Chem 156
Additional Problems
1. System A has ΩA states, and an entropy of SA (in units of J/K). If there is a system B
with an entropy of SB = ( SA + 1 J/K ), then how many states does system B have?
2. You have a system of particles in which you have 3 possible energy levels:
.
2
5
,
2
3
,
2210
ω
ω
ω
hhh === EEE
(a) Calculate the probability that a particle has an energy of 5ħω/2.
(b) Suppose that you have one mole of particles. Calculated the total expected energy of the
system. How many particles would you expect to see in each state?
3. A new protein you discovered has two different conformations: one conformation, I, is
inactive, and cannot bind any ligand, B. The other conformation, A, can bind two ligands in a
cooperative fashion in its binding site. Here is a diagram that illustrates this point:
L-1 K1 K2
I A A·B A·B2
(a) Which equilibrium constant is larger, K1 or K2? Explain why.
(b) Calculate the mean free energy of this protein in the presence of ligand. Assume that GA,
the free energy of conformation A, is zero.
(c) Calculate the mean number of ligands bound to this protein.
4. When a molecule is in solution, it has two transport mechanisms: by diffusion, and by
random thermal motion. You want to compare the two mechanisms in riboclease (MW 13,683).
(a) Assume D = 1.1 × 10-6 cm2/sec at 20°C, C = 1 µM, and dC/dX = 0.1 mM/cm. Calculate
the velocity of molecule moving as a result of diffusion.
(b) Now calculate the root mean square speed of the molecule resulting from random thermal
motion. How does this compare with the speed of the molecule due to diffusion?
