Chapter 13.3, Problem 48SSC

Interpretation Introduction

Interpretation:

The value of temperature and pressure needs to be determined on increasing number of moles but keeping the volume fixed.

Concept introduction:

To answer this question, the basic of gas laws can be used:

Answer to Problem 48SSC

• By doubling the pressure, keeping the temperature fix can solve the purpose.
• This can be done by decreasing temperature to half and keeping pressure fixed.
• This can also be done by decreasing the temperature and increasing the pressure both at a time in various manners.

Explanation of Solution

Ideal gas equation helps to solve this.

According to ideal gas equation:

$\mathrm{PV}=nRT$

Or

$\begin{array}{l}\frac{P_1{V}_1}{n_1{T}_1}=\frac{P_2{V}_2}{n_2{T}_2}\end{array}$

$\begin{array}{l}\therefore \frac{n_2}{n_1}=\frac{P_2{V}_2{T}_1}{T_2{P}_1{V}_1}\\ \&\frac{n_2}{n_1}=\frac{P_2{T}_1}{T_2{P}_1}(\because {\text{V}}_1={\text{V}}_2)\end{array}$

This equation shows -to increase number of moles keeping volume fixed, pressure has to be increased and temperature has to be decreased.

Conclusion

Decreasing the temperature of gas and increasing the pressure of will help to fit $2molofgas\mathrm{int}o22.4Lcontainer$