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

Step-by-step 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,

`(P_1)/(T_1)=(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:

`(685)/(285)=(P_2)/(328)\\\\P_2=788`

Hence, the new pressure will be 788 torr