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# (a) The van van der Waals equation for $n$ moles of a gas is$(P + \frac {n^2 a}{V^2})(V - nb) = nRT$where $P$ is the pressure, $V$ is the volume, and $T$ is the temperature of the gas. The constant $R$ is the universal gas constant and $a$ and $b$ are positive constants that are characteristic of a particular gas. If $T$ remains constant, use implicit differentiation to rind $dV/dP.$ (b) Find the rate of change of volume with respect to pressure of 1 mole of carbon dioxide at a volume of $V = 10L$ and a pressure of $P = 2.5$ atm. Use $a = 3.592 L^2 -atm/mole^2$ and $b = 0.04267 L/mole,$

## (a) $d V / d P=\frac{(n b-V) V^{3}}{2 n^{3} a b+P V^{3}-n^{2} a V}$(b) -4.04

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