If `Ag^(+)+NH_(3)hArr[Ag(NH_(3))]^(+)`, `K_(1)=3.5xx10^(-3)` and `[Ag(NH_(3))]^(+)+NH_(3)hArr[Ag(NH_(3))_(2)]^(+)`, `K_(2)=1.74xx10^(-3)`. The formation constant of `[Ag(NH_(3))_(2)]^(+)` is :

Options

A. `6.08 xx 10^(-6)`
B. `6.08 xx 10^(6)`
C. `6.08 xx 10^(-9)`
D. None of these

Answer

A

Explanation

If a reaction occurs in two steps, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants for the individual steps.
`Ag^(o+) +NH_(3) hArr [Ag(NH_(3))]^(o+), K_(1) = 3.5 xx 10^(-3)`
`[Ag(NH)_(3)]^(o+) +NH_(3) hArr [Ag(NH_(3))_(2)]^(o+), K_(2) = 1.7 xx 10^(-3)`
`Ag^(o+) +2NH_(3) hArr [Ag(NH_(3))_(2)]^(o+)`,
Over all `K = K_(1) xx K_(2)`
`= 3.5 xx 10^(-3) xx 1.7 xx 10^(-3)`
`= 5.95 xx 10^(-6)`