Chapter 2
Measurements
Homework
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Do “Questions and Problems”
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Do “Understanding the Concepts”
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2.75, 2.79
Do “Additional Questions and Problems”
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2.1 through 2.73 (odd)
2.83 through 2.103 (odd)
Do “Challenge Questions”
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2.105-2.113 (odd)
Measurement
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The most useful tool of the chemist
Most of the basic concepts of chemistry
were obtained through data compiled by
taking measurements
How much…?
How long…?
How many...?
These questions cannot be answered
without taking measurements
The concepts of chemistry were
discovered as data was collected and
subjected to the scientific method
Measurement
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The estimation of the magnitude of an
object relative to a unit of measurement
Involves a measuring device
 ie: meterstick, scale
The device is calibrated to compare the
object to some standard (inch/centimeter,
pound/kilogram)
Quantitative observation with two parts:
A number and a unit
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Number tells the total of the quantity measured
Unit tells the scale (dimensions)
Measurement
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A unit is a standard (accepted) quantity
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Describes what is being added up
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Units are essential to a measurement
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For example, you need “six of sugar”
 teaspoons?
 ounces?
 cups?
 pounds?
Units of measurement
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Units tells the magnitude of the standard
Two most commonly used systems of units of
measurement
 US system: Used in everyday commerce
(USA and Britain*)
 Metric system: Used in everyday commerce
and science (The rest of the world)
SI Units (1960): A modern, revised form of the
metric system set up to create uniformity of
units used worldwide (world’s most widely
used)
Metric System
A decimal system of measurement based
on the meter and the gram
 It has a single base unit per physical
quantity
 All other units are multiples of 10 of the
base unit
 The power (multiple) of 10 is indicated by
a prefix

