Gold metal is extracted from its ore by treating the crushed rock with an aerated cyanide solution. The unbalanced equation for the reaction is (b) Use any of the following data at 25 °C to calculate ∆G° for this reaction at 25 °C: Kf for Au(CN)2- = 6.2 x 10^38, Ka for HCN = 4.9 x 10^-10, and standard reduction potentials are

Verified step by step guidance

1. Identify the balanced chemical equation for the extraction of gold using cyanide. The general form involves gold (Au), cyanide ions (CN^-), and oxygen (O2) to form the complex ion Au(CN)2^-.
2. Use the given formation constant (Kf) for Au(CN)2^- to find the standard Gibbs free energy change (∆G°) for the formation of the complex ion. The relationship is given by ∆G° = -RT ln(Kf), where R is the universal gas constant and T is the temperature in Kelvin.
3. Consider the dissociation of HCN in water, which is represented by its acid dissociation constant (Ka). Use the relationship ∆G° = -RT ln(Ka) to find the Gibbs free energy change for the dissociation of HCN.
4. Use the standard reduction potentials to calculate the standard Gibbs free energy change for the redox reactions involved. The relationship between standard reduction potential (E°) and Gibbs free energy is ∆G° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant.
5. Combine the Gibbs free energy changes from the formation of the complex ion, the dissociation of HCN, and the redox reactions to find the overall ∆G° for the extraction process. This involves summing the individual ∆G° values calculated in the previous steps.

Key Concepts

Gibbs Free Energy (∆G°)

Gibbs Free Energy (∆G°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It indicates the spontaneity of a reaction; a negative ∆G° suggests that the reaction can occur spontaneously, while a positive value indicates non-spontaneity. Understanding how to calculate ∆G° using equilibrium constants or standard reduction potentials is crucial for predicting reaction behavior.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For reactions involving complex ions, such as Au(CN)2-, the formation constant (Kf) is particularly important, as it reflects the stability of the complex in solution. The relationship between K and ∆G° is given by the equation ∆G° = -RT ln(K), linking thermodynamics and chemical equilibrium.

Standard Reduction Potentials

Standard reduction potentials (E°) are measures of the tendency of a chemical species to gain electrons and be reduced, expressed in volts. Each half-reaction has a specific E° value, and the overall cell potential can be calculated by combining these values. This concept is essential for understanding redox reactions and calculating ∆G° using the equation ∆G° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant.