Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 10, Problem 10.60QA
Interpretation Introduction

To find:

The effect of the following conditions on the pressure of gas:

a) The absolute temperature is halved, and the volume is doubled.

b) Both the absolute temperature and the volume are doubled.

c) The absolute temperature is increased by 75 %, and the volume is decreased by 50 %.

Expert Solution & Answer
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Answer to Problem 10.60QA

Solution:

a) When the absolute temperature is halved and the volume is doubled, the pressure would be (1/4)th of the initial pressure

b) When both the absolute temperature and the volume are doubled, there would be no change in the pressure.

c) When the absolute temperature is increased by 75 % and the volume is decreased by 50 %, the pressure would increase 3.5 times the initial pressure.

Explanation of Solution

1) Concept:

To find the change in the pressure of a gas, we have to apply the combined gas law for the given three conditions. We have to plug the values for final temperatures and volumes as described in the condition to get a value of the final pressure.

2)  Formula:

The combined gas law

P1V1T1=P2V2T2

3)  Given:

i) Absolute temperature T2=12 T1 and volume V2=2 V1

ii) Absolute temperature T2=2 T1 and volume V2=2 V1

iii) 75 % increase in absolute temperature and 50 % decrease in volume.

4)  Calculations:

a) The absolute temperature is halved and the volume doubled.

P1V1T1=P2V2T2

Putting T2=12 T1 and V2=2 V1

P1V1T1=P22 V112 T1

P2=14P1

When the absolute temperature is halved and the volume doubled, the pressure would be (1/4)th of the initial pressure.

b) Both the absolute temperature and the volume doubled.

P1V1T1=P2V2T2

Putting T2=2 T1 and V2=2 V1

P1V1T1=P22 V12 T1

P2=P1

If both the absolute temperature and the volume are doubled, there would be no change in pressure.

c) The absolute temperature increased by 75 % and the volume decreased by 50 %.

T2=T1+0.75 T1=1.75 T1

V2=V1-0.50 V1=0.50 V1

Applying the combined gas law

P1V1T1=P2V2T2

Inserting T2=1.75 T1 and V2=0.50 V1

P1V1T1=P2×0.50 V11.75 T1

P2=1.750.50 P1

P2=3.5 P1

When the absolute temperature is increased by 75 % and the volume is decreased by 50 %, the pressure would increase 3.5 times the initial pressure.

Conclusion:

Applying the combined gas law, we have estimated the change in pressure for all the three conditions.

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Chapter 10 Solutions

Chemistry: An Atoms-Focused Approach

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