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Auto Protolysis of Water

A recent inve...

Question

A recent investigation of the complexation of $S C N^{-}$ with $F e^{3 +}$ led of $130, 16$ and $1.0$ for $K_{1}, K_{2}$ and $K_{3}$ , respectively. What is the overall formation constant of $F e (S C N)_{3}$ from its component ions, and what is the dissociation constant of $F e (S C N)_{3}$ into its simplest ions on the basis of these data?

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Solution

${F e}^{3 +} (a q) + {S C N}^{-} (a q) ⇌ {[F e (S C N)]}^{2 +} (a q)$
$∴$ $K_{1} = \frac{C_{{[F e (S C N)]}^{2 +}}}{C_{{F e}^{3 +}} . C_{{S C N}^{-}}}$
${[F e (S C N)]}^{2 +} + {S C N}^{-} ⇌ {[F e {(S C N)}_{2}]}^{+}$
$K_{2} = \frac{C_{{[F e {(S C N)}_{2}]}^{+}}}{C_{{[F e (S C N)]}^{2 +}} . C_{{S C N}^{-}}}$
Similarly, $K_{3} = \frac{C_{[F e {(S C N)}_{3}]}}{C_{{[F e {(S C N)}_{2}]}^{+}} . C_{{S C N}^{-}}}$
now, ${F e}^{3 +} (a q) + 3 {S C N}^{-} (a q) ⇌ {F e (S C N)}_{3}$
$K = \frac{C_{{F e (S C N)}_{3}}}{C_{{F e}^{3 +}} . C_{{S C N}^{-}}^{3}}$
$= \frac{C_{{F e (S C N)}_{3}}}{C_{{[F e {(S C N)}_{2}]}^{+}} \times C_{{S C N}^{-}}} \times \frac{C_{{[F e {(S C N)}_{2}]}^{+}}}{C_{{[F e (S C N)]}^{2 +}} \times C_{{S C N}^{-}}} \times \frac{C_{{[F e (S C N)]}^{2 +}}}{C_{{F e}^{3 +}} \times C_{{S C N}^{-}}}$
$= K_{1} \times K_{2} \times K_{3}$
$∴$ The dissociation constant of ${F e (S C N)}_{3}$ into its simplest ions, i.e, $K = \frac{C_{{F e (S C N)}_{3}}}{C_{{F e}^{2 +}} . C_{{S C N}^{-}}^{3}}$

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A recent investigation of the complexation of SCN− with Fe3+ led of 130,16 and 1.0 for K1,K2 and K3, respectively. What is the overall formation constant of Fe(SCN)3 from its component ions, and what is the dissociation constant of Fe(SCN)3 into its simplest ions on the basis of these data?