Question

A sample of gas in a closed container at a temperature of 76°c and a pressure of 5.0 atm is heated to 399°c. What pressure does the gas exert at the higher temperature?

Answer 1

Answer: The pressure that the gas exert at high temperature is 9.63 atm

Explanation:

To calculate the final pressure of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

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

where,

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

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

We are given:

$P_1=5.0atm\\T_1=76^oC=[76+273]K=349K\\P_2=?\\T_2=399^oC=[273+399]K=672K$

Putting values in above equation, we get:

$\frac{5.0atm}{349K}=\frac{P_2}{672K}\\\\P_2=9.63atm$

Hence, the pressure that the gas exert at high temperature is 9.63 atm