Chapter 1 (Part 2) Measurements in Chemistry
1.7 Physical Quantities
English Units
Those of us who were raised in the US are very accustomed to these.
Elsewhere in the world, these are very confusing.
Weight: ounce (oz)
pound (lb) [16 ounces = 1 pound]
ton [2000 pounds = 1 ton]
Notice that the English
system of units uses
ounces to describe both
weight and volume
measurements, which
adds to the confusion.
Length: inch (in)
foot (ft) [12 inches = 1 foot]
yard (yd) [3 feet = 1 yard]
mile (mi) [5280 feet = 1 mile]
Volume: teaspoon (tsp)
tablespoon (Tbsp) [3 tsp = 1 Tbsp]
cup [16 Tbsp = 1 cup = 8 oz]
pint (pt) [2 cups = 1 pint = 16 oz]
quart (qt) [4cups = 2 pints = 1 quart = 32 oz]
gallon (gal) [4 quarts = 1 gallon=64oz]
SI Units
 The scientific community has chosen a modified version of the metric system as
the standard for recording and reporting measurements.
 Designated as SI (Systeme International) or International System of Units
Some SI Base Units
Measurement
Name of Unit
Abbr.
Mass
kilogram
kg
Length
meter
m
Time
second
s
Temperature
Kelvin
K
Amount of substance
mole
mol
Derived Units
Volume
Energy
cubic decimeter
= liter
Joule
Chapter 1 (Part 2) Page 1 of 22
dm3=10-3m3
L = dm3
J=kg x m2/sec2
Unit Prefixes
Selected Prefixes in the Metric System
Know
by
heart
Prefix
Abbr.
Means Examples
mega
M
106
kilodecicentimillimicronano-
k
d
c
m

n
103
10-1
10-2
10-3
10-6
10-9
pico-
p
10-12
1 Megawatt = 1,000,000
watts
1 kilogram = 1,000 grams
1 dL = 0.1 liters
1 cm = 0.01 meters
1 mg = 0.001 grams
1 microliter = 0.000001 liters
1nanometer = 0.00000001
meters
1 picometer =
0.000000000001 meters
1,000,000 watt =
1 Mwatt
1000g = 1 kg
10 dL = 1 L
102 or 100 cm = 1 m
103 or 1000 mg = 1 g
106 L = 1L
109 nm = 1 m
1012 pm= 1 m
Metric System
This is a slight variation on the SI units of measure that is in
common use in most countries other than the United States.
 Unit of mass is the gram (g) rather than the kilogram (1kg =1000g).
 Unit of volume is the liter (L) instead of the cubic meter
(1 m3 = 1000L).
 Unit of temperature is the Celsius degree (C) rather than the Kelvin.
 Also known as the centigrade degree.
Chapter 1 (Part 2) Page 2 of 22
1.8 Measuring Mass, Length, & Volume
Mass Measurements
The terms mass and weight are often confused and interchanged.
• Mass - A measure of the amount of matter in an object.
(how much stuff is present)
• Weight - A measure of the gravitational force that the earth
or other large body exerts on an object.
e.g. We “weigh” less on the moon than on earth, but we have the
same mass.
Most useful:
1 lb = 16 oz = 454g
1 kg = 2.205 lb
Length, Area and Volume Measurements
For Length:
Most useful:
1 inch = 2.54 cm exactly
For Areas, that is easy to see:
A square meter (m2) is an area 1 meter on each side.
For volumes this is also true, but the final unit is often given a
new name.
A cubic centimeter (cm3 or cc) is an area 1 cm on each side = 1mL = 1cc
A cubic decimeter (dm3) is an area 1 dm on each side = 1 L
Chapter 1 (Part 2) Page 3 of 22
Most useful:
1 L = 1.057 qt
32 oz = 1 qt
1.9 Measurement and Significant Figures
Numbers vs Data – Significant Figures
 In math class
 , numbers are theoretical, exact species.
 In science, most numbers are associated with measurements.
Uncertainty of Data
All measurements contain some uncertainty.
 We make errors
 Tools have limits
We need to be able to show what degree of
confidence we have in a piece of data.
• The value recorded should use all the digits
known with certainty,
plus one estimated digit.
Chapter 1 (Part 2) Page 4 of 22
• Significant figures –
The number of meaningful digits used
to express a value.
Determining Significant Digits
 Last digit is uncertain
 Non-zero digits are ALWAYS significant.
 Zeros depend on whether they are leading, captive, or trailing

