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Qube

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When calculating a Ksp for a salt with a significantly basic anion, e.g. silver cyanide, AgCN, given the experimental molar solubility value (s), should one write the Ksp expression as:

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{x}[/itex], where x is the fraction of the concentration cyanide ion at equilibrium with respect to s ...

or as

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{x}[HCN]^{1-x}[/itex]?

I'm thinking it's the latter because Ksp is defined as the ion concentration product and obviously when silver cyanide dissolves in water solution we get not only cyanide ion in water but also hydrocyanic acid. The first expression would be incomplete. The complete dissolution equation of AgCN is:

[itex]AgCN \leftrightharpoons Ag^{+} + (1/9)CN^{-} + (8/9)HCN[/itex]

The coefficients represent the hydrolysis of the cyanide ion factored in with the ionization of hydrocyanic acid to make more cyanide ion. Hydrolysis of the cyanide ion with molar solubility given by Wikipedia to be s = 0.00023 M is about 91%. However, about 1.7% of the HCN which is formed through cyanide ion hydrolysis ionizes to form cyanide ion again. So call "net" hydrolysis about 88%. There is approximately 1 cyanide ion to every 9 hydrocyanic acid molecules in solution. So should the Ksp therefore be:

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{1/9}[HCN]^{8/9}[/itex]?

Which, because of mass balance:

[itex] s = [Ag^{+}] = [CN^{-}] + [HCN][/itex]

is equivalent to:

[itex]K_{sp} =~~[s/9]^{1/9}[8s/9]^{8/9}[/itex]?~~

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{x}[/itex], where x is the fraction of the concentration cyanide ion at equilibrium with respect to s ...

or as

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{x}[HCN]^{1-x}[/itex]?

I'm thinking it's the latter because Ksp is defined as the ion concentration product and obviously when silver cyanide dissolves in water solution we get not only cyanide ion in water but also hydrocyanic acid. The first expression would be incomplete. The complete dissolution equation of AgCN is:

[itex]AgCN \leftrightharpoons Ag^{+} + (1/9)CN^{-} + (8/9)HCN[/itex]

The coefficients represent the hydrolysis of the cyanide ion factored in with the ionization of hydrocyanic acid to make more cyanide ion. Hydrolysis of the cyanide ion with molar solubility given by Wikipedia to be s = 0.00023 M is about 91%. However, about 1.7% of the HCN which is formed through cyanide ion hydrolysis ionizes to form cyanide ion again. So call "net" hydrolysis about 88%. There is approximately 1 cyanide ion to every 9 hydrocyanic acid molecules in solution. So should the Ksp therefore be:

[itex]K_{sp} = [Ag^{+}][CN^{-}]^{1/9}[HCN]^{8/9}[/itex]?

Which, because of mass balance:

[itex] s = [Ag^{+}] = [CN^{-}] + [HCN][/itex]

is equivalent to:

[itex]K_{sp} =

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