Chapter 2
Measurements in Chemistry
Measurement – is the determination of the dimensions, capacity
quantity or extent of something.
Common measurements are





______________
______________
______________
______________
______________
2 Systems of Units
1.
English

•
More widely used in US than the rest of the
world
Metric


Rest of the world and scientific world
Why?



One base unit for each type of measurement
Decimals = multiples of 10
The use of Prefixes to indicate quantities
1
2 Systems of Units
English Units
•
•
•
•
Mass (ounce, pound, ton)
Length (inches, feet, yard, mile)
Volume (teaspoon, tablespoon, cup, quart, gallon,
cubic foot)
Temperature (Fahrenheit)
2 Systems of Units
Metric
•
•
•
•
Mass (gram)
Length (meter)
Volume (liter, cubic centimeter, cubic meter)
Temperature (Celsius or Kelvin)
2 Systems of Units
Common measurements taken in a laboratory and the metric
units used are:
1. mass
2. Volume
3. length
4. time
5. temperature
6. pressure
7. concentration
grams (g)
liters (L)
meters (m)
seconds (s or sec)
Celsius or Kelvin (˚C or K)
Atmospheres (atm)
Molarity (M)
2
Commonly used prefixes in the metric system are:
Greater than one:
gigaG
109 = 1,000,000,000
billion
megaM
106 = 1,000,000
million
kilok
103 = 1,000
thousand
2
hecto
h
10 = 100
hundred
deka
da
10
ten
Less than one:
decid
10-1 = 0.1
one-tenth
centic
10-2 = 0.01
one-hundredth
millim
10-3 = 0.001
one-thousandth
micro- µ(u)
10-6 = 0.000001
one-millionth
nanon
10-9 = 0.000000001
one-billionth
picop
10-12 = 0.000000000001
one-trillionth
Commonly used by chemists is the Angstrom (Å) = 10-10 meter.
Prefixes
The prefix represents a numerical value
Substituting symbols for numbers
 1000 grams = 1 kilogram
kilo = 1000
1 x 1000 grams
 0.0000675 Liters = 67.5 microliters
micro = 10-6
67.5 x 10-6 liters
More In-depth Look at Measurements
1. What is a meter?


Almost the length of a yard (1.09 yd)
Meter stick vs yard stick
2. What is a gram?
Very small compared to the ounce or pound
Approx 28 grams/ounce and 454 grams/pound
 Units of grams and milligrams are used in the lab,
because kilograms is too large.


3
Weight vs Mass
Although mass and weight are used interchangeably,
they do have different meanings
Mass – is the measure of the total quantity of matter in an
object
Weight – is a measure of the force exerted on an object by
the pull of gravity.

e.g. A man on the moon would weigh less than on
earth, but he would still have the same mass.
More In-depth Look at Measurements
3. What is a liter?

Unit of measure for volume
How do we measure volume?


Length x Width x Height
One Liter = cube of 10 cm on each side
4
More In-depth Look at Measurements
3. What is a liter?

Unit of measure for volume
How do we measure volume?
Length x Width x Height
One Liter = cube of 10 cm on each side
 1 cm3 = 1 mL
 Gases and liquids reported in mL
 Solids in cm3
 1 liter = 1.06 qt


Uncertainty in Measurements
There are 2 components to a measurement
1.
2.
___________
___________
7.498 grams

The unit tells the type of measurement and how big or
small relative to the base unit.

