IChO 1998 · Theory problem 5

Cyanide extraction of gold

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Metallic gold frequently is found in aluminosilicate rocks and it is finely dispersed among other minerals. It may be extracted by treating the crushed rock with aerated sodium cyanide solution. During this process metallic gold is slowly converted to \(\ce{[Au(CN)2]-}\), which is soluble in water (reaction 1).

After equilibrium has been reached, the aqueous phase is pumped off and the metallic gold is recovered from it by reacting the gold complex with zinc, which is converted to \(\ce{[Zn(CN)4]^2-}\) (reaction 2).

5.1 Write balanced ionic equations for reactions (1) and (2).

Gold in nature is frequently alloyed with silver which is also oxidized by aerated sodium cyanide solution.

5.2 Five hundred litres (500 L) of a solution 0.0100 M in \(\ce{[Au(CN)2]-}\) and 0.0030 M in \(\ce{[Ag(CN)2]-}\) was evaporated to one third of the original volume and was treated with zinc (40 g). Assuming that deviation from standard conditions is unimportant and that all these redox reactions go essentially to completion, calculate the concentrations of \(\ce{[Au(CN)2]-}\) and of \(\ce{[Ag(CN)2]-}\) after reaction has ceased.

\(\ce{[Zn(CN)4]^2- + 2e- -> Zn + 4CN-}\) \(E^\circ=-1.26\ \mathrm{V}\)
\(\ce{[Au(CN)2]- + e- -> Au + 2CN-}\) \(E^\circ=-0.60\ \mathrm{V}\)
\(\ce{[Ag(CN)2]- + e- -> Ag + 2CN-}\) \(E^\circ=-0.31\ \mathrm{V}\)

5.3 \(\ce{[Au(CN)2]-}\) is a very stable complex under certain conditions. What concentration of sodium cyanide is required to keep 99 mol% of the gold in solution in the form of the cyanide complex? \(\{\ce{[Au(CN)2]-}:K_f=4\times10^{28}\}\)

5.4 There have been several efforts to develop alternative gold extraction processes which could replace this one. Why? Choose one of the options on the answer sheet.

Official English text of the problem.

Answers

  • 5.1 \[ \ce{4Au + 8CN- + O2 + 2H2O -> 4[Au(CN)2]- + 4OH-} \tag{1} \] \[ \ce{2[Au(CN)2]- + Zn -> 2Au + [Zn(CN)4]^2-} \tag{2} \]

  • 5.2 \[ \boxed{[\ce{[Au(CN)2]-}]=0.0300\ \mathrm{mol\,L^{-1}}} \] \[ \boxed{[\ce{[Ag(CN)2]-}]\approx1.7\times10^{-3}\ \mathrm{mol\,L^{-1}}} \] Silver consumes the available reducing capacity; gold remains in solution.

  • 5.3 \[ \boxed{[\ce{CN-}]_{\mathrm{free}}\approx5\times10^{-14}\ \mathrm{mol\,L^{-1}}} \] This is the equilibrium free cyanide concentration. The total analytical sodium cyanide concentration must also account for bound cyanide.

  • 5.4 Choose the option stating that cyanide is highly toxic and its use creates serious environmental and health hazards.

Solution

The molecular and ionic species used in the solution have the following names and SMILES. For coordination complexes, the SMILES use dative-bond notation, with cyanide carbon donating to the metal.

Formula Name SMILES
\(\ce{NaCN}\) Sodium cyanide [Na+].[C-]#N
\(\ce{CN-}\) Cyanide ion [C-]#N
\(\ce{[Au(CN)2]-}\) Dicyanidoaurate(I) ion N#[C-]->[Au+]<-[C-]#N
\(\ce{[Ag(CN)2]-}\) Dicyanidoargentate(I) ion N#[C-]->[Ag+]<-[C-]#N
\(\ce{[Zn(CN)4]^2-}\) Tetracyanidozincate(II) ion [Zn+2](<-[C-]#N)(<-[C-]#N)(<-[C-]#N)<-[C-]#N
\(\ce{Au+}\) Gold(I) ion [Au+]
\(\ce{O2}\) Dioxygen O=O
\(\ce{H2O}\) Water O
\(\ce{OH-}\) Hydroxide ion [OH-]

The gold(I) and silver(I) complexes are linear, with carbon-bound cyanide ligands; the zinc(II) complex is tetrahedral. These geometries are not specified by the SMILES. Elemental gold, silver and zinc have atom SMILES [Au], [Ag] and [Zn], respectively; these do not describe their metallic lattices.

5.1 — Balanced ionic equations

In reaction (1), gold is oxidized from oxidation state \(0\) to \(+1\):

\[ \ce{Au + 2CN- -> [Au(CN)2]- + e-}. \]

Oxygen from the aerated solution accepts the electrons. In alkaline solution its reduction half-equation is

\[ \ce{O2 + 2H2O + 4e- -> 4OH-}. \]

Multiplying the gold half-equation by four and adding gives

\[ \boxed{\ce{4Au + 8CN- + O2 + 2H2O -> 4[Au(CN)2]- + 4OH-}}. \]

In reaction (2), zinc is oxidized from \(0\) to \(+2\):

\[ \ce{Zn + 4CN- -> [Zn(CN)4]^2- + 2e-}. \]

Gold(I) is reduced to metallic gold:

\[ \ce{[Au(CN)2]- + e- -> Au + 2CN-}. \]

Multiplying the gold reduction by two and adding cancels both the electrons and free cyanide:

\[ \boxed{\ce{2[Au(CN)2]- + Zn -> 2Au + [Zn(CN)4]^2-}}. \]

5.2 — Concentrations after treatment with zinc

Evaporation changes the volume but preserves the amounts of dissolved metal complexes:

\[ n_{\mathrm{Au},0} =(500\ \mathrm L)(0.0100\ \mathrm{mol\,L^{-1}}) =5.00\ \mathrm{mol}, \]

\[ n_{\mathrm{Ag},0} =(500\ \mathrm L)(0.0030\ \mathrm{mol\,L^{-1}}) =1.50\ \mathrm{mol}. \]

The final solution volume is

\[ V_f=\frac{500}{3}\ \mathrm L=166.7\ \mathrm L. \]

Both complexes can be reduced by zinc:

\[ E^\circ_{\mathrm{cell,Au}} =-0.60-(-1.26)=+0.66\ \mathrm V, \]

\[ E^\circ_{\mathrm{cell,Ag}} =-0.31-(-1.26)=+0.95\ \mathrm V. \]

The silver complex has the higher reduction potential. Furthermore, any deposited gold can reduce silver complex:

\[ \ce{Au + [Ag(CN)2]- -> [Au(CN)2]- + Ag}, \]

with

\[ E^\circ_{\mathrm{cell}}=-0.31-(-0.60)=+0.29\ \mathrm V. \]

Thus, under the stipulated completion approximation, metallic gold cannot remain while appreciable silver complex remains: the available reducing capacity is used to deposit silver first.

Using \(M(\ce{Zn})=65.4\ \mathrm{g\,mol^{-1}}\),

\[ n_{\mathrm{Zn}}=\frac{40\ \mathrm g}{65.4\ \mathrm{g\,mol^{-1}}} =0.6116\ \mathrm{mol}. \]

Each mole of zinc supplies two moles of electrons, whereas each mole of silver complex requires one:

\[ \ce{Zn + 2[Ag(CN)2]- -> [Zn(CN)4]^2- + 2Ag}. \]

Consequently,

\[ n_{\mathrm{Ag\ deposited}}=2n_{\mathrm{Zn}} =1.2232\ \mathrm{mol}<1.50\ \mathrm{mol}. \]

All zinc is consumed before all the silver can be deposited. The remaining amounts are therefore

\[ n_{\mathrm{Ag},f}=1.50-1.2232=0.2768\ \mathrm{mol}, \qquad n_{\mathrm{Au},f}=5.00\ \mathrm{mol}. \]

Neglecting any volume change on adding zinc,

\[ [\ce{[Au(CN)2]-}] =\frac{5.00}{500/3} =\boxed{0.0300\ \mathrm{mol\,L^{-1}}}, \]

\[ [\ce{[Ag(CN)2]-}] =\frac{0.2768}{500/3} =1.66\times10^{-3}\ \mathrm{mol\,L^{-1}} \approx\boxed{1.7\times10^{-3}\ \mathrm{mol\,L^{-1}}}. \]

5.3 — Cyanide concentration for 99 mol% complexation

The formation equilibrium is

\[ \ce{Au+ + 2CN- <=> [Au(CN)2]-}, \]

with

\[ K_f= \frac{[\ce{[Au(CN)2]-}]} {[\ce{Au+}][\ce{CN-}]^2} =4\times10^{28}. \]

Assuming dissolved gold occurs only as free gold(I) and its dicyanido complex, a complexed fraction of \(0.99\) means

\[ \frac{[\ce{[Au(CN)2]-}]}{[\ce{Au+}]} =\frac{0.99}{0.01}=99. \]

Hence, using concentrations numerically in \(\mathrm{mol\,L^{-1}}\),

\[ [\ce{CN-}]^2=\frac{99}{4\times10^{28}}, \]

and

\[ [\ce{CN-}] =4.97\times10^{-14}\ \mathrm{mol\,L^{-1}} \approx\boxed{5\times10^{-14}\ \mathrm{mol\,L^{-1}}}. \]

This is the minimum free cyanide concentration for at least 99% complexation within this model.

A total sodium cyanide requirement also includes cyanide incorporated into complexes. For example, if gold is the only cyanide-binding species and protonation is neglected,

\[ C_{\mathrm{CN,total}} =[\ce{CN-}]+2[\ce{[Au(CN)2]-}] =[\ce{CN-}]+1.98C_{\mathrm{Au,total}}. \]

Thus the very small free cyanide concentration does not by itself specify the total sodium cyanide dose.

5.4 — Reason for seeking alternative processes

Cyanide is highly toxic. Cyanide-bearing solutions and wastes can endanger workers, contaminate water, and harm wildlife, particularly following leaks or accidental releases. These health and environmental hazards motivate alternative extraction processes.

The appropriate answer-sheet option is therefore the one identifying cyanide toxicity and its environmental consequences.

The solution was checked against the official solution.