what is the maximum concentration of ag+ that can be added to a 0.00780 m solution of na2co3 before a…

Explanation:

Step1: Write the solubility product expression

For (Ag_2CO_3(s)\rightleftharpoons 2Ag^{+}(aq)+CO_3^{2 - }(aq)), the solubility - product constant (K_{sp}=[Ag^{+}]^{2}[CO_3^{2 - }])

Step2: Substitute the known values into the (K_{sp}) expression

We know that (K_{sp}=8.10\times 10^{-12}) and ([CO_3^{2 - }]=0.00780M) (from (Na_2CO_3) which dissociates completely as (Na_2CO_3 = 2Na^{+}+CO_3^{2 - })).

From (K_{sp}=[Ag^{+}]^{2}[CO_3^{2 - }]), we can solve for ([Ag^{+}]). Rearranging the formula gives ([Ag^{+}]=\sqrt{\frac{K_{sp}}{[CO_3^{2 - }]}})

Substitute the values: ([Ag^{+}]=\sqrt{\frac{8.10\times 10^{-12}}{0.00780}})

First, calculate (\frac{8.10\times 10^{-12}}{0.00780}=1.03846\times 10^{-9})

Then ([Ag^{+}]=\sqrt{1.03846\times 10^{-9}} = 3.22\times 10^{-5}M)

Answer:

(3.22\times 10^{-5}M)