Question

A sample of ideal gas is in a sealed container. The pressure of the gas is 685 torr , and the temperature is 12 ∘C . If the temperature changes to 55 ∘C with no change in volume or amount of gas, what is the new pressure, P2, of the gas inside the container?Express your answer with the appropriate units.

Answer 1

Answer: 788 torr

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:

$P_1=685torr\\T_1=12^0C=(12+273)=285K\\P_2=?=27.5psi\\T_2=55^0C=(55+273)K=328K$

Putting values in above equation, we get:

$\frac{685}{285}=\frac{P_2}{328}\\\\P_2=788$

Hence, the new pressure will be 788 torr