Question

Given the equilibrium constants
$HgC{l}^{\oplus }+C{l}^{\ominus }\to HgC{l}_2,K_1=3\times {10}^6$
$HgC{l}_2+C{l}^{\ominus }\to HgC{l}_3^{\ominus },K_2=8.9$
The equilibrium constant for the disproportionation equilibrium
$2HgC{l}_2\to HgC{l}^{\oplus }+HgC{l}_3^{\ominus }$ is :

• A. $-3.3\times {10}^5$
• B. $3\times {10}^{-5}$
• C. $3.3\times {10}^5$
• D. $3\times {10}^{-6}$

Answer 1

The correct option is D $3\times {10}^{-6}$

a. $HgC{l}^{\oplus }+C{l}^{\ominus }\to HgC{l}_2....K_1$
b. $HgC{l}_2+C{l}^{\ominus }\to HgC{l}_3^{\ominus }......K_2$
The eq. constant (k) for the reaction,
$2HgC{l}_2\to HgC{l}^{\oplus }+HgC{l}_3^{\ominus }$
Can be obtained by reversing equation(a) and adding to equation (b).
$K=\frac{1}{K_1}\times K_2=\frac{K_2}{K_1}=\frac{8.9}{3\times {10}^6}\approx 3\times {10}^{-6}$