Measurements in Chemistry
The Standard Units
 Scientists have agreed on a set of international
standard units for comparing all our measurements
called the SI units
 Système International = International System
Quantity
Unit
Symbol
meter
m
kilogram
kg
Time (t)
second
s
Temperature (T)
kelvin
K
Mole (mol)
Mole
mol
Length (L)
Mass
(m)
Length
 SI unit = meter

A meter is the distance that light travels in a vacuum (space with
no matter) in 1/299,792,458 second
 Commonly use centimeters (cm)
 1 m = 100 cm
 1 cm = 10 mm
 1 inch = 2.54 cm (exactly)
Time
 SI base unit: second (s)
 A second is the frequency of the radiation given off by a
cesium-133 atom.
Mass
 Measure of the amount of matter
present in an object
 A kilogram is defined by a platinumiridium cylinder kept at Sèvres, France.
 SI unit = kilogram (kg)
 1 kg = 2.2046 pounds
 1 kg = 1000 g
 1 g = 1000 mg
Volume (V)
 Measure of the amount of space occupied
 SI unit = cubic meter (m3)
 a Derived Unit
 Commonly measure solid volume in cubic centimeters (cm3)
 1 m3 = 1x106 cm3
 Commonly measure liquid or gas volume in milliliters (mL)
 1 L = 1000 mL
1L=1 dm3
1 mL = 1 cm3
 Volume for geometric figures:
 Rectangle: V =Length x width x height
 Cylinder : V= r2h
h: height r: radius
Temperature
 SI base unit: Kelvin (K)
 Lowest temperature is 0 K
 Celsius (C)
 Fahrenheit (F)
 K= C + 273
 F = (1.8xC) + 32
Related Units in the SI System
 All units in the SI system are related to the standard
(base) unit by a power of 10
 The power of 10 is indicated by a prefix
 The prefixes are always the same, regardless of the
standard unit Ex. cm (centimeter), cg (centigram), cL
(centiliter)
Greek Prefixes SI System Table
Prefix
Gigamegakilo-
Decimal
Symbol
Equivalent
G
1000,000,000
M
k
1,000,000
1,000
Power of 10
1 x 109
1 x 106
1 x 103
BASE UNIT (Ex. m, g)
deci-
d
0.1
1 x 10-1
centimillimicro-
c
m
m
0.01
0.001
0.000 001
1 x 10-2
1 x 10-3
1 x 10-6
nano-
n
0.000 000 001 1 x 10-9
Writing relationships between
units.
 Write down the relationship between meters ,m (base
unit) and kilometers, km.
1. Km are greater than m
2. 1km =
3. 1km= 1000 m
 Relationship between mL and cL?
1. cL is greater than mL
2. 1cL=
3. 1cL = 10mL
Relationship between mm and dm.
1. dm is greater than mm
2. 1dm=
3. 1dm = 100000mm

Learning Check
 Write relationships between the following units:
1. mm and km
2. Mg and dg
3. ks and ms
Learning Check
 Write relationships between the following units:
1. mm and km
1km = 1,000,000 mm
2. Mg and dg
1 Mg= 10,000,000 dg
3. ks and ms
1ks = 1,000, 000 ms
Cw
 Metric units conversions
Dimensional Analysis (factor
labeled method):
 Always write every measurement with its number and
with its associated unit
 Always include units in your calculations
 you can do the same kind of operations on units as
you can with numbers
 cm × cm = cm2
 cm + cm = cm
 cm ÷ cm = 1
 using units as a guide to problem solving is called
dimensional analysis
Problem Solving and Dimensional Analysis
 Many problems in Chemistry involve using relationships
to convert one unit of measurement to another
 Conversion Factors are ratios between two units
 May be exact or measured
 Both parts of the conversion factor have the same
number of significant figures
 Conversion factors generated from equivalence
statements
 Ex. 1 inch = 2.54 cm can give
2.54cm
or
1in
1in
2.54cm
Using Dimensional Analysis
1) Write down Given Amount and Unit
2) Write down what you want to Find and Unit
3) Write down needed Conversion Factors or
Equations
Write down equivalence statements for each
relationship
b) Change equivalence statements to Conversion Factors
a)
Dimensional Analysis
4) Plan a Solution for the Problem


order conversions to cancel previous units or
arrange Equation to solve for the variable wanted
5) Apply the Steps in the Plan


check that units cancel properly
multiply terms across the top and divide by each
bottom term
6) Check the Answer to see if its Reasonable

correct size and unit
Ex. 1 How many cm are in 1.32 meters?
equality: 1 m = 100 cm
applicable conversion factors:
______
1m
100 cm
? cm = 1.32 m
or
(
100 cm
______
1m
100 cm
______
1m
)
= 132 cm
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.
Ex. 2 How many meters is 8.72 cm?
equality: 1 m = 100 cm
applicable conversion factors:
______
1m
100 cm
? m = 8.72 cm
or
(
1m
______
100 cm
100 cm
______
1m
)
=
0.0872 m
Again, the units must cancel.
How many kilometers is
15,000 decimeters?
1m = 10 dm
1km=1000m
? km = 15,000 dm
( )(
1m
____
1 km
______
10 dm
1,000 m
)
=
1.5 km
How many seconds is
4.38 days?
? s = 4.38 d
( )(
24 h
____
1d
60
min
_____
1h
)( )
60 s
____
1 min
= 378,432 s
accounting for significant figures,
change this to…
3.78 x 105 s
Learning Check
a) An object has a mass of 0. 125kg. How many grams is
this?
1kg= 1000g
0.125 kg
1000g
1kg
= 125g
b) How many km are in 5.78x108 mm?
1km = 1x106 mm
5.78x10 8mm
1km
1x106 mm
= 578 km
Conversion Factors (units with a
power)

