Question

2. The formation of complexes of cobalt with ethylenediamine takes place in stages where successive pairs of water molecules on Co(H20)624 are replaced by the diamine. Similar chemistry occurs with cadmium. a. Write down the equilibria for the reactions with Co(H2O)62* together with the corresponding expression for the appropriate cumulative formation constant, Bi.

Answer 1

2

(a) Overall formation constant is the product of the stepwise formation constants, stepwise formation constant is the formation constant for each individual solvent replacement in the synthesis of the complex.

Individual steps in the formation of [Co(en)₃]²⁺ : (since water is in excess , we are not writing it in equilibrium expression)

1. [Co(H₂O)₆]²⁺ + en $\rightleftharpoons$  [Co(en)(H₂O)₄]²⁺ +2H₂O K₁ =  [Co(en)(H₂O)₄]²⁺  / [Co(H₂O)₆]²⁺  [en]

$\beta$1 =  K₁

2.  [Co(en)(H₂O)₄]²⁺+en $\rightleftharpoons$   [Co(en)₂(H₂O)₂]²⁺ +2H₂O  

  K₂ = [Co(en)₂(H₂O)₂]²⁺ / [Co(en)(H₂O)₄]²⁺[en] ;   

  $\beta$2=  K₁*K₂ = [Co(en)₂(H₂O)₂]²⁺ /   [Co(H₂O)₆]²⁺ [en]²

3.[Co(en)₂(H₂O)₂]²⁺ + en $\rightleftharpoons$  [Co(en)₃]²⁺ +2H₂O    K₃ =   [Co(en)₃]²⁺ / [Co(en)₂(H₂O)₂]²⁺[en]

Overall complex formation reaction :

[Co(H₂O)₆]²⁺ + 3 en $\rightleftharpoons$  [Co(en)₃]²⁺   +6H₂O

Cumulative formation constant ($\beta$3) = [Co(en)₃]²⁺ /   [Co(H₂O)₆]²⁺ [en]³

We can write ,$\beta$3 =  K_1*K_2*K₃ = [Co(en)₃]²⁺ /   [Co(H₂O)₆]²⁺ [en]³

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(b) [Co(H₂O)₆]²⁺ in 2M of en

Cumulative formation constant ($\beta$3) =  K_1*K_2*K₃

We are not provided with formation  constants of Co²⁺ and en complexes.

From online sources : $\beta$3 = 8.7×10¹³  = [Co(en)₃]²⁺ /   [Co(H₂O)₆]²⁺ [en]³

8.7×10¹³  = [Co(en)₃]²⁺ /   [Co(H₂O)₆]²⁺ [2.0]³

[Co(en)₃]²⁺ /   [Co(H₂O)₆]²⁺ = 6.96 *10¹⁴

^or    [Co(H₂O)₆]²⁺ = [Co(en)₃]²⁺ / 6.96 *10¹⁴

(c) From appendix data :

Complex formed by [Cu(H₂O)₆]²⁺  in 2M en =  [Cu(en)₂]²⁺

Complex formed by [Cd(H₂O)₆]²⁺  in 2M en =  [Cd(en)₃]²⁺

For Cu²⁺ cumulative formation constant data is for addition of only 2-ligands , thus it forms 4-coordinated complex.For Cd²⁺ cumulative formation constant data is for addition 3-ligands , thus it forms 6-coordinated complex. Cu²⁺ (d⁹ ) always prefer 4-coordinated complexex, which are of low in symmetry to prevent effect of John-teller distortion, it is indicated by larger value for $\beta$2 =19.99 ~ 10²⁰​​​​​​​.

(d)

[Cd(H₂O)₆]²⁺ in 2M of en

Cumulative formation constant ($\beta$3) =  K_1*K_2*K₃

From appendix-I data : $\beta$3 = log 12.80 =6.3*10¹²

6.3*10¹²  = [Cd(en)₃]²⁺ /   [Cd(H₂O)₆]²⁺ [en]³

6.3*10¹²  = [Cd(en)₃]²⁺ /   [Cd(H₂O)₆]²⁺ [2.0]³

[Cd(en)₃]²⁺ /   [Cd(H₂O)₆]²⁺ = 5.05 *10¹³

^or    [Cd(H₂O)₆]²⁺ = [Cd(en)₃]²⁺ / 5.05 *10¹³