What information is in the number?
Uncertainty in Measurements
What information is in the number?
 The magnitude of the value

magnitude is indicated in the digit value

How big or small compared to other values with the
same units
 The uncertainty of the measurement
 Where errors in measurements may arise.
5
Uncertainty in Measurements
What influences whether there is error in a
measurement?
Is a number considered
Exact number or Inexact number
Uncertainty in Measurements
 Exact number – a number whose value has __________________
associated with it – that it is known exactly.
 Occur in definitions (dozen = 12; 3 feet in a yard)
 Counting
 Simple fractions
 Inexact numbers – a number whose value has a ______________
_____________________ associated with it.
 Any time a measurement is made because it is impossible to make
an exact measurement
 Instrumentation limitations
 Examples of how uncertainty can occur



Flaws in measuring devices
Improper calibration
User skills
Uncertainty in Measurements
How do you know where that uncertainty or error is
in the number?
 The uncertainty is always in the last digit of the
measurement.
All digits that are recorded are known with
certainty except __________________________


based on the increments of the measuring device
6
Uncertainty in Measurements
(Sig figs) – all digits that are known with
certainty plus one digit that has uncertainty.
 Significant figures

3
The number of digits recorded when taking a
measurement defines the number of significant
figures.
4
5
6
7
cm = 4.2 & mm = 42.4
cm
3 l l l l l l l l l 4 l l l l l l l l l 5 l l l l l l l l l 6 l l l l l l l l l 7 mm
Uncertainty in Measurements
 So the measurement taken with centimeter
incremental marks will have a different number of
sig figs than the measurement taken with
millimeter incremental marks.

Centimeter incremental marks = ___________________

Millimeter incremental marks = ____________________
Guidelines for determining Sig Figs
 If you are taking the measurement
 Taking measurements properly
 Recording measurements properly
7
What measurement would you record?
 17.6 mL not 17 mL or 17.60 mL
 Why?
 Lines are in 1 mL increments
 Known with certainty that the volume falls
between 17 and 18 mL
 Estimate where the volume is between 17 and 18
mL


Liquids at bottom of meniscus
LAST DIGIT REPORTED is the ESTIMATED
DIGIT
Guidelines for determining Sig Figs
What if someone else takes the measurement, how
will you know which digits are significant and
which ones are not?
 Not all estimated digits are after the decimal place
(tenths place, hundredths place).
 How do you know which are significant?????
8
For Example, what if the measurement was 200 mL?
 Which numbers are significant and which are
not???
 What were the incremental marks on the
graduated cylinder?

10 mL, 100 mL increments
 What do you do if you don’t know?
Guidelines for determining Sig Figs
Rules/Guidelines for significant figures
1.
In any measurement, all non-zero digits are
significant
2.
Zeros may or may not be included depending on
they way they are used
Guidelines for determining Sig Figs
If zeros are present in a measured number follow these rules
1. Leading Zeros (at the beginning of a number) are NOT significant
These are just place holders to keep the magnitude of the number
0.00286 = ______________
0.000000025 = ________________
2. Confined Zeros - zeros between non-zero digits are ALWAYS significant.
1.0587 = ________________
0.000504 = __________________
3. Trailing Zeros - If a decimal pt is present those at the end of the number ARE significant
98.00 = ________________
0.02040 = _____________________
4. Trailing Zeros - If the number LACKS a decimal pt, those at the end are NOT significant
These are just place holders to keep the magnitude of the number.
27,000,000 = ___________________
5010 = ______________________
9
Sig Figs and Mathematical Operations
Problems with calculators –
Calculators do not report the correct number of sig
figs. So you must decide.
 Too many digits
 Round to correct number of sig figs.
 Not enough digits (dropped zeroes)
 Make sure to record the correct number of sig figs.
Sig Figs and Mathematical Operations
Rounding Rules
 If the first digit being dropped is < 4 then just simply drop
that number and all digits following.


Round 0.0054486947 to 2 sig figs = __________________
Round 1.027520084 to 4 sig figs = ___________________
 If the first digit being dropped is > 5, then drop that
number and all digits following and the last retained digit
is increased by one.


Round 0.0485789450 to 3 sig figs = __________________
Round 5.0475858585 to 4 sig figs = __________________
Sig Figs and Mathematical Operations
Operational Rules
 multiplication/division
 addition/subtraction
 Multiple operations
10
Mathematical Operations
Different Rules for different
mathematical operations!!!
Sig Figs and Mathematical Operations
Multiplication/division
 The measurement that contains the FEWEST
number of sig figs dictates the number of sig figs
in the final answer.