LEADING zeroes are NEVER significant

IMBEDDED zeros are ALWAYS significant

TRAILING zeroes Depend
after a decimal point ARE significant
at the end of a # with no decimal point – we can’t tell
 Numbers with decimal points will be considered to be significant.
(Confusion can be avoided by using scientific notation)
 Numbers that are definitions (e.g. 1 gallon = 4 quarts) have an infinite
number of significant figures.
 Anything that gets counted in integer values is treated as exact.
Problem: How many significant figures are in:
a) 4009
b) 0.0455
c) 2806.0
d) 0.8904
e) 27.401
f) 4200.
g) 4200
Chapter 1 (Part 2) Page 5 of 22
1.10 Scientific Notation
Scientific notation is typically used to express very large or very
small numbers or to clarify the number of significant digits present





Expressed as N x 10n
N is the digit term and is a number between 1 and 10.
n is the exponential term.
In scientific notation, all digits are significant.
When converting a number to scientific notation:
 For every place you move the decimal to the left, add a power of 10.
Example: 1 2 3 , 0 0 0 , 0 0 0 = 1.23 x 108
(positive powers of 10 are for BIG numbers)
 For every place you move the decimal to the Right, subtract a power
of 10.
Example: 0 . 0 0 0 0 0 0 1 2 3 = 1.23 x 10-7
(negative powers of 10 are for SMALL numbers)
Chapter 1 (Part 2) Page 6 of 22
Problem: Write the following in scientific notation:
a) 38666
b) 0.00407
c) 1300 to 2 sf
d) 1300 to 3 sf
e) 0.0000590
We also need to be able to convert values that are shown in
scientific notation back to standard notation.
Problem: Write the following in standard notation:
a) 4.85 x 10-3
b) 3.270 x 103
c) 3.270 x 102
d) 8.819 x 10-6
e) 4.5500 x 103
1.11 Rounding Off Numbers
Calculators often display more digits than are justified by the precision of
the data.
 The last digit to be retained is increased by one if the following digit is
5 or greater. (i.e., 5,6,7,8, or 9)
 Example: 0.57266 rounded to 2 sf =
 The last digit to be retained is left unchanged if the following digit is 4
or less. (i.e., 0,1,2,3, or 4)
 Example: 0.57266 rounded to 3 sf =
Chapter 1 (Part 2) Page 7 of 22
Round off the following numbers to the correct number of
significant figures:
Raw
# Sig Figs
Rounded
In sci. not.
1.6753
1.6753
1.6753
1099.7
1099.7
1099.7
In the second example, we cannot tell once the number is rounded,
how many significant figures the number represents.
Scientific Notation (and Sig Figs) on Calculators
When calculators display numbers in scientific notation, the
display may show
 an E followed by a number
 10x
 simply a number set off to the right side.
Chapter 1 (Part 2) Page 8 of 22
To change a value to scientific notation:
Using your calculator, convert the following to scientific notation:
a) 38666
3.8666 x 104
b) 0.00407
4.07 x 10-4
c) 1300 to 2 sf
1.3 x 103
d) 1300 to 3 sf
1.30 x 103
To change a value to standard notation:
Using your calculator, convert the following to standard notation:
a) 4.85 x 10-3
0.00485
b) 3.270 x 103
3270. (decimal is import)
c) 3.270 x 102
327.0 (zero is import)
d) 8.819 x 10-6
0.000008819
e) 4.5500 x 103
4550.0
Chapter 1 (Part 2) Page 9 of 22
Calculators do not give us significant figures. We must figure that
part out for ourselves!
Express the following in scientific notation.
a) 21357
2.1357 x 104
b) 0.00374
3.74 x 10-3
c) 238500000 to 4sf
2.385 x 107
d) 238500000 to 7 sf
2.385000 x 107
e) 0.00089700 to 4 sf
8.970 x 10-4
f) 0.00089700 to 2 sf
9.0 x 10-4
Significant Digits in Calculations
The answer to a problem cannot have more significance (accuracy)
than the quantities used to produce it.
 Rule 1: Multiplying or Dividing
The answer should have the same number of significant figures as the
quantity with the fewest significant figures.
Problem: Calculate (3.23 x 0.02704)/(250. x 15) to the correct # of s.f.
 When you have mixed multiplication and division, determine
the # of sig figs in each intermediate result as you go along.
 Do not round any answers until the very end.
