Problem 4

Gold Capital of Asia. Chiufen, northeast Taiwan, was one of the largest gold mines in Asia. PART A. KCN extracts gold from ore:

\ce{4Au(s) + 8CN-(aq) + O2(g) + 2H2O(l) -> 4[Au(CN)2]-(aq) + 4OH-(aq)}

. (4.A-1) State the geometry of

\ce{[Au(CN)2]-}

. (4.A-2) How many grams of KCN are needed to extract 20 g of gold? (

M(\ce{Au}) = 197

M(\ce{KCN}) = 65.12

g mol

^{-1}

.) Aqua regia (3:1 conc. HCl:

\ce{HNO3}

) dissolves gold by redox:

\ce{Au(s) + 3NO3-(aq) + 6H+(aq) + 4Cl-(aq) -> [AuCl4]-(aq) + 3NO2(g) + 3H2O(l)}

. (4.A-3) Write the half-reactions and the balanced equation. (4.A-4) Identify the oxidizing and reducing agents. (4.A-5) Given

\ce{Au^{3+} + 3e- -> Au(s)}

(

E^\circ = +1.50

V) and

\ce{[AuCl4]- + 3e- -> Au(s) + 4Cl-}

(

E^\circ = +1.00

V), calculate the formation constant

K_f = \frac{[\ce{[AuCl4]-}]}{[\ce{Au^{3+}}][\ce{Cl-}]^4}

25\ ^\circ\mathrm{C}

(

RT\ln10/F = 0.059

V). PART B. Gold nanoparticles (AuNPs). In the Brust-Schiffrin synthesis, aqueous

\ce{HAuCl4}

is phase-transferred to toluene by tetraoctylammonium bromide, dodecanethiol is added, and excess

\ce{NaBH4}

reduces Au(III) to AuNPs of controlled diameter. (4.B-1) Is this top-down or bottom-up? (4.B-3) What is the function of

\ce{NaBH4}

? (4.B-4) If the average diameter of an AuNP is 3.0 nm and the atomic radius of Au is 0.144 nm, estimate the number of Au atoms per nanoparticle. (4.B-5) Estimate the percentage of Au atoms located at the nanoparticle surface.

Step 2 of 4: Formation constant of [AuCl4]-

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E^\circ_{\text{cell}} = 1.50 - 1.00 = +0.50\ \text{V} \;\Rightarrow\; K_f = 10^{3\times0.50/0.059} = 10^{25.42} = 2.6\times10^{25}

Analysis

Combining the reduction of $\ce{Au^{3+}}$ ( $+1.50$ V) with the reverse of the reduction of $\ce{[AuCl4]-}$ ( $+1.00$ V) yields the net complexation $\ce{Au^{3+} + 4Cl- -> [AuCl4]-}$ with $E^\circ = +0.50$ V ( $n = 3$ ). At equilibrium $E = 0 = E^\circ - \frac{0.059}{3}\log(1/K_f)$ , so $K_f = 2.6\times10^{25}$ .