Chapter 20, Problem 82A

Interpretation Introduction

Interpretation:

The new volume of gas after the change in temperature and pressure of the system is to be calculated.

Concept introduction:

According to Boyle’s law, the pressure of a gas of known mass is inversely proportional to its volume at a constant temperature.

According to Charles’ law, the volume of gas at constant pressure is directly proportional to the absolute temperature (Kelvin).

Answer to Problem 82A

The volume of gas will become 8.778 L.

Explanation of Solution

Given information : Initial volume of gas

$V_1=8.2L$

Initial temperature $T_1=306K$

Initial pressure $P_1=1.2atm$

Final temperature $T_2=273K\left(STP\right)$

Final pressure $P_2=1atm\left(STP\right)$

Final volume V₂=?

According to Boyle’s law,

$P_1{V}_1=P_2{V}_2$

According to Charles’ law,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Combining both laws,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Substituting the values,

$\begin{array}{l}\frac{8.2\times 1.2}{306}=\frac{1\times V_2}{273}\\ V_2=\frac{1.2\times 8.2\times 273}{306\times 1}\\ V_2=8.778L\end{array}$

Conclusion

The volume was found to be 8.778L using Boyle’s and Charles’ law.