Question

4. Mercury (II) forms the soluble neutral complex Hg(SCN)2 with the ligand SCN The overall formation constant B2 for binding of SCN to Hg?* is 2.0 x 10" Calculate the equilibrium molar concentrations of Hg2+ and SCN and Hg(SCN) in a solution prepared by mixing 10 mL of 0.0200 M Hg2+ with 10 mL of 0.0200 M SCN Make reasonable simplifying assumptions... and state them!

I have posted this question like a million times and keep getting different answers. Please explain thoroughly. thanks

Answer 1

Answer:

In the reaction between Hg²⁺ and SCN^- ions, two formation constant involves K₁ and K₂ where, total formation constant K =  β₂ = K₁.K₂ = 2.0 x 10¹⁷

Now the concentration of solution after mixing both the solution;

[Hg²⁺] = 0.01 M and [SCN^-] = 0.01 M

Constructing an ICE table

	Hg2+ +	SCN- -->	Hg(SCN)2
Initial	0.01	0.01	0.00
After reaction	0.005	0.0	0.005
Change	a	2a	-a
Equilibrium	0.005 + a	2a	0.005 -a

Here, the limiting reagent is [SCN^-], Hence maximum amount of product (complex) formed = 0.005 M

K_f = [0.005-a]/[2a]²[0.005+a]

8 x 10¹⁷a³ + 4 x 10¹⁵ a² = 0.005 - a

The equation will be 8x10¹⁷a³ + 4x10¹⁵a² + a - 0.005 = 0

This will gives a = -0.005, -1.11803 x 10^-9 and 1.11803 x 10^-9 M

As a cannot be negative here.

a = 1.11803 x 10^-9 M

The equilibrium concentrations are

[Hg²⁺] = 0.005 + 1.11803 x 10^-9 ~~ 0.005 M;

[SCN^-] = 2 x 1.11803 x 10^-9 = 2.23606 x 10^-9 M

[Hg(SCN)₂] ~~ 0.005 M

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Thanks