Chapter 10, Problem 6CQ

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A container filled with an ideal gas is connected to a reservoir of the same gas so that the number of moles in the container can change. If the pressure and volume of the container are each doubled while the temperature is held constant, what is the ratio of the final to the initial number of moles in the container?

To determine
The ratio of final ( nf ) and initial number of moles ( ni ).

Explanation

From the Ideal gas equation, the number of moles is,

n=PVRT

• P is the pressure.
• R is the gas constant.
• T is the temperature.
• V is the volume.

At a constant temperature, the number of moles is directly proportional to the product of pressure and volume. Therefore, the ratio of final and initial number of moles is,

nfni=PfVfPiVi Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (I)

• Pi and Pf are the initial and final pressures respectively.
• Vi and Vf are the initial and final volumes respectively

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