For the complex formation reaction where M is any metal and L is any ligand,
M^2+ + 2L ⇌ [ML2]^+
Kf is the formation constant for the complex at equilibrium and ΔG° is the Gibbs free energy change for the reaction at equilibrium.
The formation constant (Kf) can be related to the Gibbs free energy change (ΔG°) for a reaction by the equation
ΔG° = -RT ln Kf
where T is the temperature in kelvins and R is the gas constant equal to 8.314 J·K^-1·mol^-1. The complex formation is generally a spontaneous process; thus, the Gibbs free energy change is negative.
Calculate the formation constant for the formation of [Ni(NH3)2(H2O)4]^2+ from [Ni(H2O)6]^2+, given that ΔG is -29.0 kJ·mol^-1 at 298 K.
Express your answer numerically to three significant figures.