Question

Consider binding of a ligand L to a metal centerM^z+, where binding is characterized by K₁, K₂, and K₃. (When looking at tabulated data for
formation (aka binding) constants, watch whether it is logK_i or -pK_i.) The following are written for a neutral ligand, which bpy and phen
are. L can also undergo reactions with H⁺ as shown, here characterized by pK_A1 and pK_A2

RXN1 M^z+ + L --> ML^z+ -pK₁
RXN2 ML^z+ + L --> ML₂^z+ -pK₂
RXN3 ML₂^z+ + L --> ML₃^z+ -pK₃
RXN4 H₂L⁺² + H₂O --> H₃O⁺ + HL⁺ pK_A1
RXN5 HL⁺ + H₂O --> H₃O⁺ + L pK_A2

1. Use the cosmic general rules. Specify the generic expressions for c_M, c_L, and [H3O⁺]. Include all ligated complexes and all species of L.
Label EQs and MBs and CB (if appropriate). Ignore activity and autoprotolysis. Note, it will be easier/neater to solve this problem later if

 β1 = K1, β2 = K1K2, and β3 = K1K2K3 are used. (Do the derivation symbolically; do not enter any numbers yet.) Define [H3O+] in 

terms of pH, which will be specified later.
2. Nickel solutions are prepared at c*_M = 0:0200 F. The solutions are buffered to pH = 3:50. Bipyridine (bpy) is added until [L] = 10.00μM and
[Ni²⁺]= 139 nM is found by ICP-MS To the second solution, phenanthroline (phen) is added until [L] = 5.00μM and [Ni²⁺]= 0:201 nM.
Calculate c*_bpy and c*_phen. (A spreadsheet is recommended.) A similar method allows determination of formation constants. Relevant data
(Can. J. Chem. 45 2093 (1967) McBryde) are:
pK_A1 pK_A2 -pK₁ -pK₂ -pK₃
bpy -0.20 4.49 7.07 6.86 6.20
phen -1.6 4.90 8.00 8.00 7.90
3. Is the fraction of NiL₃²⁺ compared to c*_L the same or different for bpy and phen? Is the fraction [L] /c*_L needed to form the complexes larger
for bpy or phen? Explain in terms of equilibrium constants and Le Chatelier’s principle.