Question

Use the van der Waals equation of state to calculate the pressure of 4.00 mol of Xe at 483 K in a 4.20-L vessel. Van der Waals constants can be found here.

Use the ideal gas equation to calculate the pressure under the same conditions.

Answer #1

Given that

no of moles n = 4.0 mol

volume V = 4.2 L

temperature T = 483 K

Van der walls constants for Xe a = 4.192 L^{2}.
atm/mol^{2} , b = 0.05156 L/mol

R = 0.0821 L.atm/K/mol

Pressure of Xe using Van der walls equation :

Van der walls equation is

(P + an^{2}/V^{2}) (V-nb) = nRT

P = [ nRT / (V -nb)] - [an^{2}/V^{2]}

= [(4)(0.0821)(483) / (4.2 - 4 x 0.05156)] - [ 4.192 x
4^{2} / 4.2^{2}]

= 35.91 atm

Pressure of Xe = 35.91 atm

Pressure of Xe using Ideal gas equation :

PV = n RT

P = nRT/V

= 4 x 0.0821 x 483/ 4.2

= 37.76 atm

Pressure of Xe = 37.76 atm

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