Question

Given that the concentration of silver ion in a saturated solution of `Ag_2Cr_2O_7(aq)` is `4.0xx10^-4*mol*L^-1`, how do we assess `K_"sp"` for `Ag_2Cr_2O_7`?

Answer 1

`K_"sp"=3.2xx10^-11`....for `Ag_2Cr_2O_7`

Explanation:

We address the `"solubility equilibrium....."`

`Ag_2Cr_2O_7(s) rarr2Ag^+ + Cr_2O_7^(2-)`

For which `K_"sp"=[Ag^+]^2[Cr_2O_7^(2-)]=?`

`[Ag_2Cr_2O_7(s)]` does NOT appear in this expression because a SOLID cannot express a concentration....

We know that `Ag_2Cr_2O_7` has a `"molar solubility"` of `0.00020*mol*L^-1`, the which is given in the boundary conditions of the question...And thus FOR this problem..

`[Ag^+]=4.0xx10^-4*mol*L^-1`; `[Cr_2O_7^(2-)]=2.0xx10^-4`

Why is `[Ag^+]` DOUBLE that of its counterion....?

....And thus `K_"sp"=[Ag^+]^2[Cr_2O_7^(2-)]=(4.0xx10^-4)^2xx(2.0xx10^-4)=3.20xx10^-11`, the which value speaks that the stuff is VERY insoluble....