1.025 x 0.127 x 25.11875 = 3.2698000
Final answer = _________after rounding
Multiplication & Division
93,429  3.9 = ?
93,429  3.9 = 23,956.15385
93,429  3.9 = ___________ (_____ sig figs and no decimal)
0.250 x 100.5  34.866 = ?
0.250 x 100.5  34.866 = 0.720202947
0.250 x 100.5  34.866 = ____________ (_____sig figs)
11
Sig Figs and Mathematical Operations
Addition/Subtraction
 The measurement that has the fewest decimal
places or digits to the right of the decimal point
determines the number of sig figs in the final
answer.

1.5894 + 2.6 + 10.795 =
Sig Figs and Mathematical Operations
1.5894
2.6
+ 10.795
14.9844
Why least number of decimals?
cannot determine whether it is 2.63 or 2.56
cannot compare beyond fewest decimals
Sig Figs and Mathematical Operations
Addition/Subtraction
 The measurement that has the fewest decimal places or
digits to the right of the decimal point determines the
number of sig figs in the final answer.




1.5894 + 2.6 + 10.795 = 14.9844
2.6 has the least decimal places
Only one decimal in the final answer
Final answer =________(follow normal rounding rules)
**the number of sig fig may change, INCREASE OR
DECREASE in addition and subtraction because decimal
places counts and not sig figs.
12
Addition & Subtraction
A. 10.568 – 3.77 = ?
10.568 – 3.77 = 6.798
B. 2.533 + 9.975 =
2.533 + 9.975 = 12.508
10.568
– 3.77
6.798 = ________
2.533
+ 9.975
12.508 = _________
Sig Figs and Mathematical Operations
Multiple operations Guidelines:
1. Must follow the order of operations (Which
comes first)




Parentheses
Exponents
Addition/subtraction
Multiplication/division
2. Round at each step before proceeding to the next
operation
Sig Figs and Mathematical Operations
3.45 + 27.54(1.030 - 0.12) =
What would be the order of operations?
13
Sig Figs and Mathematical Operations
3.45 + 27.54(1.030 - 0.12) =
 Step 1
1.030
- 0.12
0.910 = ________ (_____ sig figs)
 Step 2
3.45 + 27.54(0.91) =
0.91 x 27.54 = 25.0614 = ________ (_____ sig figs)
 Step 3
3.45 + 25 =
3.45
+ 25
28.45 = _________ (_____sig figs)
Sig Figs and Mathematical Operations
 10.1 + 8.110 (3.250 – 3.200) = ?
 Step 1
3.250
- 3.200
(_____ sig figs)
 Step 2
10.1 + 8.110 x 0.050 =
8.110 x 0.050 = 0.4055 = _________(_____ sig figs)
 Step 3
10.1 + 0.41 =
10.1
+ 0.41
10.51 = __________ (_____ sig figs)
Sig Figs and Mathematical Operations
 2 schools of thought
 Stop, Drop & round (your book uses)
 Plug-n-chug on calculator and then round at the
very end with the correct number of sig figs

Either way is acceptable.
14
Scientific Notation
 Scientific Notation – a shorthand method for writing numbers
containing a large number of zeros.

