Question

Assume that you have 0.480 mol of N2 in a volume of 0.700 L at 300 K .

1)Calculate the pressure in atmospheres using the ideal gas law.

2)Calculate the pressure in atmospheres using the van der Waals equation. For N2 , a=1.35 (L2⋅atm)/mol2 , and b=0.0387 L/mol .        

Answer 1

1) Use the ideal gas law:

PV = nRT where P = pressure in atmospheres, V = volume in L, n = number of moles and T = temperature in the absolute scale.

Given V = 0.700 L, n = 0.480 mol and T = 300 K, plug in the values in the expression to obtain

P.(0.700 L) = (0.480 mol)*(0.082 L-atm/mol.K)*(300 K)

====> P = (0.480 mol)*(0.082 L-atm/mol.K)*(300 K)/(0.700 L) = 16.868 atm ≈ 16.87 atm (ans).

2) The Vander Waal’s equation is

(P + n²a/V²)(V – nb) = nRT where a and b are Vander Waal’s constants. Given a = 1.35 L²-atm/mol² and b = 0.0387 L/mol, we have

P = nRT/(V – nb) – n²a/V²

===> P = [(0.480 mol)*(0.082 L-atm/mol.K)*(300 K)/{0.700 L – (0.480 mol).(0.0387 L/mol)}] – (0.480 mol)²(1.35 L²-atm/mol²)/(0.700 L)²

===> P = (11.808 L-atm)/[0.700 L – 0.018576 L) – (0.31104 L²-atm)/0.49 L²

===> P = (11.808 L-atm)/(0.681424 L) – (0.31104 atm/0.49) = (17.3284 atm) – (0.63477 atm) = 16.69363 atm ≈ 16.694 atm (ans).