# PS6 - University of California Santa Barbara Department of...

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University of California Santa Barbara, Department of Chemical Engineering ChE 210A: Thermodynamics and Statistical Mechanics Problem set #6 Due: Friday, November 6, 2009 Objective: To understand and manipulate the thermodynamic properties of ideal and nonideal solutions and solids. 1. Statistical antics : You’ve been asked to play a part in a murder mystery movie. Which character would you most enjoy playing: (1) a witty employee of the castle (the butler / cook / nanny / etc), (2) a secret government scientist, (3) the local police detective, (4) a bitter, rich old heir/heiress, (5) a quirky psychic/clairvoyant, or (6) a mysterious stranger from a foreign land? 2 . Conceptual problem (1 point). Show that g1855 g3023 and g1855 g3017 are always positive, as long as g1846 is positive. 3. Applied problem (2 points). Consider a solution of two components, A and B, at vapor-liquid equilibrium. Henry’s law is an approximation that states that, if component A is very dilute, then g1842 g3002 g3404g1837g1876 g3002 where g1842 g3002 is the partial pressure of A in the gas phase, g1876 g3002 is the solution-phase mole fraction of A, and g1837 is Henry’s constant, specific to the two components involved but independent of concentration. a) Assuming ideal gases and solutions, express g1837 in terms of standard chemical potentials. What makes Henry’s law different from Raoult’s law ( g1842 g3002 g3404g1842 g3002 vap g1876 g3002 )? b) [MDF problem 16.2] Divers can get the ‘bends’ from nitrogen bubbles in their blood. Assume that blood is largely water. The Henry’s law constant for N 2 in water at 25 g1320 is 86,000 atm. The hydrostatic pressure is 1atm at the surface of a body of water and increases by approximately 1 atm for every 33 feet of depth. Calculate the N 2 solubility in the blood at 0 and 30 ft deep, and explain why the bends occur. Assume ideal gases and solutions, and note that the atmosphere is roughly 80% nitrogen.

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5. Applied problem (3 points). How strong must cell walls be?
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