The stepwise stability constants of a complex are given below. What is its overall reaction stability constant `(beta_(4))` ?
`M + L hArr ML , K_(1) = 1.0 xx 10^(4)`
`ML + L hArr ML_(2) , K_(2) = 1.0 xx 10^(3)`
`ML_(2) + L hArr ML_(3) , K_(3) = 1.0 xx 10^(3)`
`ML_(3) + L hArr ML_(4) , K_(4) = 1.0 xx 10^(2)`
(Overall reaction : `M + 4L hArr ML_(4)`)

Options

A. `1.0 xx 10^(12)`
B. `12.1 xx 10^(3)`
C. `1.0 xx 10^(6)`
D. `1.0 xx 10^(8)`

Answer

A

Explanation

Given,
`M + L hArr ML , K_(1) = 1.0 xx 10^(4)`
`ML + L hArr ML_(2), K_(2) = 1.0 xx 10^(3)`
`ML_(2) + L hArr ML_(3), K_(3) = 1.0 xx 10^(3)`
`ML_(3) + L hArr MK_(4) , K_(4) = 1.0 xx 10^(2)`
Overall reaction,
`M + 4L hArr ML_(4)`
The overall stability constant,
`beta_(4) = K_(1) xx K_(2) xx K_(3) xx K_(4)`
`beta_(4) - 1.0 xx 10^(4) xx 1.0 xx 10^(3) xx 1 xx 10^(3) xx 1 xx 10^(2) = 1 xx 10^(12)`