$3\mathrm{.}3$ The critical constants for water are $374C,22\mathrm{.}1$MPa, and $0\mathrm{.}0566\frac{L}{m}ol.$ Calculate values of $a,b,$ and $R$; using the van der Waals equation, compare the value of $R$ with the correct value and notice the discrepancy. Compute the constants a and $b$ from $p_c$ and $T_c$ only. Using these values and the correct value of $R,$ calculate the critical volume and compare with the correct value.

$3\mathrm{.}4$ Find the relation of the constants a and $b$ of the Berthelot equation to the critical constants.

$3\mathrm{.}5$ Find the relation of the constants a and $b$ of the Dieterici equation to the critical constants. $($Note that this cannot be done by setting three roots of the equation equal to one another.$)$