Method of Branch and Calvin

For species 12, we hrst estimate the pA a of HO-S02 using the method of Branch and Calvin (see Appendix), knowing full well that this will not be accurate because the central atom is highly charged, the estimate for sulfuric acid with is too acidic, and resonance will also make a contribution, so that the crude estimate will not be acidic enough. However, the errors may partly cancel. 

Numbers used in this cycle AG° for hydroxide plus monomethyl sulfate, assumed to be the same as for dimethyl sulfate estimated above AG° for ionization of monomethyl sulfate AG° for tautomerization of the anionic adduct, based on pK values estimated by the method of Branch and Calvin AG° for ionization of the apically protonated adduct, based on a pK estimated by the method of Branch and Calvin.)... 

Numbers used in the cycle AG° for addition of hydroxide to p-nitrophenyl sulfate, see above AG° for proton transfer from p-nitrophenyl sulfate to hydroxide, based on pA a values AG° for ionization of the monoanionic adduct of p-nitrophenyl sulfate, estimated by the method of Branch and Calvin, supplemented by the difference in pATa between sulfuric acid and p-nitrophenyl sulfate.)... 

Since no pK values are available for hydroxyphosphoranes, the pK of pentahydroxyphosphorane is estimated by the method of Branch and Calvin (1941) as 8.5. The application of the free-energy change for reaction (4) to... 

---