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

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Unformatted text preview: 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 g G and g ¡ are always positive, as long as ¢ 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 £ ¤ ¥ ¦§ ¤ where £ ¤ is the partial pressure of A in the gas phase, § ¤ is the solution-phase mole fraction of A, and ¦ is Henry’s constant, specific to the two components involved but independent of concentration. a) Assuming ideal gases and solutions, express ¦ in terms of standard chemical potentials. What makes Henry’s law different from Raoult’s law ( £ ¤ ¥ £ ¤ vap § ¤ )? 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 ¨ 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. 5. Applied problem (3 points).Applied problem (3 points)....
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PS6 - University of California Santa Barbara Department of...

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