When in a M-L system, if I have different species such as MLH2 , MLH and ML, Logβ for MLH2 is higher than for MLH and this one is higher than for ML, why this could be happening ?
Because i think the coordinating cappacity should increase while the ligand lose protons on donor atoms (like N, O or S) so I should expect the Logβ to increase while losing protons.
Yahia Z Hamada's answer above is correct, but let me give an explicit example to demonstrate his point.
For a system with citrate (Cit) and calcium (Ca) (ignoring charges) we have the following log Ks from the NIST database:
Ca + cit = Ca(cit) Log K_ML = 4.85
Ca + H(cit) = CaH(cit) Log K_MLH = 2.86
Ca + H2(cit) = CaH2(cit) Log K_MLH2 = 1.4
Note that logK value decreases with each protonation step, just like it does for the (reversed) traditional log Ka values:
H + cit = H(cit) Log K_a3* = 6.396
H + H(cit) = H2(cit) Log K_a2* = 4.761
H + H2(cit) = H3(cit) Log K_a1* = 3.128
The positive log K indicates that the reaction is favorable, the decreasing value of log K indicates that each protonation step makes the reaction less favorable than the previous.
When we compare log B values, we are talking about equilibria of varying order.
Consider the Log B for MLH:
Ca + H + cit = CaH(cit) Log B_MLH = Log K_MLH + Log K_a3* = 9.256
The log B_MLH may be higher than Log K_ML, but the equilibria involves three reactants instead of two.
We can also consider the Log B for MLH2:
Ca + 2H + cit = CaH2(cit) Log B_MLH2 = Log K_MLH2 + Log K_a3* + Log K_a2* = 12.557
Again, log B_MLH2 is higher than Log B_MLH, but the equilibria involves four reactants instead of three.
You need to think in terms of charge and character of the donating (coordinating) atoms.
A) First of all: If you complex [M(LH2)] looses a proton, the resulting complex is [M(LH)]-. Cleaving another proton yields [M(L)]2-.
Or the series is [M(LH2)]2+, [M(LH)]+, [M(L)]
The charge of a complex is important for the stability in a given solvent.
B) some coordinating atoms gain a lot of strength upon deprotonation. e.g. while H2O is a poor ligand, OH- is strong. This is even more pronounced for HOR (alkohols) vs. -OR (alkoholates), or HSR (thiols) vs -SR (thiolates), or NHR2 (amines) vs. -NR2 (amides)
And finally, the pKA of a coordinated molecule (ligand) can be very different to the uncoordinated molecule. E.g. pKA of H2O = 15.75, pKA of the H2O ligand in [Pd((H2O)4]2+ = 6.
I can (really) recommend:
Bioinorganic Chemistry -- Inorganic Elements in the Chemistry of Life: An Introduction and Guide, 2nd Edition, Wolfgang Kaim, Brigitte Schwederski, Axel Klein, Wiley Chichester, ISBN: 978-0-470-97523-7, 2013, 426 Pages
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