Question

For ethane, P_c = 48.2 atm and Tc = 305.4 K. Calculate the pressure exerted by 50.0 g of C₂H₆ in a 200-cm³ vessel at 37.5°C using (a) the ideal-gas law; (b) the van der Waals equation. R= 82.06 cm³.atm/mol.K, T(K)=T(°C)+273.1.

(a) P = ? atm

(b) P = ? atm

Answer 1

a) Ideal gas law:

PV=nRT=m/M*RT

M(ethane)=30 g/mol

P=m/MV*RT

P=50.0 g * 82.06 * (37.5+273.1) / (30 g/mol * 200 ml) = 212.4 atm

b) van der Waals equation:

(P+n²a/V²)(V-nb)=nRT

n-moles

n=m/M = 50 g / 30 g/mol = 1.67 mol

a-is a measure of the average attraction between particles

b-is the volume excluded by a mole of particles

van der waals parameter ethan are:

a=5.562 L²·bar/mol²

b=0.0638 L/mol

Thus:

(P+n²a/V²)(V-nb)=nRT

P+n²a/V²=nRT/(V-nb)

P=nRT/(V-nb)-n²a/V²=1.67 mol * 8.31*10^-2 L*bar/K mol * 310.6 K / (0.2 L - 1.67 mol * 0.0638 L/mol) - (1.67 mol)²*5.562 L²·bar/mol² / 0.04 L² = 460.34 bar - 387.80 bar = 72.54 bar = 71.6 atm