A very large or small number (with a lot of zeros) is expressed as the product
of a number between 1 and 10 and 10 raised to a power.
 Written with 2 terms

Coefficient
 a number between 1 and 10
 Written first

Exponent –
 10 raised to a power X.
 X can be a positive or a negative number.
 Always follows multiplication sign.
 Positive exponent is a number greater than 1
 Negative exponent is a number less than 1
Standard form = Coefficient x 10 x
Example = 6.836 x 10-6
Scientific Notation
Converting from decimal form into scientific
notation
 0.00000000000589 = ________________
 27,000,000 = _________________
You need to know how to put these numbers into your calculators
Scientific Notation
Converting from scientific notation to decimal form
 5.386 x 105 = _______________
 8.25 x 10-3 = _______________
You should be able to go in either direction
Scientific notation  decimal form
Decimal form  scientific notation
15
Scientific Notation
 Why use Scientific notation
 More concise way of expressing numbers
 Eliminated uncertainty in the number of significant
figures in a number especially when zeros are
present.
Scientific Notation
 Scientific Notation and Significant Figures
 Only digits that are significant are written as the
coefficient

An example of the same number written with 2,3,or
4 significant figures



82
82.0
82.00
8.2 x 101
8.20 x 101
8.200 x 101
2 sig figs
3 sig figs
4 sig figs
Scientific Notation
 So the 200 mL from previous slide
 Written in scientific notation would remove any
uncertainty in the number of sig figs.
 2.00 x 102 mL

Information when written like this


10 mL incremental marks = estimate ones place
3 sig figs
16
Scientific Notation &
Mathematical Operations
 Multiplication
 Division
 Addition
 Subtraction
Scientific Notation &
Mathematical Operations
Multiplication
 When multiplying numbers written in scientific
notation, the coefficients are multiplied and the
exponents are added
7.44 x 103 x 1.15 x 105 = ?
Scientific Notation &
Mathematical Operations
 When multiplying numbers written in scientific
notation, the coefficients are multiplied and the
exponents are added
1.
Multiply Coefficients
7.44 x 103 x 1.15 x 105 =
7.44 x 1.15 = _____________
2.
Add exponents
7.44 x 103 x 1.15 x 105 = 8.556 x 108
103+5 = _________________
3.
Combine both components
Final answer = ___________________
17
Scientific Notation &
Mathematical Operations
6.935 x 102 x 9.3 x 10-2 =
1. Multiply Coefficients
6.935 x 102 x 9.3 x 10-2 =_________________
6.935 x 9.3 = _________________
2. Add exponents
6.935 x 102 x 9.3 x 10-2 =
102+(-2) = ________________
3. Combine components
64.4955 x 100 =
needs to be in proper scientific notation
6.44955 x 101 x 100 = 6.4 x 101+0 = _______________
Scientific Notation &
Mathematical Operations
Division
 When dividing numbers written in scientific notation, the
coefficients are divided and the exponents are subtracted
 Follow the same procedure as with multiplication.
4.86 x 105  3.80 x 10-2 = ?
4.86  3.80 = _______________
105-(-2) = _________ (subtracting a negative number is like adding)
Answer ________________
Scientific Notation &
Mathematical Operations
Addition/Subtraction
When adding or subtracting numbers in scientific notation,
numbers should be converted out of proper scientific
notation so that there is a common exponent. This allows
for the coefficients to be added.

Remember that when adding and subtracting, the decimal
must line up.
3.58 x 10-2 + 4.35 x 10-3 =
If doing this in decimal form, then
0.0358
+ 0.00435
0.04015 = ___________ _______________
18
Scientific Notation &
Mathematical Operations
 Numbers are not always this easy to work with.
 Find common exponent
3.58 x 10-2  35.8 x 10-3
35.8 x 10-3 + 4.35 x 10-3 = 40.15 x 10-3
Just like with fractions and a common denominator, the exponent stays
the same after adding the coefficients together.
Convert back into proper scientific notation
4.02 x 10-2
Scientific Notation &
Mathematical Operations
 The general rule when manipulating scientific notation
 If decimal is moving to the right, then the exponent gets
smaller.
 As the coefficient gets larger the exponent must get smaller
by the same amount.
2  _____________________
 4.02 x 10

If decimal is moving to the left, then the exponent gets
bigger.


As the coefficient gets smaller the exponent must get bigger
by the same amount.
7.85 x 10-3  _____________________
Measurements
Conversion factors and Dimensional Analysis
 Conversion Factors – a ratio that specifies how one
unit of measure relates to another unit of measure.

