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Quiz04 - Physical Chemistry(I 1(20 For a Bertholet equation...

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Physical Chemistry (I) Quiz 04 Nov. 22, 2007 1. (20%) For a Bertholet equation, 2 m m RT a P V b TV = - - , expand this expression in a Taylor series. (a) Based on a Taylor series expansion for the low density condition to obtain 2 m RT a V b P RT + - . (10%) (b) Find an expression for the Boyle temperature in terms of a , b , and R . (10%) 2. (20%) The experimental critical constants of H 2 O are T c = 647.14 K, P c = 220.64 bar, and V c = 55.95 × 10 –3 L. (a) Predict the density of water vapor at T = 700 K and P = 300 atm. (6%) (b) If one measured the density of H 2 O at 1200 bar and 800 K to be 537 g L –1 , calculate z and V m based on the above information. (6%) (c) Following (b), calculate the relative error if the law of corresponding states is applied. (8%) 3. (20%) The fugacity f can be viewed as the effective pressure that a real gas exerts. (a) Derive an expression for f as a function of z and P . (10%) (b) Following (a), find the fugacity coefficient for a hard-sphere gas (the van der Waals gas with the a parameter set to zero). (5%) (c) Following (b), find the expression for f as a function of z and P at the low density condition. (5%) 4. (15%) The vapor pressure of methanol ( l ) is given by 3 3.6791 10 ln 23.593 Pa 31.317 K P T ×   = -     - . (a) Calculate the standard boiling temperature. (5%) (b) Calculate Δ H vaporization by the vapor pressures at 298 K and at the standard boiling temperature. (10%) 5. (10%) The densities of a given solid and liquid of molecular weight 122.5 at its
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