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# If $\beta_1, \beta_2$ and $\beta_3$ are stepwise formation constants of $MCl, MCl_2, MCl_3$ and K is the overall formation constants of $MCl_3$, then (charges ommitted) :

(a) $K = \beta_1 + \beta_2 + \beta_3$

(b) $\frac{1}{K} = \frac{1}{\beta_1} + \frac{1}{\beta_2} + \frac{1}{\beta_3}$

(c) $log K = log \beta_1 + log \beta_2 + log \beta_3$

(d) $\rho_K = log \beta_1 + log \beta_2 + log \beta_3$

Answer: $log K = log \beta_1 + log \beta_2 + log \beta_3$

Given,

For $MCl, M + Cl \rightarrow MCl; K_1 = \beta_1$

For $MCl_2, MCl + Cl \rightarrow MCl_2; K_2 = \beta_2$

For $MCl_3, MCl_2 + Cl \rightarrow MCl_3; K_3 = \beta_3$

$\therefore M + 3Cl \rightarrow MCl_3; K_{eqm} = K$

At equilibrium, equilibrium constant K is
$K = K_1 \times K_2 \times K_3$
$K = \beta_1 \times \beta_2 \times \beta_3$

taking logarithm on both sides we get,
$log K = log \beta_1 + log \beta_2 + log \beta_3$