A sample of ammonia gas at 65.5°c and 524 torr has a volume of 15.31 l. what is its volume when the temperature is - 15.8°c and its pressure is 524 torr?

This problem is being solved using Ideal Gas Equation.

PV = nRT

Data Given:

Initial Temperature = T₁ = 65.5 °C = 338.5 K

Initial Pressure = P₁ = 524 torr

Initial Volume = V₁ = 15.31 L

Final Temperature = T₂ = - 15.8 °C = 257.2 K

Final Pressure = P₂ = 524 torr

Final Volume = V₂ = ?

As,

Gas constant R and Pressures are constant, so, Ideal gas equation can be written as,

V₁ / T₁ = V₂ / T₂

Solving for V₂,

V₂ = (V₁ * T₂) : T₁

Putting Values,

V₂ = (15.31 L * 257.2 K) : 338.5 K

V₂ = 11.63 L

According to gases formula:

P1V1/T1 = P2V2/T2

when P1 is the initial pressure = 524 torr

V1 is the initial volume = 15.31 L

T1 is the initial temperature = 65.5 + 273 = 338.5

P2 is the final pressure = 524 torr

T2 is the final temperature = - 15.8 + 273 = 257.2

by substitution:

524*15.31 / 338.5 = 524*V2/257.2

∴ V2 = 6095.6 / 524

= 11.6 L

∴ the final Volume = 11.6