Chapter 14, Problem 48R

To determine

The final volume of the gas.

Answer to Problem 48R

The final volume of the gas is $18.32\text{L}$ .

Explanation of Solution

Given info:

Initial volume of the gas, $V_1=25\text{L}$

Initial pressure of the gas, $P_1=200\text{kPa}$

Initial temperature of the gas, $T_1=25°\text{C}=\left(25°\text{C}+273\right)\text{K}=298\text{K}$

Final pressure of the gas, $P_2=250\text{kPa}$

Final temperature of the gas, $T_2=0°\text{C}=\left(0°\text{C}+273\right)\text{K}=273\text{K}$

Formula Used:

Write the expression to calculate the final volume of the gas.

  $V_2=\frac{P_1\cdot V_1\cdot T_2}{P_2\cdot T_1}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_2=\frac{\left(200\text{kPa}\right)\left(25\text{L}\right)\left(273\text{K}\right)}{\left(250\text{kPa}\right)\left(298\text{K}\right)}\\ =18.32\text{L}\end{array}$

Conclusion:

Thus, the final volume of the gas is $18.32\text{L}$ .