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Question: What mass of \(AgI\) will dissolve in \(1.0L\) of \(1.0M\) \(N{H_3}\) ? Neglect change in conc. of \...

What mass of AgIAgI will dissolve in 1.0L1.0L of 1.0M1.0M NH3N{H_3} ? Neglect change in conc. of NH3−NH_3^ - [ Given: Ksp(AgI){K_{sp}}(AgI) =1.5×10−16 = 1.5 \times {10^{ - 16}} ; Kf[Ag(NH3)2+]=1.6×107]{K_f}[Ag(N{H_3})_2^ + ] = 1.6 \times {10^7}]
(At Wt =108;I=127 = 108;I = 127 )

Explanation

Solution

The equilibrium constant for the dissolution of a solid substance into an aqueous solution is the solubility product constant. The symbol Ksp{K_{sp}} is used to represent it. When 1.00 mole of a nonvolatile nonionizing solute dissolves in one kilogram of solvent is called Kf{K_f}(molal freezing point depression constant). It represents how many degrees the freezing point of the solvent changes.
Formula used:
Keq=Ksp×Kf{K_{eq}} = {K_{sp}} \times {K_f}
Keq{K_{eq}}= Equilibrium constant
Ksp{K_{sp}} = Solubility product
Kf{K_f} = Molal freezing point depression constant

Complete answer:
Given: Ksp(AgI){K_{sp}}(AgI) =1.5×10−16 = 1.5 \times {10^{ - 16}}
Kf[Ag(NH3)2+]=1.6×107{K_f}[Ag(N{H_3})_2^ + ] = 1.6 \times {10^7}
To find: Mass of AgIAgI that will dissociate
Now,
AgI(s)⇌Ag+(aq)+I−(aq)AgI(s) \rightleftharpoons A{g^ + }(aq) + {I^ - }(aq)
Ag+(aq)+2NH3(aq)⇌Ag(NH3)2+(aq)A{g^ + }(aq) + 2N{H_3}(aq) \rightleftharpoons Ag(N{H_3})_2^ + (aq)
The overall reaction is as follows:
AgI+2NH3⇌Ag(NH3)2++I−AgI + 2N{H_3} \rightleftharpoons Ag(N{H_3})_2^ + + {I^ - }
The substituted values of equilibrium are as follows:
AgI(s)+2NH3(aq)AgI(s) + 2N{H_3}(aq) =1−x = 1 - x
Ag(NH3)2Ag{(N{H_3})_2} =x = x
I−(aq){I^ - }(aq) =x = x
Therefore,
Keq=Ksp×Kf{K_{eq}} = {K_{sp}} \times {K_f}
Ksp×Kf=x212{K_{sp}} \times {K_f} = \dfrac{{{x^2}}}{{{1^2}}}
1.5×10−16×1.6×107=x21.5 \times {10^{ - 16}} \times 1.6 \times {10^7} = {x^2}
x=4.9×10−5molL−1x = 4.9 \times {10^{ - 5}}mol{L^{ - 1}}
Mass of AgIAgI required =4.9×10−5×= 4.9 \times {10^{ - 5}} \times Molecular mass of AgIAgI
Mass of AgIAgI required =4.9×10−5×235 = 4.9 \times {10^{ - 5}} \times 235
Mass of AgIAgI required =0.011g = 0.011g
And hence the required mass of AgI will be 0.11g.

Additional information: The equilibrium constant (Keq{K_{eq}}) for a solid material dissolving in an aqueous solution is the solubility product constant, Ksp{K_{sp}} . It denotes the concentration at which a substance dissolves in water. The greater the Ksp{K_{sp}} value of a material, the more soluble it is. The following are some major elements that influence the solubility product constant: The action of the common ion (the presence of a common ion lowers the value of Ksp{K_{sp}}). The ion-diversity effect (if the ions of the solutes are uncommon, the value of Ksp{K_{sp}} will be high). There are ion-pairs present.

Note:
The solubility product is a type of equilibrium constant whose value is temperature dependent. Due to increasing solubility, Ksp{K_{sp}} normally rises as the temperature rises. Ksp{K_{sp}} is used to describe solutes that are just slightly soluble in solution and do not entirely dissolve. Ksp{K_{sp}} is the amount of solute that will dissolve in solution.