The van der Waals equation of state (Equation 5.3-7) is to be used to estimate the specific molar volume V^(L/mol) of air at specified values of T(K) and P(atm). The van der Waals constants for air are a 1:33 atmL2/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 fV^ c3V^3 c2V^2 c1V^ 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 V^ be if the ideal-gas equation of state were used for the calculation? Use this value as an initial estimate of V^ 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: T(K) P(atm) c3 c2 c1 c0 V(ideal) (L/mol) V(L/mol) f(V) % error 223 1.0 . . . . . . . . . . . . . . . . . . . . . . . . 223 10.0 . . . . . . . . . . . . . . . . . . . . . . . . 223 50.0 . . . . . . . . . . . . . . . . . . . . . . . . 223 100.0 . . . . . . . . . . . . . . . . . . . . . . . . 223 200.0 . . . . . . . . . . . . . . . . . . . . . . . . The polynomial expression for V^f c3V^3 c2V^2 should be entered in the fV column, and the value in the V column should be determined using Goal Seek or Solver in Excel.