Chapter 5.3, Problem 5.2P

Interpretation Introduction

Interpretation: The constant volume of the oxygen gas ${\text{O}}_{\text{2}}$ is heated from ${120}^{\circ }\text{C}$ to ${212}^{\circ }\mathrm{C}$ . The initial pressure should be calculated if the final pressure is $20.3\text{ atm}$ .

Concept Introduction: The initial pressure of the gas at the varying temperatures can be calculated using Gay-Lussac’s law, which states the relationship between pressure and temperature of the gas

According to Gay-Lussac’s Law, for the gas held at constant volume, the pressure of a given amount of gas is directly proportional to the temperature of the gas. Mathematically, it is given as

  $P\propto T$

  $\frac{P}{T}=\text{constant}=k$

We consider two different sets of temperature and pressure of the gas, the above equation becomes as follows:

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

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