5.78. The van der Waals equation of state (Equation 5.3-7) is to be used to estimate the specific molar
volume \(\tilde{V}\) (L/mol) of air at specified values of T(K) and P(atm). The van der Waals constants for air are
a = 1.33 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
$f(\tilde{V}) = c_3 \tilde{V}^3 + c_2 \tilde{V}^2 + c_1 \tilde{V} + c_0 = 0$
where the coefficients $c_3$, $c_2$, $c_1$, and $c_0$ 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.)