Problem: Calculate (3.01-1.2)/(3.56 +9.23) to the correct # of sig figs.
Problem: Calculate 1.68 x 10-1 / 08.40 x 102 to the correct # of sig figs.
Chapter 1 (Part 2) Page 10 of 22
 Rule 2: Adding or Subtracting
The number of decimal places the answer should equal to the number
of decimal places in the number with the fewest decimal places.
Problem: Add 3.295 + 10.2 + 0.00001 to the correct # of sig figs.
Problem:Subtract 4.2 from 15.723 to the correct # of sig figs.
Where do the significant digits that we claim in the previous
exercises come from? – Measurements!!!
Chapter 1 (Part 2) Page 11 of 22
Accuracy and Precision
These two terms are often confused for being synonymous.
Accuracy vs Precision
 Precision
The precision of a measurement indicates how well several
determinations of the same quantity agree with each other.
 Accuracy
describes how well a measured value agrees with the established
correct value.
Precise
Accurate
Both
Neither
Chapter 1 (Part 2) Page 12 of 22
1.12 Problem Solving: Unit Conversion and Dimensional Analysis
Unit Conversions
• Information is often not given in the units we need or that we
can relate to.
Example Problem: if a horse stands 16 hands tall, the average
person would want to know the height in inches or feet or meters
to better comprehend the information.
• The simplest way to carry out calculations involving different
units is to use the
factor-label method
(aka dimensional analysis or unit cancellation).
To solve the problem above we would need to know that
1 hand = 4 inches
• Units are treated like numbers and can thus be multiplied and
divided.
• Anything divided by itself = 1
• Anything multiplied by 1 = original value (in new units)
• Set up an equation so that all unwanted units cancel.
For above problem:
SOLUTION
Problem : A child is 21.5 inches long at birth. How long is this in
centimeters?
Chapter 1 (Part 2) Page 13 of 22
What if units are squares or cubes?
Problem: Convert 24.5 in2 to m2.
Significant Figures for Unit Conversions
 All English/English conversion factors have unlimited sig figs.
 All Metric/Metric conversion factors have unlimited sig figs.
 All English/Metric conversions have limited sf except 1in=2.54cm.
Problem: (Metric Conversion)
How many centigrams are in a kilogram?
If you are asked to convert from one prefix to another,
remove the first, then add the second.
Chapter 1 (Part 2) Page 14 of 22
1.13 Temperature, Heat, & Energy
Energy
 The capacity to do work or supply heat.
Temperature
 The measure of the average kinetic energy (energy of motion) of the
particles.
 Simple definition:
A measure of how hot or cold an object is.
 Temperature – a measure of the heat energy.
Fahrenheit Temperature
Scale
 Defined by German scientist
Daniel Gabriel Fahrenheit in
late 1600s or early 1700s.
 Defined by freezing
temperature of saturated salt
solution (intended to be 0F)
and temperature of the human
body (intended to be 100F,
turned out to be 98.6F)
 Current markers are freezing temperature of water (___) and boiling
point of water (____)
 Currently in use primarily only in the United States
Celsius Temperature Scale
 Suggested by Swedish astronomer Anders Celsius in the mid 1700s.
 Sometimes referred to as the _________.
Chapter 1 (Part 2) Page 15 of 22
 Defined by freezing temperature of water ( _C ) and
boiling point of water ( C)
Kelvin Temperature Scale
 Both Fahrenheit and Celsius temperature scales require the use of
negative numbers.
 However, there is a limit to how low temperature can go.
 This was discovered through hundreds of experiments.
 William Thompson (a.k.a. Lord Kelvin ) suggested in mid to late
1800s a scale that does not use negative numbers.
 The Kelvin scale assigns a value of 0 K to the coldest possible
temperature, __________, which is equal to  273.15 C
 It uses the same degree size as the Celsius scale, but starts at absolute
zero, or -273.15C. (Expressed simply as K not K)
Temperature Conversions
Conversion Factors
9

