Given the equilibrium constants
`HgCl^(o+)+Cl^(ɵ) rarr HgCl_(2), K_(1)=3xx10^(6)`
`HgCl_(2)+Cl^(ɵ) rarr HgCl_(3)^(ɵ), K_(2)=8.9`
The equilibrium constant for the disproportionation equilibrium
`2HgCl_(2) rarr HgCl^(o+)+HgCl_(3)^(ɵ)` is

Options

A. `-3.3xx10^(5)`
B. `3xx10^(-5)`
C. `3.3xx10^(5)`
D. `3xx10^(-6)`

Answer

D

Explanation

a. `HgCl^(o+)+Cl^(ɵ) rarr HgCl_(2) … K_(1)`
b. `HgCl_(2)+Cl^(ɵ) rarr HgCl_(3) …K_(2)`
The eq. constant (k) for the reaction,
`2HgCl_(2) rarr HgCl^(o+)+HgCl_(3)^(ɵ)`
Can be obtained by reversing equation (a) and adding to equation (b).
`K=1/K_(1)xxK_(2)=K_(2)/K_(1)=8.9/(3xx10^(6))~~3xx10^(-6)`