Question

Van der Waals equation of state is (P+(n²a)/V²)(V-nb)=nRT where a and b are temperature-independent parameters that have different values for each gas. For CO₂, a=0.3640 Pa m⁶/mol² and b=4.267*10^-5 m³/mol

a) Write this equation as a cubic equation in V

Answer 1

for 1 mole of gas, vander waal equation;

(P + a/(Vm)^2) (Vm-b)= RT

This equation can be written as:

PVm-Pb +a/Vm-ab/(Vm)^2-RT=0

Multiplying by (Vm)^2 and dividing by P and rearranging in decreasing power of Vm, the equation can be written as

(Vm)^3-(b+RT/P) (Vm)^2 + a/P. Vm- ab/P = 0

This is a cubic equation in the variable Vm and therefore, for any single set of values of P and T, there should be three values of Vm, all of which may be real or only one may real and other two imaginary.