A 0.125-M solution of Mn(NO3)2 is saturated with H2 S([H2 S]=0.10 M) . At what pH does MnS begin

step 1 Hello, everyone. This is Ricky, and today we're working on problem number 99. So we have to calc

A 0.125-M solution of Mn(NO3)2 is saturated with H2 S([H2...

A $0.125-M$ solution of $\mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2}$ is saturated with $\mathrm{H}_{2} \mathrm{S}\left(\left[\mathrm{H}_{2} \mathrm{S}\right]=0.10 \mathrm{M}\right) .$ At what pH does MnS begin to precipitate? $$ \operatorname{Mn} S(s) \rightleftharpoons \operatorname{Mn}^{2+}(a q)+S^{2-}(a q) \quad K_{\mathrm{sp}}=4.3 \times 10^{-22} $$ $$ \mathrm{H}_{2} \mathrm{S}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{S}^{2-(a q)} \qquad K=1.0 \times 10^{-26} $$

A $0.125-M$ solution of $\mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2}$ is saturated with $\mathrm{H}_{2} \mathrm{S}\left(\left[\mathrm{H}_{2} \mathrm{S}\right]=0.10 \mathrm{M}\right) .$ At what pH does MnS begin to precipitate?
$$
\operatorname{Mn} S(s) \rightleftharpoons \operatorname{Mn}^{2+}(a q)+S^{2-}(a q) \quad K_{\mathrm{sp}}=4.3 \times 10^{-22}
$$
$$
\mathrm{H}_{2} \mathrm{S}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{S}^{2-(a q)} \qquad K=1.0 \times 10^{-26}
$$

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Key Concepts

pH and Ion Speciation

The pH of a solution determines the speciation of certain ions, especially when they originate from weak acids or bases. As pH changes, the balance between different forms of an ion shifts, significantly impacting reactions like precipitation where the concentration of a particular ion is critical.

Coupled Equilibria

Coupled equilibria occur when two or more equilibrium reactions share a common species. The equilibrium position of one reaction can affect the other. In such systems, changes in pH due to acid-base reactions can shift the balance in a precipitation equilibrium by altering the concentration of an ion common to both processes.

Solubility Product (Ksp)

The solubility product constant defines the equilibrium between a sparingly soluble solid and its ions in solution. It specifies the maximum product of the ion concentrations before precipitation occurs. In precipitation reactions, if the product of the ion concentrations exceeds the Ksp, the salt will begin to precipitate.

Acid-Base Equilibrium

Acid-base equilibria describe how acids and bases ionize in solution. In systems where weak acids or bases are present, the degree of ionization is pH-dependent, meaning that the actual concentration of reactive species (such as anions from a weak acid) changes with pH.

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