Question 3: Gibbs Free Energy and Cell Potential
a) Gibbs Free Energy and Reaction Spontaneity:
Explain the relationship between Gibbs free energy and spontaneity for a hydrometallurgical
reaction. If $\Delta G^\circ$ is negative for a leaching process, what does this indicate about the process?
b) Cell Potential Calculation:
For the leaching of copper using $Fe^{3+}$ as an oxidizing agent (ferric leaching), the following half-
reactions occur:
$Fe^{3+} + e^- \rightarrow Fe^{2+}$, $E^\circ = +0.77 V$
$Cu \rightarrow Cu^{2+} + 2e^-$, $E^\circ = -0.34 V$
i) Calculate the standard cell potential ($E^\circ_{cell}$) for this reaction.
ii) Use the following equation to calculate the Gibbs free energy change ($\Delta G^\circ$) for the reaction:
$\Delta G^\circ = -nFE^\circ_{cell}$
Where:
n = number of moles of electrons transferred (n = 2 for this reaction)
F = Faraday's constant (96,485 C/mol)
$E^\circ_{cell}$ = standard cell potential (in V)
iii) Interpret the result. Is this leaching reaction thermodynamically favorable?
Question 4: Eh-pH Diagrams and Reaction Kinetics
a) Eh-pH Diagrams:
Using the provided Eh-pH diagram for copper (or draw one if not provided), identify the stability
regions for $Cu^{2+}$, $Cu$, and $Cu_2O$.
i) At a pH of 2 and an Eh of 0.2 V, which copper species is most stable?
ii) Explain how an Eh-pH diagram helps in selecting the appropriate leaching conditions for
copper extraction from oxide ores.
b) Reaction Kinetics and Order of Reactions:
The leaching of nickel from pentlandite ($Ni_xFe_{1-x}S$) is carried out in an acidic solution with oxygen
as the oxidant. The reaction rate was measured as a function of the concentration of nickel in
solution. The following data were obtained for the initial rate of reaction:
[Ni] (mol/L) Rate (mol/L·s)
0.01 $1.2 \times 10^{-4}$
0.02 $2.4 \times 10^{-4}$
0.04 $4.8 \times 10^{-4}$
i) Determine the order of reaction with respect to nickel concentration.
ii) If the reaction is first-order, write the rate law for the leaching of nickel.
