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 4 of 4: Surface atom fraction

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P_{\text{surface}} = \frac{V(r) - V(r - 2r_{\ce{Au}})}{V(r)} = 1 - \left(\frac{1.5 - 0.288}{1.5}\right)^3 = 1 - 0.808^3 = 47\% \approx 40\text{--}50\%

Analysis

The surface atoms form an outer shell of thickness one atomic diameter ( $2r_{\ce{Au}} = 0.288$ nm). The shell volume fraction is $1 - ((1.5 - 0.288)/1.5)^3 \approx 47\%$ , putting the answer in the 40–50 % range (choice b).