Table 2.

State energies derived from pK_as in Table 1 using different reference states or reference pHs.

		pH =0	pH=7		pH=0	ΔΔG°jC - ΔΔG°jB
State j	ΔmjB	ΔG°jB	ΔG°’jB	ΔmjC	ΔG°jC
A	1	2.17	9.17	2	−3.44	−5.61
B	0	0	0	1	−5.61	−5.61
C	−1	5.61	−1.39	0	0	−5.61
D	−2	19.37	5.37	−1	13.77	−5.61

With B as the reference state ΔG°_jB and ΔG°_jC obtained with eqn 2b given pK_AB and pK_CB; ΔG°_DB = ΔG°_DC+ΔG°_CB (Table 1). ΔG°’_jB, the relative state energies with the reference pH=7, is obtained with eqn 2c. When C is the reference state the ΔG° relative to states B and D are obtained directly from the reported pK_as using equation 2b. ΔG°_AC = ΔG°_AB+ΔG°_BC. There is a constant offset for all ΔG°s moving from a system that uses state B or state C as the reference state. ΔG represents unitless free energies where a unit change in ΔG yields a 10-fold population change.