Question

Sodium sulfate is slowly added to a solution containing 0.0500 M Ca 2 + ( aq ) and 0.0390 M Ag + ( aq ) . What will be the concentration of Ca 2 + ( aq ) when Ag 2 SO 4 ( s ) begins to precipitate?

Answer 1

The given question is incomplete. The complete question is as follows.

Sodium sulfate is slowly added to a solution containing 0.0500 M
`Ca^(2+)(aq)` and 0.0390 M
`Ag^(+)(aq)`. What will be the concentration of
`Ca^(2+)`(aq) when
`Ag_(2)SO_(4)(s)` begins to precipitate? What percentage of the
`Ca^(2+)(aq)` can be separated from the Ag(aq) by selective precipitation?

Step-by-step explanation:

The given reaction is as follows.

`Ag_(2)SO_(4) \rightleftharpoons 2Ag^(+) + SO^(2-)_(4)`

`[Ag^(+)]` = 0.0390 M

When
`Ag_(2)SO_(4)` precipitates then expression for
`K_(sp)` will be as follows.

`K_(sp) = [Ag^(+)]^(2)[SO^(2-)_(4)]`

`1.20 * 10^(-5) = (0.0390)^(2) * [SO^(2-)_(4)]`

`[SO^(2-)_(4)]` = 0.00788 M

Now, equation for dissociation of calcium sulfate is as follows.

`CaSO_(4) \rightleftharpoons Ca^(2+) + SO^(2-)_(4)`

`K_(sp) = [Ca^(2+)][SO^(2-)_(4)]`

`4.93 * 10^(-5) = [Ca^(2+)] * 0.00788`

`[Ca^(2+)]` = 0.00625 M

Now, we will calculate the percentage of
`Ca^(2+)` remaining in the solution as follows.

`(0.00625)/(0.05) * 100`

= 12.5%

And, the percentage of
`Ca^(2+)` that can be separated is as follows.

100 - 12.5

= 87.5%

Thus, we can conclude that 87.5% will be the concentration of
`Ca^(2+)(aq)` when
`Ag_(2)SO_(4)(s)` begins to precipitate.