Question

Part A A sample of ideal gas is in a sealed container. The pressure of the gas is 725 torr , and the temperature is 18 ∘C . If the temperature changes to 75 ∘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.

Part B Using the same sample of gas (P1 = 725 torr , T1 = 18 ∘C ), we wish to change the pressure to 7250 torr with no accompanying change in volume or amount of gas. What temperature T2, in Celsius, is needed to reach this pressure? Express your answer with the appropriate units.

Answer 1

According to Gay-Lussac’s law, the pressure of a gas is directly related to the temperature when volume and the number of moles remain constant.

P1 = 725 torr, T1 = 18 ⁰C = (18 + 273) K = 291 K

P2 = ? T2 = 75 ⁰C = (75 + 273) K = 348 K

Now, P2/T2 = P1/T1

P2 = (P1/T1) x T2 = (725 torr) x (348 K) / (291 K) = 867.01 torr

PART B

P1 = 725 torr, T1 = 18 ⁰C = (18 + 273) K = 291 K

P2 = 7250 torr, T2 = ?

So,

Now, P2/T2 = P1/T1

T2 = (P2/P1) x T1 = (7250 torr) x (291 K) / (725 torr) = 2910 K = 2637 ⁰C.