PART A: For the complex formation reaction where M is any metal and L is any lig

Question

PART A:

For the complex formation reaction where M is any metal and L is any ligand,

M++2L?[ML2]+

Kf is the formation constant for the complex at equilibrium and ?G? is the Gibbs free energy change for the reaction at equilibrium.The formation constant (Kf) can be related to the Gibbs free energy change (?G?) for a reaction by the equation

?G?=?RTln 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)4(H2O)2]2+ from [Ni(H2O)6]2+, given that ?G? is ?46.3kJ?mol?1 at 298 K.

Express your answer numerically to three significant figures.

PART B:

When a metal ion in aqueous solution interacts with a monodentate ligand, the ligand can displace water molecules coordinated to the metal center only when it is a stronger Lewis base than water. As the water molecules are replaced by ligands, you need to consider the equilibrium at each step. The number of steps depends on the coordination number of the metal ion.

The equilibrium calculated at each step is called the stability constant or formation constant. For example, [Ni(NH3)6]2+ is formed from [Ni(H2O)6]2+ and aqueous NH3 in six steps, with the successive formation of [Ni(H2O)5(NH3)]2+, [Ni(H2O)4(NH3)2]2+, [Ni(H2O)3(NH3)3]2+, [Ni(H2O)2(NH3)4]2+, and [Ni(H2O)(NH3)5]2+, respectively.

The overall formation constant (Kf) is the product of the formation constant of the individual steps:

?n=Kf=K1K2K3?Kn

In calculating the concentration of [Cu(NH3)4]2+ from [Cu(H2O)4]2+, the stepwise formation constants are as follows:

K1=1.90104

K2=3.90103

K3=1.00103

K4=1.50102

Calculate the overall formation constant (Kf) for the formation of [Cu(NH3)4]2+ from [Cu(H2O)4]2+.

Express your answer numerically to three significant figures.

Explanation / Answer

Part A:

Given delta G = -46.3kJ/mol = 46300J/mol

T = 298K

deltaG = –RT ln(Kf)

(-46300J/mol) = – (8.314J/Kmol) (298K) ln(Kf)

-46300 = -2477.572 ln(Kf)

Kf = e^(-74.2 / -2.478)

Kf = 1.3E8

Formation constant Kf = 1.3 x10^8

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