Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
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Chapter 1, Problem 56QP

Carry out the following conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms, (c) 556 mL to liters, (d) 10 .6 kg/m 3 to g/cm 3 .

Expert Solution & Answer
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Interpretation Introduction

Interpretation: The given conversions are to be carried out by dimensional analysis.

Concept introduction:

Dimensional analysis is a way to convert units of measurement. In order to convert from one unit to another, we need to know the relationship between those units. These relationships are called conversion factors. Dimensional analysis is used to set up and solve a unit conversion problem using conversion factors.

The conversion factor is a fraction obtained from a relationship between the units. It is written as a ratio and can be inverted to give two conversion factors for every relationship.

1 m = 10 dm, to convert meter to decimeters, the conversion factor is

10 dm1 m

1 mg = 1×103 g, to convert milligram to gram, the conversion factor is

1×103 g1 mg

1 g = 1×10-3 kg, to convert gram to kilogram, the conversion factor is

1×10-3 kg1 g

1 kg = 1000 g, to convert kilogram to gram, the conversion factor is

1000 g1 kg

1  mL = 1×10-3 L, to convert milliliters to liters, the conversion factor is

1×10-3 L1 mL

1 m = 100 cm, to convert m to centimeter, the conversion factor is

100 cm1 m

Answer to Problem 56QP

Solution:

a)

226 dm

b)

2.54×105 kg

c)

0.556 L

d)

0.0106 g/cm3

Explanation of Solution

a) 22.6 m to decimeters.

Convert the quantity 22.6 m to decimeters.

The conversion factors for the relationship 1 m = 10 dm are as follows:

1 m10 dm or 10 dm1 m

Now, set up the unit conversion problem using the appropriate conversion factor.

22.6 m × 10 dmm= 226 dm

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence, 22.6 m = 226 dm.

b) 25.4 mg to kilograms.

Convert the quantity 25.4 mg to kilograms.

The conversion factors for the relationship 1 mg = 1×103 g are as follows:

1 mg1×103 g or 1×103 g1 mg

The conversion factors for the relationship 1 g = 1×10-3 kg are as follows:

1 g1×10-3 kg or 1×10-3 kg1 g

Now, set up the unit conversion problem using the appropriate conversion factors.

(25.4 mg × 1×103 gmg × 1×103 kgg) = 2.54×105 kg

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence,

25.4 mg = 2.54×105 kg.

c) 556 mL to liters.

Convert the quantity 556 mL to liters.

The conversion factors for the relationship 1  mL = 1×10-3 L are as follows:

1 mL1×10-3 L or 1×10-3 L1 mL

Now, set up the unit conversion problem using the appropriate conversion factor.

(556 mL × 1×10-3 LmL) = 0.556 L

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence,

556 mL=0.556 L

d) 10.6 kg/m3 to g/cm3.

Convert the quantity 10.6 kg/m3 to g/cm3.

The conversion factors for the relationship 1 kg = 1000 g are as follows:

1 kg1000 g or 1000 g1 kg

The conversion factors for the relationship 1 m = 100 cm are as follows:

1 m100 cm or 100 cm1 m

Now, set up the unit conversion problem using the appropriate conversion factors.

(10.6 kgm3×1000 gkg×(m100 cm)3)=0.0106 g/cm3

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence,

10.6 kg/m3= 0.0106 g/cm3.

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