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Q.

If $β_{1}, β_{2} and β_{3}$ are stepwise formation constants of MCl, ${MCl}_{2}, {MCl}_{3}$ and K is the overall formation constant of ${MCl}_{3},$ then

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a

$pK = \log β_{1} + \log β_{2} + \log β_{3}$

b

$\frac{1}{K} = \frac{1}{β_{1}} + \frac{1}{β_{2}} + \frac{1}{β_{3}}$

c

$\log K = \log β_{1} + \log β_{2} + \log β_{3}$

d

$K = β_{1} + β_{2} + β_{3}$

answer is C.

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Detailed Solution

$M + Cl \overset{}{\to} HCl : β_{1} MCl + Cl \overset{}{\to} {MCl}_{2} : β_{2} {MCl}_{2} + Cl \overset{}{\to} {MCl}_{3} : β_{3} K = β_{1} \times β_{2} \times β_{3} \log K = \log (β_{1} \times β_{2} \times β_{3}) = {logβ}_{1} + \log β_{2} + \log β_{3}$

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If β1, β2 and β3 are stepwise formation constants of MCl, MCl2, MCl3 and K is the overall formation constant of MCl3, then