Question

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?

Answer 1

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

Answer 2

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