Using the same sample of gas (P1 = 565 torr , T1 = 27 ∘C ), we wish to change the pressure to 5650 torr with no accompanying change in volume or amount of gas. What temperature T2, in Celsius, is needed to reach this pressure?

2726.85 °C

Explanation:

Given data:

Initial pressure = 565 torr

Initial temperature = 27°C

Final temperature = ?

Final pressure = 5650 torr

Solution:

Initial temperature = 27°C (27+273 = 300 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:

T₂  = P₂T₁ /P₁

T₂  = 5650 torr × 300 K / 565 torr

T₂  = 1695000 torr. K /565 torr

T₂ = 3000 K

Kelvin to degree Celsius:

3000 K - 273.15 = 2726.85 °C