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 3 of 4: Number of Au atoms per nanoparticle

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N_{\ce{Au}} \approx \left(\frac{r_{\text{NP}}}{r_{\ce{Au}}}\right)^3 = \left(\frac{1.5\ \text{nm}}{0.144\ \text{nm}}\right)^3 \approx 1.1\times10^3\ \text{atoms}

Analysis

Approximating the volume by packed spheres, the number of gold atoms is $V_{\text{NP}}/V_{\text{atom}} = (r_{\text{NP}}/r_{\text{Au}})^3 = (1.5/0.144)^3 \approx 1.1\times10^3$ atoms (order $10^3$ ).