Question

For the following equilibrium (omitting charges)
I. $M+Cl\leftrightharpoons MCl,K_{eq}={\beta }_1$
II. $MCl+Cl\leftrightharpoons MC{l}_2,K_{eq}={\beta }_2$
III. $MCl+Cl\leftrightharpoons MC{l}_3,K_{eq}={\beta }_3$
IV. $M+3Cl\leftrightharpoons MC{l}_3,K_{eq}=K$

Then relationship between $K,{\beta }_1,{\beta }_2$ and ${\beta }_3$ is:

• A. $K={\beta }_1{\beta }_2{\beta }_3$
• B. $\log K=\log {\beta }_1+\log {\beta }_2+\log {\beta }_3$
• C. $pK=p{\beta }_1+p{\beta }_2+p{\beta }_3$
• D. All of the above

Answer 1

Answer: (D)

All of the above

When we add reactions I, II and III, we get reaction IV.
When individual reactions are added, their equilibrium constant values are multiplied.
$K={\beta }_1{\beta }_2{\beta }_3$
Taking logarithm on both sides
$\log K=\log {\beta }_1+\log {\beta }_2+\log {\beta }_3$
But
$pK=-logK$
Hence,
$pK=p{\beta }_1+p{\beta }_2+p{\beta }_3$
Hence, the option $\left(D\right)$ all of the above is the correct answer.