Question

A 1.0 L container holds a sample of hydrogen gas at 300 K and 101.5 k Pa. If the pressure increases to 508 k Pa and the volume remains constant, what will the temperature be?

Answer 1

Answer: The temperature will be 1501.47 K.

Explanation:

To calculate the temperature of the gas when pressure is increased, we use the equation given by Gay-Lussac's Law.

This law states that pressure is directly proportional to the temperature of the gas at constant volume and number of moles.

Mathematically,

$P\propto T$

or,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where,

$P_1\text{ and }T_1$ are the initial pressure and initial temperature of the gas.

$P_2\text{ and }T_2$ are the final pressure and final temperature of the gas.

We are given:

$P_1=101.5kPa\\T_1=300K\\P_2=508kPa\\T_2=?K$

Putting values in above equation, we get:

$\frac{101.5kPa}{300K}=\frac{508kPa}{T_2}\\\\T_2=1501.47K$

Hence, the temperature will be 1501.47 K