Using the van der Waals relations, estimate the critical density of methane (molar mass $16 g mo l^{- 1}$ , $T_{c} = 190 K$ , $P_{c} = 45.8 atm$ , $R = 0.0821 L atm K^{- 1} mo l^{- 1}$ ) in $g L^{- 1}$ (nearest integer).

Numerical answer type, answer in g/L, tolerance 2.

Answer: 125 g/L

b = \frac{R T _{c}}{8 P _{c}} = \frac{15.599}{366.4} = 0.04257 L mo l^{- 1}

, so

V_{c} = 3 b = 0.1277 L mo l^{- 1}

ρ_{c} = M / V_{c} = 16/0.1277 = 125.3 g L^{- 1}

, i.e.

125 g L^{- 1}

. The experimental value is

162 g L^{- 1}

, higher because real

V_{c}

is below

3 b