DIMENSIONAL ANALYSIS
Problem solving using equalities
How many Japanese yen can you get for $5.00?
An EQUALITY STATEMENT between yen and dollars is needed
$1.00 = ¥131
An equality statement can be written as a fraction called a CONVERSION
FACTOR
$1.00
_______
¥131
or
¥131
1B-1 (of 24)
_______
$1.00
$5.00 x
¥131
________
$1.00
=
¥655
How many British pounds can you get for $5.00?
£1.00 = $1.80
£1.00
_______
$1.80
1B-2
$1.80
or
_______
£1.00
$5.00 x
£1.00
________
$1.80
=
£2.78
How many Japanese yen can you get for 5.00 British pounds?
Equality statement between ¥ and £?
No
£1.00 = $1.80
$1.00 = ¥131
£5.00 x
$1.80
________
£1.00
1B-3
x
¥131
________
$1.00
=
¥1,179
How many miles are in 1,000,000. inches?
1 ft = 12 in
1 mi = 5,280 ft
1,000,000. in
x
1 ft
_______
12 in
1B-4
x
1 mi
__________
5,280 ft
=
15.78283 mi
How many seconds are in 1.0000 year?
1B-5
How many cubic yards of air are in 18 cubic feet of air?
1 yd = 3 ft
(1 yd)3 = (3 ft)3
18 ft3 x (1 yd)3
________
(3 ft)3
18 ft3 x
1 yd3
________
27 ft3
1B-6
=
0.67 yd3
Convert 35 mi/h into ft/min
1 mi = 5,280 ft
1 h = 60 min
35 mi
________
h
1B-7
x
5,280 ft x
1h
__________
_________
1 mi
60 min
=
3,080 ft/min
=
3,100 ft/min
TEMPERATURE SCALES
TEMPERATURE – A property of a system based upon the average energy of
the particles making up the system
Solid – vibrational energy of the atoms or molecules
Liquid or Gas – vibrational, rotational, and translational energy of the
atoms or molecules
1B-8
Two common temperature scales are the Fahrenheit and Celsius scales
← Boiling point of water
← Room Temperature
← Freezing point of water
1B-9
y = mx
+ b
ºF = mºC + b
m =
212 - 32
= 9
100 - 0
5
__________
32 = __
9 (0) + b
5
32 = b
ºF = __
9 ºC + 32
5
1B-10
___
What is the Celsius temperature when it is 90ºF?
ºF = __
9 ºC + 32
5
ºF - 32 = __
9 ºC
5
5
__ (ºF - 32) = ºC
9
5
__ (90 - 32) = 32ºC
9
1B-11
Scientists believe there is a lowest possible temperature : -273ºC
ABSOLUTE SCALE – A scale with 0 as its lowest possible value
The Kelvin scale is an absolute scale
K = ºC + 273
← Boiling point of water
← Freezing point of water
← Absolute Zero
1B-12
METRIC CONVERSIONS
METRIC PREFIXES
Prefix
mega
kilo
BASE UNIT
deci
centi
milli
micro
nano
1B-13
Symbol
M
k
d
c
m
μ
n
Base Unit Multiplying Factor
106
103
100
10-1
10-2
10-3
10-6
10-9
How many kilometers are 525 meters?
1 km = 103 m
103 m
1 km
_______
103 m
1B-14
or
_______
1 km
525 m x
1 km
________
103 m
=
0.525 m
How many centigrams are 8.93 grams?
1 cg = 10-2 g
8.93 g
x
1 cg
________
=
893 g
10-2 g
How many liters are 25.0 milliliters?
1B-15
How many kilograms are 150 decigrams?
Equality statement between kg and dg?
No
1 dg = 10-1 g
1 kg = 103 g
150 dg x
10-1 g
________
1 dg
1B-16
x
1 kg
________
103 g
=
0.015 kg
How many micrometers are 0.37 centimeters?
1B-17
Convert 22.5 mL/s into L/min
1 mL = 10-3 L
1 min = 60 s
22.5 mL x 10-3 L
___________
________
s
1 mL
1B-18
x
60 s
________
1 min
=
1.35 L/min
THE PROPERTY OF DENSITY
DENSITY – Mass per unit volume
D = m
___
V
Material
Lead
Water
Cork
Air
Helium
1B-19
Density
11.34
1.00
0.24
0.0013
g/mL
g/mL
g/mL
g/mL
0.0001 g/mL
What is the density of a solid in which 2.20 g occupies 1.50 mL?
D = m
___
V
1B-20
=
2.20 g
__________
1.50 mL
=
1.47 g/mL
What is the mass of 12.0 mL of a solid if it has a density of 3.50 g/mL?
D = m
____
V
VD = m
1B-21
=
(12.0 mL)(3.50 g/mL)
=
42.0 g
What volume does 6.2 g of a liquid occupy if its density is 1.4 g/mL?
D = m
____
V
VD = m
V = m
____
D
1B-22
=
6.2 g
____________
1.4 g/mL
=
4.4 mL
REVIEW FOR TEST
Identify laboratory equipment
Location of safety equipment
Accuracy of graduated glassware
Safety procedures
Scientific notation
Reading graduated equipment
Significant figures
Operations with significant figures
1B-23
REVIEW FOR TEST
Metric prefixes
Dimensional analysis
Know metric and time equalities
Temperature scales
Know equalities between them
Denisty
Solve for D, m, or V
1B-24