Question

Complex-ions that have multiple ligands bonded to a metal ion actually form in a stepwise process. For example, the cadmium ion Cd2+ forms complexes with the cyanide ligand, CN− as follows:

Cd2+(aq)+CN−(aq)⇌Cd(CN)+(aq), Kf1=3.0x10^5
Cd(CN)+(aq)+CN−(aq)⇌Cd(CN)2(aq), Kf2=1.3x10^5
Cd(CN)2(aq)+CN−(aq)⇌Cd(CN)3−(aq), Kf3=4.3x10^4
Cd(CN)3−(aq)+CN−(aq)⇌Cd(CN)42−(aq), Kf4=3.5x10^3
Calculate the complex formation constant, Kf , for the overall reaction:
Cd2+(aq)+4 CN−(aq)⇌Cd(CN)42−(aq), Kf=?

Answer 1

The complex formation constant, Kf, for the overall reaction Cd2+(aq) + 4 CN−(aq) ⇌ Cd(CN)42−(aq) can be calculated by multiplying the equilibrium constants of the individual steps. The formation constants for each step are given as Kf1=3.0x10^5, Kf2=1.3x10^5, Kf3=4.3x10^4, and Kf4=3.5x10^3. Thus, Kf = Kf1 x Kf2 x Kf3 x Kf4.

Step-by-step explanation:

The formation of complex ions can be described through a stepwise process, in which multiple ligands bond with a metal ion. In the case of the cadmium ion, Cd2+, it forms complexes with the cyanide ligand, CN−. The stepwise reactions are as follows:

1. Cd2+(aq) + CN−(aq) ⇌ Cd(CN)+(aq) with Kf1 = 3.0x10⁵
2. Cd(CN)+(aq) + CN−(aq) ⇌ Cd(CN)2(aq) with Kf2 = 1.3x10⁵
3. Cd(CN)2(aq) + CN−(aq) ⇌ Cd(CN)3−(aq) with Kf3 = 4.3x10⁴
4. Cd(CN)3−(aq) + CN−(aq) ⇌ Cd(CN)42−(aq) with Kf4 = 3.5x10³

To calculate the complex formation constant, Kf, for the overall reaction: Cd2+(aq) + 4 CN−(aq) ⇌ Cd(CN)42−(aq), we simply need to multiply the equilibrium constants of the individual steps together. Thus, Kf = Kf1 x Kf2 x Kf3 x Kf4 = 3.0x10⁵ x 1.3x10⁵ x 4.3x10⁴ x 3.5x10³.

Answer 2

The complex formation constant (Kf) for the formation of Cd(CN)42- is calculated by multiplying the stepwise formation constants. The overall Kf is found to be 6.069 x 10^17.

Step-by-step explanation:

To calculate the complex formation constant, Kf, for the overall formation of the Cd(CN)42- complex ion, we need to multiply the stepwise formation constants (Kf1, Kf2, Kf3, and Kf4). The first reaction has a Kf1 of 3.0 x 105, the second a Kf2 of 1.3 x 105, the third a Kf3 of 4.3 x 104, and the fourth a Kf4 of 3.5 x 103:

• Kf1 = 3.0 x 105
• Kf2 = 1.3 x 105
• Kf3 = 4.3 x 104
• Kf4 = 3.5 x 103
• The complex formation constant, Kf, for the overall reaction Cd2+(aq) + 4 CN-(aq) → Cd(CN)42-(aq) can be calculated by multiplying the equilibrium constants of the individual stepwise reactions. In this case, the Kf value is obtained by multiplying Kf1, Kf2, Kf3, and Kf4.

The overall Kf is calculated by multiplying these constants together:

Kf = Kf1 x Kf2 x Kf3 x Kf4

Kf = (3.0 x 105) x (1.3 x 105) x (4.3 x 104) x (3.5 x 103) = 6.069 x 1017

Therefore, the equilibrium constant for the formation of the complex ion Cd(CN)42- is 6.069 x 1017.