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Problem 71 Hard Difficulty

(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, $

Answer

(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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