This can be within the same system of units or
different system of units


Same system are defined and considered exact
numbers. (no sig figs)
Different system of units are experimentally
determined therefore, have error associated with it (sig
figs count)
19
Measurements
Conversion factors and Dimensional Analysis
 Conversion Factors – a ratio that specifies how one unit of
measure relates to another unit of measure.

Values in different units that describe the same quantity.





Equivalent quantities just different units
1 foot = 12 inches
1 ft and 12 in
equivalent relationships
12 in
1 ft
Always come in pairs (reciprocal forms)
Numerically equal to 1.
Measurements
Conversion factors and Dimensional Analysis
 English System
 Many conversion factors








12 in = 1 ft
16 oz = 1 lb
4 qt = 1 gal
3 ft = 1 yd
4 cups = 1 qt
8 fl oz = 1 cup
60 sec = 1 min
60 min = 1 hr
Measurements
Conversion factors and Dimensional Analysis
 Metric system
 Many conversion factors (related to prefixes)



1 km = 1000 m
1 mL = 0.001 L
1 ug = 10-6 g
20
Measurements
Conversion factors and Dimensional Analysis
 Between system of units
 Experimentally determined
 Found in a table/Appendix (See Table 2.2)
Measurements
Conversion factors and Dimensional Analysis
Using Conversion factors in problem solving
Dimensional Analysis
Measurements
Conversion factors and Dimensional Analysis
 Dimensional Analysis – a general problem solving method that
treats units like numbers (multiply, divide, or cancel), and the units
associated with numbers are used as a guide in setting up calculations
to convert from one unit of measure to another unit of measure.

Determining the area of a square






5 cm x 6 cm =
5 x 6 = 30
Treat units like numbers
8 x 8 = 82
cm x cm = cm2
Answer = 30 cm2
21
Measurements
Conversion factors and Dimensional Analysis
 Conversion factors exist in equivalent pairs.
1 ft
12 in

and
12 in
1 ft
equivalent relationships
The form of the conversion factor used will allow for
the units that are not wanted to cancel out, and the
units wanted to remain.
Measurements
Conversion factors and Dimensional Analysis
 Conversion factors exist in equivalent pairs.
1 ft
12 in


and
12 in
1 ft
equivalent relationships
The form of the conversion factor used will allow for
the units that are not wanted to cancel out, and the
units wanted to remain.
How many centimeters is 15.0 inches?
 Identify the conversion factor that relates these units if
possible
 Sometimes this process takes more than one conversion
factor.
22
Measurements
Conversion factors and Dimensional Analysis
 How many centimeters are in 15.0 inches?

Identify the conversion factor that relates these to units if
possible.

Sometimes the process of converting to a new unit requires the
use of multiple conversion factors.
 Conversion factor is 2.54 cm = 1.00 in
Set-up
15.0 in x _________= _________________
Measurements
Conversion factors and Dimensional Analysis
 How many feet is 2.50 meters?
 Requires more than one conversion factor


m  in
In  ft
Measurements
Conversion factors and Dimensional Analysis
 What about area and volume units
 Multi-dimensional units


Area = l x w = unit2 (unit squared)
Volume = l x w x h = unit3 (unit cubed)
23
Measurements
Conversion factors and Dimensional Analysis
 How to deal with multi-dimensional units
cm3 = cm x cm x cm
Everytime a unit exists, a conversion factor must be
applied
cm3  applied 3x’s
cm2  applied 2x’s
Measurements
Conversion factors and Dimensional Analysis
 How many cubic feet are in 25.0 cm3?
 Is this a 1 step process?
NO

Conversion factor must be applied 3 x’s for each conversion factor
used
cm in (3x’s)
in  ft (3x’s)
Measurements
Density
 Density – the ratio that relates the mass of an object to
the volume occupied by an object.
𝑑=
𝑚
𝑉
A brick vs a block of wood of same size


The brick weighs more.
The brick has a greater density than the block of
wood.
24
Measurements
Density
 Units of density
 Solid
g/cm3
 Liquid g/mL
 Gas
g/L


Temperature must be specified because substances
contract and expand with changes in temperature.
Pressure also for gases (compressibility)
Measurements
Density
 Mathematical applications of Density.

