Transcript CH_1_8_Writing_Conversion_Factors

Chapter 1
Chemistry and Measurements
1
1.8
Writing Conversion Factors
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Equalities
2
Equalities
• use two different units to describe the same measured
amount
• are written for relationships between units of the metric
system, U.S. units, or between metric and U.S. units
For example,
1m
=
1 lb
= 16 oz
2.20 lb =
1000 mm
1 kg
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Exact and Measured Numbers in
Equalities
3
Equalities between units in
• the same system of measurement are definitions that use
exact numbers
• different systems of measurement (metric and U.S.) use
measured numbers that have significant figures
Exception:
The equality 1 in. = 2.54 cm has been defined as an exact
relationship and therefore 2.54 is an exact number.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Some Common Equalities
4
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Equalities on Food Labels
5
The contents of
packaged foods
• in the U.S. are listed
•
in both metric and
U.S. units
indicate the same
amount of a substance
in two different units
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Conversion Factors
6
A conversion factor is
• obtained from an equality and written in the form of a
fraction with a numerator and denominator
Equality: 1 in. = 2.54 cm
• inverted to give two conversion factors for every equality
1 in.
2.54 cm
and
2.54 cm
1 in.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
7
Write conversion factors from the equality for each of the
following:
A. L and mL
B. hours and minutes
C. meters and kilometers
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
8
Write conversion factors from the equality for each of the
following:
A. 1 L = 1000 mL
1L
and 1000 mL
1000 mL
1L
B. 1 h = 60 min
1h
and
60 min
60 min
1h
C. 1 km = 1000 m
1 km
1000 m
1000 m
1 km
and
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Conversion Factors in a Problem
9
A conversion factor
• may be obtained from information in a word problem
• is written for that problem only
Example 1:
The price of one pound (1 lb) of red peppers is $2.39.
1 lb red peppers
and
$2.39
$2.39
1 lb red peppers
Example 2:
The cost of one gallon (1 gal) of gas is $2.89.
1 gal gas
$2.89
and
$2.89
1 gal gas
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Percent as a Conversion Factor
10
A percent factor
gives the ratio of the parts to the whole
% = parts x 100
whole
• uses the same unit in the numerator and denominator
• uses the value of 100
• can be written as two factors
Example: A food contains 30% (by mass) fat:
30 g fat
and
100 g food
100 g food
30 g fat
•
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Percent Factor in a Problem
11
The thickness of the skin fold at
the waist indicates 11% body
fat. What factors can be written
for percent body fat (in kg)?
Percent factors using kg:
11 kg fat and
100 kg mass
100 kg mass
11 kg fat
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Smaller Percents: ppm and ppb
12
Small percents are given as ppm and ppb.
•
•
Parts per million (ppm) =
mg part
kg whole
Example: The EPA allows 15 ppm cadmium in food colors.
15 mg of cadmium = 1 kg of food color
Parts per billion (ppb) = μg part
kg whole
Example: The EPA allows 10 ppb arsenic in public water.
10 μg of arsenic = 1 kg of water
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
13
Write the conversion factors for 10 ppb arsenic in public
water from the equality.
10 μg of arsenic = 1 kg of water
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
14
Write the conversion factors for 10 ppb arsenic in public
water from the equality.
10 μg of arsenic = 1 kg of water
Conversion Factors
10 μg arsenic
1 kg water
and
1 kg water
10 μg arsenic
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Study Tip: Conversion Factors
15
An equality
• is written as a fraction (ratio)
• provides two conversion factors that are the inverse of
each other
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
16
Write the equality and conversion factors for each of the
following.
A. meters and centimeters
B. jewelry that contains 18% gold
C. one gallon of gas is $3.40
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
17
A. meters and centimeters:
1 m = 100 cm
1m
and 100 cm
100 cm
1m
B. jewelry that contains
18% gold: 100 g of jewelry = 18 g of gold
18 g gold and 100 g jewelry
100 g jewelry
18 g gold
C. one gallon of gas is $3.40: 1 gal gas = $3.40
1 gal gas and
$3.40
$3.40
1 gal gas
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Risk-Benefit Assessment
18
A measurement of toxicity is
•
LD50 or “lethal dose”
•
the concentration of the substance that causes death
in 50% of the test animals
•
in milligrams per kilogram (mg/kg or ppm) of body mass
•
in micrograms per kilogram (g/kg or ppb) of body mass
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
19
The LD50 for aspirin is 1100 ppm. How many grams of
aspirin would be lethal in 50% of persons with a body
mass of 85 kg?
A. 9.4 g
B. 94 g
C. 94 000 g
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
20
The LD50 for aspirin is 1100 ppm. How many grams of
aspirin would be lethal in 50% of persons with a body
mass of 85 kg?
85 kg x 1100 mg
1 kg
x
1g
1000 mg
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
= 94 g of aspirin
Copyright © 2012 by Pearson Education, Inc.