Calculate the Pressure

Question

Calculate the pressure (in atm) of a 6.70 mol sample of methane gas at 350.0 K in a 1.50 L container using the van der Waals equation. For methane, a = 2.25 L²･atm/mol² and b = 0.0428 L/mol.

Answer 1

The van der Walls equation is

(P + an² / V²)(V - nb) = nRT

Solving for P, we have...

P = nRT / V - nb - n²a / V²

P = pressure = ?

V = volume in liters = 1.50 L

n = moles = 6.70 mols

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 350.0K

a = 2.25 L²atm/mol2

b = 0.0428 L/mol

P = (6.70)(0.0821)(350) / 1.50 - (6.70)(0.0428 ) - (6.70)²(2.25) / (1.50)²

P = 192.5 / 1.21 - 44.89

P = 159.1 - 44.9

P = 114.2 atm (be sure to check all the math for possible errors)

Let's compare this to the volume if it were treated as an ideal gas:

PV = nRT

P = nRT / V = (6.70)(0.0821)(350) / 1.50

P = 128.3 atm This represents a 12% difference compared to the above calculation