Chapter 5, Problem 5.24P

Interpretation Introduction

Interpretation:

Given that the sample of ${\text{B}}_{\text{2}}{\text{H}}_{\text{6}}$ gas in a $\text{35 mL}$ container is at a pressure of $450.\text{0 mm Hg}$ and a temperature of $62{\text{5 }}^{\text{o}}\text{C}$. The new temperature in ${}^{\text{o}}\text{C}$ if the gas is allowed to cool at a constant volume until the pressure is $\text{375 mm Hg}$ should be calculated.

Concept Introduction:

The final volume of the gas at the varying pressure 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.

$P\propto T$.

$\frac{P}{T}=const\text{a}nt=k$.

We two different sets of temperature and pressure of the gas is considered, 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.