Final answer:
To calculate Ecell for the reaction Fe³⁺(aq) + Co(s) → Fe²⁺ (aq) + Co²⁺ (aq), the relationship ΔG = -nFEcell is used with ΔG given as 12 kJ/mol, n is 1 mole of electrons, and F is 96485 C/mol. After conversion and calculation, the Ecell is found to be -0.124 V.
Step-by-step explanation:
To calculate the Ecell of the redox reaction Fe³⁺(aq) + Co(s) → Fe²⁺ (aq) + Co²⁺ (aq), we can use the relationship between the Gibbs free energy change (ΔG) and the cell potential. The relationship is given by the equation:
ΔG = -nFEcell
Where:
- n is the number of moles of electrons transferred in the reaction,
- F is the Faraday constant (approximately 96485 C/mol), and
- Ecell is the cell potential in volts.
First, we need to determine the value of 'n'. For the given reaction, we can see that 1 mole of electrons is transferred from cobalt to iron: Fe³⁺ + e⁻ → Fe²⁺. Since the question gives us ΔG as 12 kJ/mol, we can convert this to J by multiplying by 1000, getting ΔG = 12000 J/mol.
Now we can rearrange the equation to solve for Ecell:
Ecell = -ΔG / (nF)
By substituting the known values, we get:
Ecell = -12000 J/mol / (1 mol * 96485 C/mol)
Ecell = -0.124 V
Thus, the Ecell for the reaction is -0.124 volts.