A sample of a gas is in a sealed container. The pressure of the gas is 565 torr , and the temperature is 27 ∘C . If the temperature changes to 71 ∘C with no change in volume or amount of gas, what is the new pressure, P2, of the gas inside the container?

P₂ = 647 torr

Explanation:

Given data:

Initial pressure = 565 torr

Initial temperature = 27°C

Final temperature = 71°C

Final pressure = ?

Solution:

Initial temperature = 27°C (27+273 = 300 K)

Final temperature = 71°C (71+273 = 344 K)

According to Gay-Lussac Law,

The pressure of given amount of a gas is directly proportional to its temperature at constant volume and number of moles.

Mathematical relationship:

P₁/T₁ = P₂/T₂

Now we will put the values in formula:

565 torr / 300K = P₂/344 K

P₂ = 565 torr × 344 K / 300 K

P₂ = 194360 torr. K /293 K

P₂ = 647 torr

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