Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1, Problem 3KSP

Determine the density of the following object in g/c m 3 . A cube with edge length = 0 .750 m and mass = 14 .56 kg .

( a ) 0 .0345 g/cm 3 (b) 1 .74 g/cm 3 (c) 670 g/cm 3 (d) 53 .8 g/cm 3 (e) 14 .6 g/cm 3

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The density of agiven object in gram per cubic centimeter ( g/cm3)is to be determined.

Concept introduction:

The formula for the volume (V) of a cube with edge (l) is shown below:

V=l3

The relationship between density, volume, and mass is as follows:

d=mV

Here, d is the density, V is the volume, and m is the mass of the given sample.

Conversion factors are used to convert units of measurement of the same quantity without changing its value.

Conversion factors are derived from the unity bracket method of unit conversion, which consists of a fraction derived from the equality. The units of the denominator and the numerator are different.

The use of a conversion factor to solve numerical problems is called dimensional analysis.

Answer to Problem 3KSP

Option (a).

Explanation of Solution

Given information:

Thelength of the edge of the cube is l=0.750 m and the mass of the cube is m=14.56 kg.

The volume of the cube is given by the expression given below:

V=l3

Substitute the value of the length of the edge of the cube in the above expression as shown below:

V=(0.750 m)3=0.42 m3

The relation between meter (m) and centimeter (cm) is as follows:

1 m=102 cm

Thus, the conversion factor to obtain volume in (cm) from (m) is (102cm1 m). Takingitscube, the conversion factor now becomes (106cm31 m3).

Multiply the conversion factor with 0.42 m3 and cancel the units to get the expression:

0.42 m3×(106cm31 m3)=0.42×106 cm3

The calculated volume of the givencube is 0.42×106 cm3.

The relation between grams (g) and kilograms (kg) is expressed as follows:

1 kg=103 g

Thus, the conversion factor to obtain mass in (g) from (kg) is (103 g1 kg).

Multiply the conversion factor with 14.56 kg (mass of the cube) and cancel the units to get the expression:

14.56 kg×(103g1 kg)=14.56×103 g

The converted mass of thegiven cube is 14.56×103 g.

The relationship between density, volume, and mass is as follows:

d=mV

Substitute 14.56×103 g for m and 0.42×106 cm3 for V in the above expression

d=(14.56×103 g0.42×106 cm3)=0.0345 g/cm3

So, the density is 0.0345 g/cm3.

Hence, option (a) is correct.

Reasons for incorrect options:

Option (b) is incorrect because, according to the above calculation, the value 1.74 g/cm3 is not obtained. So, it is a wrong answer.

Option (c) is incorrect because, according to the above calculation, the value 670 g/cm3 is not obtained. So, it is a wrong answer.

Option (d) is incorrect because, according to the above calculation, the value 53.8 g/cm3 is not obtained. So, it is a wrong answer.

Option (e) is incorrect because, according to the above calculation, the value 14.6 g/cm3 is not obtained. So, it is a wrong answer.

Hence, options (b), (c), (d), and (e) are incorrect.

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Chapter 1 Solutions

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