Using the van der Waals equation, find the molar volume of $CO X_{2}$ ( $a = 3.59 L^{2} atm mo l^{- 2}$ , $b = 0.0427 L mo l^{- 1}$ ) at $350 K$ and $40.0 atm$ by iteration: start from the ideal value and use $V_{m} = \frac{RT}{P + a / V _{m}^{2}} + b$ until it converges. Give $V_{m}$ in $L mo l^{- 1}$ to three decimals ( $R = 0.0821 L atm K^{- 1} mo l^{- 1}$ ).

Numerical answer type, answer in L/mol, tolerance 0.003.

Answer: 0.628 L/mol

Ideal start:

V_{m} = 28.735/40 = 0.7184

. Iteration 1:

a / V_{m}^{2} = 6.957

V_{m} = 28.735/46.957 + 0.0427 = 0.6546

. Iteration 2:

a / V_{m}^{2} = 8.378

V_{m} = 28.735/48.378 + 0.0427 = 0.6367

. Continuing, the value converges to

V_{m} = 0.6278 L mo l^{- 1}

, i.e.

0.628

. The compressibility factor is

Z = 40 \times 0.6278/28.735 = 0.874