinegar to release carbon dioxide gas.
Given an experiment calling for 0.348 kg of
sodium hydrogen carbonate, express this
mass in milligrams.
103 g
0.348 kg x
103 mg
= 3.48 x 105 mg
x
1 kg
1g
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Unit conversion
Suppose you wish to convert 0.547 lb to
grams.
note that 1 lb = 453.6 g
so the conversion factor from pounds to
grams is 453.6 g / 1 lb. Therefore,
453.6 g
0.547 lb 
 248 g
1 lb
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Is the conversion factor exact?
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Is the conversion factor exact?
1 lb = 454 g
1 lb = 0.4536 kg
1 lb = 453.592 g
Many conversion factors aren’t
exact. Try and find one with more
sigfigs in it than the number you are
converting!
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Solving chemical problems
Read the textbook Section 1.5 on Solving
Chemical Problems
Read the Example Problems in-chapter to
understand the steps to solving a problem
type. Then try the Practice Problems that
follow doing the exact same steps.
Use end-of-chapter problems to work on
connecting word problems to which type of
Example Problem they represent.
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Solving chemical problems
EOC #1.32 The warmest temperature ever measured in
Canada is 45.0 ºC in southeaster Saskatchewan in
1937. What is this temperature in K?
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Solving chemical problems
Practice! Practice! Practice!
You don’t become an Olympic swimmer, a guitar
virtuoso or a world-class chef by watching
Michael Phelps swim or Yngwie Malmsteen play
guitar or Julia Childs cooking.
You don’t learn how to solve chemistry problems
by watching me do them.
You learn by doing them until you can
consistently identify the problem to solve and
consistently get them right…
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