The cyclic peptide, cyclo(L-prolyl)3, may adopt two possible conformations; one

Question

The cyclic peptide, cyclo(L-prolyl)3, may adopt two possible conformations; one is symmetric and the other is asymmetric. The symmetric conformation has a conformational potential energy of –82.7 kcal/mol. The asymmetric structure has a conformational potential energy of –81.9 kcal/mol. Use the Boltzmann distribution to calculate the absolute temperature when (A) The probability of finding the molecule in the lower level is 1.03 times the probability of the finding it in the upper level. (B) The peptide is only in the lower energy state. (C) The probability of finding the peptide in the either state is equal.

Explanation / Answer

According to Boltzmann distribution law

F2/F1 = e E1-E2/kT

where F1 and E1 is the probability and energy of state 1 respectively. F2 and E2 is the probability and energy of state 2. k is the Boltzman constant and T is the temp.

k= 1.38 * 10-23 JK-1 =

F2 = 1.03 F1 = 1 E1 =-81.9 E2 = 82.7   T= ?

1.03 = e (-81.9+ 82.7)/ 1.38 * 10-23 m2 kg s-2K-1* T

1.03 = e^ 0.58 *1023/T

ln 1.03 = ln e^ 0.58 *1023/T

0.029 = 0.58 *1023/T

T= 20 *1023 K

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