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# PS6 - Department of Chemical Engineering University of...

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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 g1855 g3023 and g1855 g3017 are always positive, as long as g1846 is positive. 3. Applied problem (3 points). How strong must cell walls be? Assume a typical cell is spherical (radius 10 g2020g1865 ) 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 = g1844g1842/2 where g1844 is the radius and g1842 is the pressure. If a cell ruptures at a tension of Σ = 0.001 g1840/g1865 , 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.

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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: g2020 g3002 = g2020 g3002 + g1863 g3003
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