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Unformatted text preview: Department of Chemical Engineering ChE 210A University of California, Santa Barbara Fall 2011 Problem Set No. 6 Due: 11/08/2011 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 (3 points). How strong must cell walls be? Assume a typical cell is spherical (radius 10 £¤ ) and stuffed full of proteins, which take up 30% volume fraction. For example, red blood cells contain numerous hemoglobin molecules. Assume a typical protein is roughly spherical in shape with a radius of 10 nm. a) Compute the pressure difference that the cell membrane would experience if placed in a container of pure water at 300 K. (Note: even at 30% volume fraction, the protein is very dilute on a molar basis because it is so much larger than a water molecule.) b) The surface tension for a spherical body is given by Σ = ¥¦/2 where ¥ is the radius and ¦ is the pressure. If a cell ruptures at a tension of Σ = 0.001 §/¤ , what happens when it is placed in pure water? c) What minimum concentration of sucrose (MW = 342 g/mol) dissolved in the water will prevent lysis? Assume sucrose is too big to partition inside of the cell. 4. Fundamentals problem (3 points). In working with a nonideal binary solution, you decide to account for deviations from nonideality by forming a second-order Taylor expansion of the chemical potential for each component A and B:...
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