Chapter 5.3, Problem 5.3QC

Interpretation Introduction

Interpretation: A gas is expanded from an initial volume of $20.5\text{ L}$ at $0.92\text{ atm}$ at room temperature ( ${23}^{\circ }\text{C}$ ) to a final volume of $340.6\text{ L}$ . During the expansion, the gas cools to ${12}^{\circ }\text{C}$ . The final pressure should be calculated.

Concept Introduction: The final pressure of the gas at the varying temperature and varying volumes can be calculated using combined gas law, which states the relationship between pressure, volume and temperature of the gas

In combined gas law, the three laws of the gas are combined. Mathematically, it is given as

  $\frac{PV}{T}=constant=k$

Two different sets of temperature and pressure of the gas is considered, the above equation becomes as follows:

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

Where $P_1$ , $V_1$ and $T_1$ are initial pressure, volume and temperature of the gas, while $P_2$ , $V_2$ and $T_2$ are final pressure, volume and temperature of the gas.