Convert Cubic Inches (in3) into Cubic Centimeters (cm3)
1)
2)
Find Relationship : 1 in = 2.54 cm
Plan a solution
in3
cm3
3) Change Relationship into Conversion
Factors with Starting Units on the Bottom
3
2.543 cm3 16.4 cm3
 2.54 cm 


 
3
3
1 in
1 in 3
 1 in 
Example:
A circle has an area of
2,659 cm2. What is the
area in square meters?
 Write down the given quantity and its units.
Given:
2,659 cm2
 Write down the quantity to find and/or its units.
Find: ? M2
 Collect Needed Conversion Factors:
1 00cm = 1m
Example:
A circle has an area of
2,659 cm2. What is the
area in square meters?
Information
Given: 2,659 cm2
Find: ? m2
Conv. Fact.: 100 cm = 1 m
 Write a Solution Map for converting the units :
cm2
m2
 1m 


 100 cm 
2
Information
Given: 2,659 cm2
Find: ? m2
Conv. Fact.
1 cm = 0.01 m
Sol’n Map:
cm2  m2  1001 mcm 
Example:
A circle has an area of
2,659 cm2. What is the
area in square meters?

2

 Apply the Solution Map:
2
1m
2
2,659 cm 

m
10000 cm 2
2
= 0.2659 m2
• Sig. Figs. & Round:
= 0.2659 m2
The units of the answer, m2, are correct. The magnitude of the answer makes sense since
square centimeters are smaller than square meters.
 Classwork
dimensional analysis handout
Density Relation of Mass & Volume
 two main characteristics of matter
 cannot be used to identify what type of matter
something is
 if you are given a large glass containing 100 g of a clear,
colorless liquid and a small glass containing 25 g of a
clear, colorless liquid - are both liquids the same stuff?
 even though mass and volume are individual
properties - for a given type of matter they are
related to each other!
Density
 Ratio of mass:volume
 Solids = g/cm3
 1 cm3 = 1 mL
 Liquids = g/mL
 Gases = g/L
Mass
Density 
Volume
 Volume of a solid can be determined by water
displacement – Archimedes Principle
 Density : solids > liquids >>> gases
 except ice is less dense than liquid water!
Density
Mass
Density 
Volume
 For equal volumes, denser object has larger mass
 For equal masses, denser object has smaller
volume
 Heating objects causes objects to expand
 does not effect their mass!!
 How would heating an object effect its density?
 In a heterogeneous mixture, the denser object
sinks
 Why do hot air balloons rise?
Platinum has become a popular metal for fine jewelry. A
man gives a woman an engagement ring and tells her that
it is made of platinum. Noting that the ring felt a little
light, the woman decides to perform a test to determine
the ring’s density before giving him an answer about
marriage. She places the ring on a balance and finds it has
a mass of 5.84 grams. She then finds that the ring
displaces 0.556 cm3 of water. Is the ring made of
platinum? (Density Pt = 21.4 g/cm3)
She places the ring on a balance and finds it has a mass of 5.84
grams. She then finds that the ring displaces 0.556 cm3 of
water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3)
Given: Mass = 5.84 grams
Volume = 0.556 cm3
m
D
V
5.84 g
0.556 cm
3
g
 10.5
cm
3
Since 10.5 g/cm3  21.4 g/cm3 the ring cannot be platinum
Density as a Conversion Factor
 can use density as a conversion factor between mass and
volume!!
 density of H2O = 1 g/mL \ 1 g H2O = 1 mL H2O
 density of Pb = 11.3 g/cm3 \ 11.3 g Pb = 1 cm3 Pb
 How much does 4.0 cm3 of Lead weigh?
4.0 cm3 Pb x
11.3 g Pb
1 cm3 Pb
= 45 g Pb
Measurement and Problem Solving
Density as a Conversion Factor
 The gasoline in an automobile gas tank has a mass of 60.0 kg
and a density of 0.752 g/cm3. What is the volume?
 Given: 60.0 kg
 Find: Volume in L
 Conversion Factors:
 0.752 grams/cm3
 1000 grams = 1 kg
Measurement and Problem Solving
Density as a Conversion Factor
 Solution Map:
kg  g  cm3
1000 g 1 cm3
60.0 kg 

 7.98 10 4 cm3
1 kg 0.752 g
 Classwork: Density handout