Question

Use the van der Waals equation of state to calculate the pressure of 2.10 mol of CH4 at 473 K in a 4.90 L vessel. Use this list of van der Waals constants. P= Use the ideal gas equation to calculate the pressure under the same conditions. p=

Answer 1

We know that

van der Waals equation is

( P + n²a/V²) (V-nb) = nRT

by simplifying for P we get

P = ( nRT /(V-nb) ) - (n²a/V²)

where

n = 2.10 mol

R = 0.083 bar.L./mol.K

T = 473 K

V = 4.90 L

a = 2.300 bar.L²/mol²

b = 0.04301 L/mol

So by using above values lets calculate P

P = ( nRT /(V-nb) ) - (n²a/V²)

P = ( 2.10 mol $\times$  0.083 bar.L./mol.K $\times$ 473 K / ( 4.90 L - 2.10 mol $\times$ 0.04301 L/mol)) - ( (2.10 mol)²$\times$ 2.300 bar.L²/mol² / (4.90)²)

= 16.72 bar

So by using van der Waals equation

Pressure = 16.72 bar

Now we know the ideal gas equation

PV = nRT

then

P = nRT / V

lets put the given values in above formula , we get

P = 2.10 mol $\times$ 0.083 bar.L./mol.K $\times$ 473 K / 4.90 L

= 16.82 bar

so by using ideal gas equation

Pressure P = 16.82 bar