1. 1000 molecules are bouncing at 300K between two wells separated by a free energy gap DG = 6·10-21 J. Calculate how many particles on average are in each well.
Boltzmann constant k = 1.38 ·10-23 J/K
T = 300K
2. A clam-shell protein (see figure below) is more stable in its compact folded state by ?G = -50 kJ/mol than in its open state.
a) What is the probability of being open for the intact protein? (give equilibrium constant Keq = [open]/[closed]) (T=300K)
b) The pair of amino acids that forms a stabilizing hydrogen bond (14 kJ/mole) in the desolvated contact was replaced by alanines with almost no interaction. How many fold the probability of opening will increase in the mutant?

3. Calculate the Bjerrum length for pairs of ions (+2, +1) and (+2, +2) in water (e=80) at 300K.
eo = 8.85 · 10-12 CV-1m-1
4. You know that one mole of water weights 18g and its density is 1g/cm3.
a. Calculate density of bulk water (molecules/nm3) and surface density at the air-water interface (molecules/nm2) assuming that average intermolecular distances are the same.
b. Given that tension at the air-water interface is 72 mN/m (enthalpy of surface formation) and enthalpy of average H-bond is 3.4 kcal/mole, how many H-bonds are dissatisfied at the surface?

c. If average number of H-bonds in the bulk is 3.5/molecule, what fraction of bonds is dissatisfied at the surface?