Question

A gas at constant volume of 5.00 L is cooled from 191 degrees C to -56.0 degrees C. The initial pressure is 825 mm Hg. Predict the new pressure.

Answer 1

Apply ideal gas equation -

PV =nRT

P = pressure

V = volume

n = number of moles

R = real gas constant

T = temperature in kelvin

Initial state -

Volume (V₁) = 5.00L

Temperature (T₁) = 191^oC or 191 + 273.15 = 464.15K ( 0^o C = 273K)

n = n₁

P = P₁ = 825mm Hg (given)

Apply PV =nRT

825*V₁ = n₁R*464.15 ------ equation 1

Final state -

P = P₂ ( to find)

V = V₂ = V₁ ( volume is constant)

n = n₂ = n₁ ( number of moles have not changed as there is no change in quantity of gas)

T = -56^o C or -56 + 273.15 = 217.15K

Apply PV =nRT

P₂V₁ =n₁R*217.15 --------equation 2

Diviinge equation 2 by equation 1 we get -

P₂/825 = 217.15/464.15

P₂ = 385.97 mm Hg