Question

If 2.5mL of 0.30M `AgNO_3` is mixed with 7.5mL of 0.015M `Na_2SO_4`, should a precipitate of `Ag_2SO_4` form? (Ksp = `1.2x10^-5`)

Answer 1

Quite probably.

Explanation:

We need to work out the ion product for the following reaction, under the given conditions:

`2Ag^(+) + SO_4^(2-) rightleftharpoonsAg_2SO_4(s)darr`

`Q_"the ion product"=[Ag^+]^2[SO_4^(2-)]`

And now, we must determine the individual concentrations:

`[Ag^+]` `=` `(2.5xx10^(-3)*Lxx0.30*mol*L^-1)/((2.5+7.5)xx10^-3L)` `=` `7.50xx10^-2*mol*L^-1`.

`[SO_4^(2-)]` `=` `(7.5xx10^(-3)*Lxx0.015*mol*L^-1)/((2.5+7.5)xx10^-3L)` `=` `1.13xx10^-2*mol*L^-1`.

`Q_"the ion product"=(7.50xx10^-2)^(2)(1.13xx10^-2) = 6.4xx10^-5`.

Since `Q_"the ion product"=6.4xx10^-5>K_"sp"=1.2xx10^-5`, precipitation of silver sulfate should occur until equilibrium is satisfied, and `Q=K_"sp"`

Please don't trust my arithmetic. The approach I took (I think) was sound; we had to add volumes and recalculate concentrations.

Temperature was not referred to in this question; we would assume room temperature for `K_"sp"`. At higher temperatures, how would you expect `K_"sp"` to evolve? Would solubility of silver sulfate increase or decrease?