Question

Calculate the molar volume, V , for a sample of carbon dioxide at 250 bar and 400 C assuming:

(a) it is an ideal gas.

(b) the carbon dioxide obeys the van der Waals equation of state.

(c) the carbon dioxide behaves like a Redlich-Kwong gas.

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Answer 1

GIVEN:

PRESSUE, P = 250 bar =246.73 atm ; Temperaure, T = (273+400)K = 673 K, R =0.08206 dm³ atm K^-1 mol^-1

(a) Ideal gas equation

V=nRT/P

for one mole of CO₂, n=1

V= RT/P = (0.08206 dm³ atm K^-1 mol^-1 x 673 K)/ 246.73 atm = 0.22 dm³ mol^-1

(b) van der Waals gas equation

(P+n²a/V²)(V-nb) =nRT

For CO_2; a = 3.59 dm⁶ atm mol^-2 and b = 0.0427. For 1 mole of CO₂ gas n=1.

Substituting the values of P, a, b, R and T in van der Waals gas equation, V value can be deterimed.

(c) Redlich-Kwong gas equation

Redlich-Kwong gas constant for CO₂ are; a = 4.620 dm⁶ atm mol^-2 and b = 0.0463.

Substituting the values of P, a, b, R and T in Redlich-Kwong gas equation, V value can be deterimed.