Question

what is the maximum concentration of ag+ that can be added to a 0.00780 m solution of na2co3 before a precipitate will form? (ksp for ag2co3 is 8.10 × 10^-12)

Explanation:

Step1: Write the solubility product expression

For \(Ag_2CO_3(s)
ightleftharpoons 2Ag^{+}(aq)+CO_3^{2 -}(aq)\), 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 \([CO_3^{2 -}]=0.007800M\) (since \(Na_2CO_3 = 2Na^{+}+CO_3^{2 -}\), and the concentration of \(CO_3^{2 -}\) is equal to the concentration of \(Na_2CO_3\)).

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 \(K_{sp}=8.10\times 10^{-12}\) and \([CO_3^{2 -}]=0.007800M\) into the formula:

$$
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$$

Step3: Calculate the value of \([Ag^{+}]\)

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

Answer:

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