Solve for any of the following variables




Mass
Volume
Density
If in a dimensional analysis problem, need to
change unit from mass to volume or vise versa.

Density can be used as a conversion factor.
Measurements
Density
Calculations with density
 Calculate the density of an object that has a mass
of 20.51 g and occupies a volume of 24.3 cm3.
25
Measurements
Density
Calculations with density
 What is the volume of a piece of aluminum that
weighed 200.48 g? (d = 2.70 g/cm3)
Measurements
Density
Calculations with density
Calculate the density of a liquid that has a mass of
50.26 g and occupies a volume of 24.3 mL.
Measurements
Density
Calculations with density
 A balloon filled with air has a volume of 4225
cm3. What is the mass of the air inside the
balloon? (dair= 1.29 g/L)
26
Heat
What is heat?
Heat is a form of energy.
Heat
How do we measure heat?
Temperature

Temperature is a measure of the amount of heat in
an object relative to other objects

General direction of the flow of heat
 Higher temperature  to lower temperature
Heat
Temperature Scales
Three Temperature scales
1. Fahrenheit (˚F)
2. Celsius (˚C)
3. Kelvin (K)
27
Heat
Temperature Scales
What makes the temperature scales different?
 The amount of heat per incremental mark
 Fahrenheit has less heat/mark than Celsius
 Celsius and Kelvin have the same amount
 Kelvin is the absolute scale (no negative temperatures)
 The reference point on the scale
 Fahrenheit and Celsius use water
 0.00 Kelvin represents the temperature at which all
molecular motion stops.
Heat
Temperature Scales
Mathematical relationship
Fahrenheit  Celsius
C = 5/9 ( F – 32)
Celsius  Fahrenheit
F = 9/5(C) + 32
Celsius  Kelvin
K = C + 273.15
9/5 = 1.8
I will give these relationships in the exam.
28
Heat
Specific Heat
What is heat energy?
The energy most commonly associated with a
chemical reaction
Heat
Specific Heat
Units for heat energy are:
calories (cal)
Calories (Cal)
 Joules (J)


Heat
Specific Heat
calorie – 2 definitions
1. calorie – a unit of measure for heat energy.
2. calorie – the amount of heat required to raise the
temperature of one gram of water one degree Celsius.
Conversion factors for units
1000 cal = 1 kcal = 1 Cal
Calorie = food calorie
1 calorie = 4.184 J
29
Heat
Specific Heat
A calorie is specific for water.
What about other substances?
Specific Heat
Heat
Specific Heat
Specific Heat – the amount of heat required to raise the
temperature of one gram of a substance one degree
Celsius.
 Different substances have different specific heats
 A measure of how quickly or slowly something will heat
up or cool down.
 higher the specific heat value the slower the change in
temperature.
Remember
Heat will flow always in the direction of hotcold
Heat
Specific Heat
30
Heat
Specific Heat
 Mathematical applications for specific heat
Heat absorbed = mass x specific heat x temp change
q = m x SH x DT
The units for specific heat – cal/g˚C or J/g˚C
Make sure units are the same!
Heat
Specific Heat
What is the change in temperature if a lump of gold
weighing 5.009 g absorbed 2.64 cal. (SHgold=0.031
cal/g°C)
 Not actual temperature, but the change in
temperature
Heat
Specific Heat
If an Aluminum tray weighing 25 g went from room
temperature (RT) to 350 ˚F, how much heat was
absorbed in Joules? (SHaluminum = 0.21 cal/g°C)
31