2003_final

# 2003_final - Page 1 of 14 Name BE.011/2.993J Spring 2003...

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Page 1 of 14 Name: BE.011/2.993J Spring 2003 FINAL EXAM May 19, 2003 You have 3 hours for this exam. CLOSED BOOK 4 pages of notes allowed 1. (60 points) 2. (20 points) 3. (10 points) 4. (40 points) 5. (65 points) 6. (30 points) total (225 points) Some constants you may need: k = 1.38 ? 10 -23 J K -1 R = 8.314 J K -1 mol -1 h = 6.626 ? 10 -34 J s 1atomic mass unit (amu) = 1.66 ? 10 -27 kg

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Page 2 of 14 Name: 1.) ( 60 points total ) The protein below has four binding sites ( ? , ? , ? , ? ) for the ligand L (look familiar?). Assume that the association and dissociation constants are equal. L L + L + ? ? ? L ? ? ? ? ? ? ? ? ? ? ? ? ? It has energies associated with each macrostate L, where L is the # of ligands: #L energy 0 8 ? 1 4 ? 2 2 ? 3 1 ? 4 0 1a.) (10 points) Plot an energy level diagram, including all microstates. Label values on the y axis in terms of the energy unit ? .
Page 3 of 14 Name: 1b.) (10 points) Write down an expression for the partition function q. Calculate its value at a temperature where kT = 3 ? . 1c.) (5 points) What is the highest macrostate that is populated at this temperature kT = 3 ? ? How many of the microstates in this macrostate are populated? 1d.) (10 points) Calculate p L for L = 0,1,2,3,4 at a temperature where kT = 3 ? . What is ? L p L ?

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Page 4 of 14 Name: 1e.) (10 points) Calculate <E> at a temperature where kT = 3 ? , (you can leave it in terms of ? ). 1f.) (5 points) What is the entropy, S, at a temperature where kT = 3 ? ? 1g.) (5 points) What is q as T ? ? ?
Page 5 of 14 Name: 1h.) (5 points) What is S as T ? ? ? 2.)( 20 points total ) Heat capacity of a molecule You have the molecule glucose, which has 66 degrees of vibrational freedom. Plot its heat capacity as a function of temperature, making sure to denote on the plot

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2003_final - Page 1 of 14 Name BE.011/2.993J Spring 2003...

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