Metric System

In the metric system there is one base unit for
each type of measurement
length
 volume
 mass
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The base units multiplied by the appropriate
power of 10 form smaller or larger units
The prefixes are always the same, regardless
of the base unit
 milligrams and milliliters both mean 1/1000 of
the base unit
Length
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Meter
Base unit of length in metric and SI system
About 3 ½ inches longer than a yard
 1 m = 1.094 yd
Length
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Other units of length
are derived from the
meter
Commonly use
centimeters (cm)
 1 m = 100 cm
 1 inch = 2.54 cm
(exactly)
Volume
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Measure of the amount
of three-dimensional
space occupied by a
object
Derived from length
SI unit = cubic meter
(m3)
Metric unit = liter (L) or
10 cm3
Commonly measure
smaller volumes in
cubic centimeters (cm3)
Volume = side × side × side
Volume = side × side × side
Volume
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Since it is a threedimensional measure,
its units have been
cubed
SI base unit = cubic
meter (m3)
This unit is too large
for practical use in
chemistry
Take a volume 1000
times smaller than the
cubic meter, 1dm3
Volume
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Metric base unit =
1dm3 = liter (L)
1L = 1.057 qt
Commonly measure
smaller volumes in
cubic centimeters
(cm3)
Take a volume 1000
times smaller than the
cubic decimeter, 1cm3
Volume
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The most commonly
used unit of volume in
the laboratory:
milliliter (mL)
1 mL = 1 cm3
1 L= 1 dm3 = 1000 mL
1 m3 = 1000 dm3 =
1,000,000 cm3
Use a graduated
cylinder or a pipette to
measure liquids in the
lab
Mass
Measure of the total quantity of matter
present in an object
 SI unit (base) = kilogram (kg)
 Metric unit (base) = gram (g)
 Commonly measure mass in grams (g) or
milligrams (mg)
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1
kg = 1000 g
 1 g = 1000 mg
 1 kg = 2.205 pounds
 1 lb = 453.6 g
Temperature
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Measurement of the intensity of heat
energy in matter
Hotness or coldness of an object
Fahrenheit Scale, °F
 Everyday Use in USA
 Not used in science
 Water’s freezes at 32°F, boils at 212°F
Temperature
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Celsius Scale, °C
Metric Unit
 Used in science (USA) and rest of world
 Temperature unit larger than the Fahrenheit unit
 Water’s freezes = 0°C, boils at 100°C
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Kelvin Scale, K
SI Unit
 Used in science
 Temperature unit same size as Celsius unit
 Water’s freezes at 273 K, boils 373 K
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Absolute zero is the lowest temperature theoretically
possible
Temperature
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Scales determined by different degree sizes and
different reference points
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There are 180 degrees between the freezing
and boiling points on the Fahrenheit scale
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The number of degree units between the
freezing and boiling point on the Celsius and
Kelvin scales are the same: 100 degrees
A change in 1 °C = a change in 1 K
A change in 1°C or 1 K = a change of 1.8 °F
212ºF
100ºC
180
Fahrenheit
degrees
100
Celsius
degrees
32ºF
Fig2_9
Boiling point
0ºC
Freezing point
Prefixes and Equalities
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One base unit for each type of measurement
Length (meter), volume (liter), and mass (gram*)
The base units are then multiplied by the appropriate
power of 10 to form larger or smaller units
base unit
Prefixes and Equalities
(memorize)
× base unit
Mega
 Kilo
 Base
 Deci
 Centi
 Milli
 Micro
 Nano
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(M) 1,000,000
(k)
1,000
1 meter liter gram
(d)
0.1
(c)
0.01
(m)
0.001
(µ)
0.000001
(n)
0.000000001
106
103
100
10-1
10-2
10-3
10-6
10-9
Remembering Metric System
 Keep
in mind which unit is larger
A
kilogram is larger than a gram, so
there must be a number of grams in
one kilogram
 This can help you check if you have
the conversion correct
n < µ < m < c < base < k < M
Scientific Notation
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A system in which an ordinary decimal
number (m) is expressed as a product of a
number between 1 and 10, multiplied by 10
raised to a power (n)
Used to write very large or very small
numbers
Based on powers of 10
m  10
n
Scientific Notation
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Consists of a number (coefficient) followed
by a power of 10 (x 10n)
2
7.03  10
exponent
coefficient exponential term
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Negative exponent: Number is less than 1
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Positive exponent: Number is greater than 1
Scientific Notation
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In an ordinary cup of water there are:
7,910,000,000,000,000,000,000,000 molecules
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Each molecule has a mass of:
0.0000000000000000000000299 gram
In scientific notation:
7.91 х 1024 molecules
2.99 х 10-23 gram
Writing in Scientific Notation
For small numbers (<1):
1) Locate the decimal point
2) Move the decimal point to the right to give a
coefficient between 1 and 10
3) The new number is now between 1 and 10
4) Add the term x10-n
 where n is the number of places you moved the
decimal point. It has a negative sign
 If the decimal point is moved to the right, then the
exponent is a negative number
Writing in Scientific Notation
For large numbers (>1):
1) Locate the decimal point
2) Move the decimal point to the left to give
a coefficient between 1 and 10
3) Add the term x10n
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where n is the number of places you moved
the decimal point. It has a positive sign.
If the decimal point is moved to the left, the
exponent is a positive number
Examples
 Write
each of the following in
scientific notation
 12,500
 0.0202
 37,400,000
 0.0000104
Examples
12,500
 Decimal place is at the far right
 Move the decimal place to between
the 1 and 2 (1.25)
 The decimal place was moved 4
places to the left (large number) so
exponent is positive
 1.25x104
Examples
 0.0202
 Move
the decimal place to between
the 2 and 0 (2.02)
 The decimal place was moved 2
places to the right (small number)
so exponent is negative
 2.02x10-2
Examples
 37,400,000
 Decimal
place is at the far right
 Move the decimal place to between
the 3 and 7 (3.74)
 The decimal place was moved 7
places to the left (big number) so
exponent is positive
 3.74x107
Examples
 0.0000104
 Move
the decimal place to between
the 1 and 0 (1.04)
 The decimal place 5 places to the
right (small number) so exponent is
negative
 1.04x10-5
Example
 6.442x105
5
is positive, move the decimal 5 places
to the right (to make the number bigger)
 644,200
 5.583x10-2
2
is negative, move the decimal 2
places to the left (to make the number
smaller)
 0.05583
Scientific Notation and
Calculators
1) Enter the coefficient (number)
2) Push the key: EE or EXP
Then enter only the power of 10
3) If the exponent is negative, use the
key: (+/-)
4) DO NOT use the multiplication key:
X
to express a number in sci. notation
Converting Back to a Standard Number
1) Determine the sign of the exponent, n
If n is + the decimal point will move to the
right (gives a number greater than one)
 If n is – the decimal point will move to the
left (gives a number less than one)
2) Determine the value of the exponent of 10
 The “power of ten” determines the
number of places to move the decimal
point
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Using Scientific Notation
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To compare numbers written in scientific
notation
First compare the exponents of 10
 The larger the exponent, the larger the
number
If the exponents are the same, then compare
coefficients directly
 Which number is larger?
21.8 х 103 or 2.05 х 104
2.18 х 104 > 2.05 х 104
Measured Numbers and
Significant Figures
 Two
kinds of numbers
 Counted (exact)
 Measured
Exact Numbers
Numbers known with certainty
 Unlimited number of significant figures
 They are either
 counting numbers
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 10
beds, 6 pills, 4 chairs
 defined
 100
numbers
cm = 1 m; 12 in = 1 ft; 1 in = 2.54 cm
 1 kg = 1000 g; 1 lb = 16 oz
 1000 mL = 1 L; 1 gal = 4 qts.
 1 minute = 60 seconds
Measured Numbers
A measurement always has some
amount of uncertainty
 Involves reading a measuring
device
 Uncertainty comes from the tool used
for comparison
 i.e. Some rulers show smaller
divisions (markings) than others
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Measured Numbers
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Always have to
estimate the value
between the two
smallest divisions on
a measuring device
Every person will
estimate it slightly
differently, so there
is some uncertainty
present as to the
true value
2.8 to 2.9 cm
Significant Figures
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To indicate the uncertainty of a single
measurement scientists use a system
called significant figures
Significant figures: All digits known with
certainty plus one digit that is uncertain
The last digit written in a measurement is
the number that is considered to be
uncertain
Unless stated otherwise, the uncertainty in
the last digit is ±1
Counting Significant Figures
 Nonzero
integers are always
significant
 Zeros (may or may not be significant)
 Leading
zeros never count as significant
figures
 Captive zeros are always significant
 Trailing zeros are significant if the
number has a decimal point
 Exact
numbers have an unlimited
number of significant figures
Rounding Off Rules
 If
the digit to be removed
• is less than 5, the preceding digit stays
the same
• is equal to or greater than 5, the
preceding digit is increased by 1
 In
a series of calculations, carry the
extra digits to the final result and then
round off
Significant Figures in Calculations
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Calculations cannot improve the precision of
experimental measurements
The number of significant figures in any
mathematical calculation is limited by the least
precise measurement used in the calculation
Two operational rules to ensure no increase in
measurement precision
 addition and subtraction
 multiplication and division
Multiplication/Division
Product or quotient has the same number
of significant figures as the number with
the smallest number of significant figures
 Count the number of significant figures in
each number
 Round the result so it has the same
number of significant figures as the
number with the smallest number of
significant figures
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Example
5 SF
4 SF
3 SF
0.10210.082103273
1.1
2.1
 2.080438
2 SF
2 SF

