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 van der Waals equation is classified as a cubic equation of state by expressing it in the form

where the coefficients c_3, c_2, 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 van 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? 

(c) Set up a spreadsheet to carry out the calculations of Part (b) for air at 223 K and several pressures. The spreadsheet should appear as follows:

The polynomial expression for  should be entered in the f(V) column, and the value in the V column should be determined using Goal Seek or Solver in Excel.

Equation 5.3-7

Transcribed Image Text:

f(V) = c3v +c2v +cıV + co = 0