Question

The van der Waals equation of state (Equation 5.3-7) is to be used to estimate the specific molar volume V̂ (L/mol) of air at specified values of T (K) and P (atm). The van der Waals constants for air are a = 1.33 atm  L2/mol2 and b = 0.0366 L/mol.

a) Show why the wan der Walls equation is classified as a cubic equation of state by expressing it in the form:

f(V̂)=c3V̂3+c2V̂2+c1V̂ +c0=0

where the coefficients c3, c2, c1, and c0 involve P, R, T, a, and b. Calculate the values of these coefficients for air at 223 K and 50.0 atm. (Include the units when giving the values.)

b) What would the value of V̂ be if the ideal-gas equation of state were used for the calculation? Use this value as an initial estimate of V̂ for air at 223 K and 50.0 atm and solve the wan der Waals equation using Goal Seek or Solver in Excel. What percentage error results from the use of the ideal-gas equation of state, taking the van der Waals estimate to be correct?