The number with the fewest
significant figures is 1.1 so the
answer has 2 significant figures
Addition/Subtraction
 Sum
or difference is limited by the
number with the smallest number
of decimal places
 Find number with the fewest
decimal places
 Round answer to the same
decimal place
Example
1 d.p.
3 d.p.
2 d.p.
236.2
171.5 72.9158.23  236.185
1 d.p.
 The
number with the fewest
decimal places is 171.5 so the
answer should have 1 decimal
place
Equalities
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A fixed relationship between two quantities
Shows the relationship between two units
that measure the same quantity
The relationships are exact, not measured
 1 min = 60 s
 12 inches = 1 ft
 1 dozen = 12 items (units)
 1L = 1000 mL
 4 quarts = 1 gallon
 1 pound = 454 grams
Conversion Factors
Many problems in chemistry involve a
conversion of units
 Conversion factor: An equality expressed
as a fraction
 Used as a multiplier to convert a quantity
in one unit to its equivalent in another unit

 May
be exact or measured
 Both parts of the conversion factor should
have the same number of significant figures
Problem Solving
Conversion Factors Stated Within a Problem

The average person in the U.S.
consumes one-half pound of sugar per
day. How many pounds of sugar
would be consumed in one year?
1) State the initial quantity given (unit):
One year
State the final quantity (unit): Pounds
2) Write a sequence of units (plan) which
begins with the initial unit and ends with the
desired unit:
year
day
pounds
1 cal 4.184 J
Problem Solving
Dimensional Analysis Example
3) For each unit change,
State the equalities:
 Every equality will have two conversion
factors
365 days = 1 year
0.5 lb sugar =1day
year
day
pounds
Problem Solving
Dimensional Analysis Example

State the conversion factors:
0.5 lb. sugar and
day
day
0.5 lb. sugar
4) Set Up the problem:
1 year 365 day(s) 0.5 lb sugar  183 lbs. sugar
day
year
Guide to Problem Solving when
Working Dimensional Analysis Problems
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Identify the known or given quantity and the
units of the new quantity to be determined
Write out a sequence of units which starts with
your initial units and ends with the desired units
(“the unit pathway”)
Write out the necessary equalities and
conversion factors
Perform the mathematical operations that
connect the units
Check that the units cancel properly to obtain
the desired unit
Does the answer make sense?
Density
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The ratio of the mass of an object to the volume
occupied by that object
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Units for solids and liquids = g/cm3
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Tells how tightly the matter within an object is
packed together
1 cm3 = 1 mL so also g/mL
Unit for gases = g/L
Density: solids > liquids >>> gases
mass
Density 
volume
Determining Density
 Weigh
 Use
the object
a scale
 Determine
the volume of the object
 Calculate
it if possible (cube)
 Can also calculate volume by
determining what volume of water is
displaced by an object
Volume of Water Displaced = Volume of Object
Densities of Substances
Can use density as a conversion factor
between mass and volume
 Given in Table 2.9, page 47
 You will be given any densities on tests
EXCEPT water
 Density of water is 1.000 g/mL at room
temperature
 1.00 mL of water weighs how much?
 How many mL of water weigh 15 g?

Density Problem
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Iron has a density of 7.87 g/cm3. If 52.4 g
of iron is added to 75.0 mL of water in a
graduated cylinder, to what volume
reading will the water level in the cylinder
rise?
Vf  ?
m  52.4 g
Vi  75.0 mL
d  7.87 g cm3

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
Density Problem
Solve for volume of iron
density  mass
volume
volume  mass
density
3
1 cm = 1 mL
52.4 g iron 1 mL iron
 6.658 mL iron
7.87 g iron

6.658 mL iron + 75.0 mL water = 81.7 mL total