Sample Solution from
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Chapter 1
Problem 1A.1ST
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Interpretation Introduction

Interpretation: The temperature that would result in the same given sample exerting a pressure of 300 atm has to be stated.

Concept introduction: The perfect gas equation of state is consistent with Boyle’s law, Charles’s law and also with Avogadro’s law.  The perfect gas law is also known as ideal gas equation.  The expression that is used to show the perfect gas equation of state is given as,

    pV=nRT

Expert Solution

Answer

The temperature that would result in the same given sample exerting a pressure of 300 atm is 900 K_.

Explanation of Solution

It is given that the sample of nitrogen gas has constant volume.

The given initial pressure of the sample (p1) is 100 atm.

The given final pressure of the sample (p2) is 300 atm.

The given initial temperature of the sample (T1) is 300 K.

The perfect gas equation that is used for the two sets of values for the given sample of nitrogen is given as,

    p1V1n1T1=p2V2n2T2        (1)

Where,

  • p1 is the initial pressure of the gas.
  • p2 is the final pressure of the gas.
  • V1 is the initial volume of the gas.
  • V2 is the final volume of the gas.
  • T1 is the initial temperature of the gas.
  • T2 is the final temperature of the gas.
  • n1 is the initial number of moles of the gas.
  • n2 is the final number of moles of the gas.

As the given sample of nitrogen gas behaves as the perfect gas, thus, the initial and final number of moles of the gas is same.

Therefore, for given sample of nitrogen gas V1=V2 and n1=n2.  Hence, the equation (1) becomes,

    p1T1=p2T2        (2)

The rearranged equation to calculate the final temperature of the given sample is given below.

    T2=p2×T1p1        (3)

Substitute the values of initial pressure, final pressure and initial temperature in equation (3).

    T2=300 atm×300 K100 K=900 K_

Thus, the final temperature for the given sample of nitrogen gas is 900 K_.

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