Chapter 5, Problem 5.18P

Interpretation Introduction

Interpretation:

Given that the methane gas is compressed from $20.\text{0 L}$ to $2.\text{5 L}$ at constant temperature. The initial pressure of the gas should be calculated if the final pressure is $12.\text{2 atm}$.

Concept Introduction:

The initial pressure of the gas at the constant temperature can be calculated using Boyle’s law, which states the relationship between pressure and volume of the gas.

According to Boyle’s Law, the volume of fixed amount of gas is inversely proportional to the pressure of the gas at constant temperature. Mathematically, it is given as.

$V\propto \frac{1}{P}$.

$PV=\text{constant}=k$.

We two different sets of volume and pressure of the gas is considered, the above equation becomes as follows:

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

where $P_1$ and $V_1$ are initial pressure and temperature of the gas, while $P_2$ and $V_2$ are final pressure and temperature of the gas.