Spectrophotometric Determination of the Thermodynamic Parameters for the First Two Protonation Reactions of Molybdate An Advanced Undergraduate Laboratory Experiment J. J. Cruywagen and J. B. 6. Heyns University of Stellenbosch, Stellenbosch 7600, South Africa The educational value of this experiment will immediately he appreciated by the reader when the protonation equilihria of molybdate, as represented by the following equations, are considered:
It is seen that an increase in the coordination number of molyhdenum(V1) is indicated to take place in the second protonation step. The values for the successive protonation constants of molyhdate are very similar, i.e., log Kl = 3.5 and log K 2 = 3.7 (1).The successive protonation constants of oxyacids usually differ by at least 4 to 5 log units (2). The anomalous small difference in the K values for the protonation of molybdate has been explained in terns of an increase in the coordination number of molybdenum during the second protonation step as indicated above (3). Hence the value of the first protonation constant is regarded as normal, hut the value of the second constant is regarded as abnormally Large. This interpretation has been based on thermodynamic results such as provided by this experiment. The relationship between the equilibrium constant and other thermodynamic constants is given by the equation -2.303RTlogK
= A@
= @- T
o
(3)
For the first protonation of molyhdate the values for H and AS"' should be normal and comparable to those for other oxyanions; i.e., this protonation reaction is expected to be entropy driven, while the entbalpy change will be either a small positive or small negative quantity. In the case of the second protonation, however, the 0and ASo values should reflect the change in coordination number. The uptake of two water molecules will result in an unfavorable entropy change, while the additional bond energy, derived from the increase in coordination number, should lead to a favorable enthalpy change. The second protonation is therefore expected to he an enthalpy driven reaction. Normally one would determine the enthalpy change for a protonation or ionization reaction by calorimetry. For the protonation of molybdate, however, a concentration of
