The Hisactophilin protein undergoes a reversible folding/unfolding transition at pH 5.5, and T = 320 K, in which q = 215 kJ/mol of heat is absorbed by the protein as it unfolds. A) Calculate AS for this process at 320 K. If the folding/unfolding happens at constant pressure, what is AH for this process?
B) Use the Gibbs-Helmholtz equation to calculate AG at 298 K. Will the protein unfold at 298 K, why or why not?
C) Use Boltzmann's formula to estimate the ratio of microstates in the unfolded state relative to the folded state (at 320 K). (Hint: If you are working in units kJ/mol, then use Boltzmann's formula as S = RinW, where "R" is the gas constant. To use Boltzmann's constant "kg", you would have to work in "per molecule" rather than "per mole" units).
D) Now lets think about whether your answer to part c) is a crazy or reasonable number. Suppose an ideal gas expands into a vacuum, doubling it's volume. How many atoms must be in the gas to get the same increase in microstates as in part c)?
E) Assume that Hisactophilin has 1000 atoms (actually pretty close...). Also assume that its entropy increase upon unfolding completely results from a volume effect, e. g. the effective volume per atom is greater in the unfolded state. Treat the atoms of Hisactophilin as an ideal gas, and compute the relative free volume of each atom in the folded and unfolded states.