The H+ titration curve of 1,2,3,4-tetracarboxyl cyclobutane should be interesting. We will...

The H+ titration curve of 1,2,3,4-tetracarboxyl cyclobutane

should be interesting. We will try to estimate it by using a simple, nearest-neighbor interaction model with the binding constant for a single COO-, K = 10-5 and τ = 10-2.

a. There are 16 possible species involving 0, 1, 2, 3, and 4 H+ bound. Give the statistical weight for each in terms of τ and S = K[H+]

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b. Write an expression for Q, the sum over states, and use Q to obtain an expression for v, the number of H+ bound per molecule.

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c. Calculate f = v/4 for pH 4, pH 5, and pH 6 and compare it with the titration curve f vs. pH) of a single COO-.