Problem 1

(1.1) Show that 0.1 mol of

\ce{Tl2S}

dissolves in one litre of a 1 M solution of any strong monoprotic non-coordinating acid. (1.2) Show that 0.1 mol of

\ce{CuS}

dissolves in 1 M

\ce{HNO3}

but not in 1 M

\ce{HCl}

. Data:

E^0(\ce{S/S^{2-}}) = -0.48

E^0(\ce{NO3^-/NO}) = 0.96

V; p

K_a(\ce{H2S}) = 7

; p

K_a(\ce{HS^-}) = 13

;

K_{sp}(\ce{Tl2S}) = 1\times10^{-20}

;

K_{sp}(\ce{CuS}) = 1\times10^{-35}

; solubility of

\ce{NO}

in water (298 K):

2.53\times10^{-2}

mol dm

^{-3}

. Assume that

\ce{Cu^{2+}}

does not form stable complexes with

\ce{Cl^-}

Step 1 of 4: Sulphide speciation in strong acid

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[\ce{S^{2-}}] = \frac{c(\mathrm{S})}{1 + [\ce{H+}]/K_{a2} + [\ce{H+}]^2/(K_{a1}K_{a2})} \approx \frac{c(\mathrm{S})}{10^{20}[\ce{H+}]^2}\ \xrightarrow{[\ce{H+}]=1}\ [\ce{S^{2-}}] \approx 10^{-21}\ \mathrm{mol\,dm^{-3}}

Analysis

Summing $\ce{S^{2-}} + \ce{HS^-} + \ce{H2S}$ with the two acid dissociations gives $[\ce{S^{2-}}] = c/(1 + [\ce{H+}]/K_{a2} + [\ce{H+}]^2/(K_{a1}K_{a2}))$ . At $[\ce{H+}] = 1$ M the last term ( $10^{20}$ ) dominates, so $[\ce{S^{2-}}] \approx 10^{-20}\,c$ ; for $c = 0.1$ M, $[\ce{S^{2-}}] \approx 10^{-21}$ M.