 F   * C   32
5

K = C + 273.15
C 
5
( F  32 F )
9
C = K – 273.15
Problem: If it is 20F outside, what is the temp. in C?
Problem: If it is 75F outside, what is the temp. in K?
Chapter 1 (Part 2) Page 16 of 22
Energy and Heat
Energy
Two basic forms of Energy
Kinetic Energy: The energy of motion.
Potential Energy:
Stored Energy
Bouncing ball converts
energy between KE &
PE
Heat
Energy (and heat) are measured in units of
Joules (J) in SI units or calories (cal) in metric.
1 cal = 4.184 J
1 cal = the heat required to raise 1 gram of water 1C.
1000 cal = 1 kcal = 1 Cal This is the dietary calorie with a capital C!
Specific Heat (c) is the amount of heat required to raise the
temperature of 1 gram of substance 1 degree Celsius.
Chapter 1 (Part 2) Page 17 of 22
Substance J/g.°C
Gold
0.126
Copper
0.386
Cast Iron
0.460
Steel
0.490
Granite
0.790
Glass
0.840
Aluminum
0.900
Water
4.186
How much energy in Joules is needed to raise the temperature of
75.0 g aluminum bar from refrigerator temperature 3.0 °C to 13.0°C?
In calories?
How much heat (calories) is removed from a 12 oz diet Coke is
removed when it is cooled from room temperature (25°C) to 3°C?
(Diet coke has the same specific heat as water =
=
).
4.186
[[HINT : 1 oz = 28.35 g]]
Chapter 1 (Part 2) Page 18 of 22
1.14 Density and Specific Gravity
Density
Density is the ratio of the mass of an object to its volume.
Mass
Density = -----------Volume
 Density is a characteristic property of a substance.
 It usually has units of g/cm3 or g/mL.
 Density is stated at a given temperature.
 Density of Water = 1.00 g/ml at 4 degrees C. (It’s maximum density.)
 Substances with lower densities will float on ones with higher
densities.
LP#1. What is the density of 5.00 mL of serum if it has a mass of
5.23 grams?
What would the mass of 1.00 liters of this serum be?
Chapter 1 (Part 2) Page 19 of 22
Measuring density of Solids
- Measure the mass of the solid before
submerging it in water to determine its
volume.
Mass =
- Volume displacement is the volume of a
solid calculated from the volume of water
displaced when it is submerged.
- To get the density, divide the mass by the
volume.
Specific Gravity
Specific Gravity is the density of a substance compared to a
reference substance
Density of Substance
Specific Gravity = ---------------------------------------------------------------------Density of Reference Substance (typically water at 4C)
 It is a ratio with no units.
At normal temperatures, the specific gravity of a substance is
numerically equal to its density, but has no units.
Chapter 1 (Part 2) Page 20 of 22
The specific gravity of a liquid can be measured using an
instrument called a hydrometer.
Hydrometers contain a weighted bulb at the
end of a calibrated glass tube. The depth to
which the hydrometer sinks in the fluid
indicates the fluid's specific gravity.
The lower the hydrometer sinks, the lower the
specific gravity.
Urinometers (a specialized hydrometer) are
used to measure dissolved solids in urine.
Urinometers can help identify dehydration.
Obesity and Body Fat
Show Galileo
thermometer picture to
class.
Body Mass Index
weight ( kg ) weight (lb)
BMI 

x 270
2
height (in) 2
height m 
BMI of 25 -30 is considered overweight.
BMI of 30 or above is considered obese.
By these standards, approximately 61% of the U.S.
population is overweight.
The lowest death risk from any cause, including cancer
and heart attack was for BMI 22-24.
By BMI of 29, the risk doubles! (McMurry 7th Ed.)
Chapter 1 (Part 2) Page 21 of 22
Practice Problem for Dimensional Analysis using BMI.
Based on the BMI scale, is a 5’10’ man who weighs 220 lb obese?
Mass =
Height =
BMI =
Chapter 1 (Part 2) Page 22 of 22