A sample of gas is in a 5 Liter rigid tank. If the gas has a pressure of 108 Kpa at 20.0 oC, what will be the new temperature at 2.50 atm?

Is it 46.9 K
Is it 413 K
Is it 686 K
Is it -148 K
Is it 125 K

T₂  = 687.6 K

Explanation:

Given data:

Initial pressure = 108 Kpa

Initial temperature = 20°C

Final temperature = ?

Final pressure = 2.50 atm

Solution:

Initial pressure = 108 Kpa = 108/101 = 1.06588 atm

Initial temperature = 20°C = 20+273.15 = 293.15 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:

1.06588 atm / 293.15 K = 2.5 atm/T₂

T₂  = 2.5  atm ×293.15 K / 1.06588 atm

T₂  = 732.875 atm. K /1.06588 atm

T₂  = 687.6 K