Final answer:
The standard free energy change for the reaction is calculated using the standard cell potential obtained from standard reduction potentials. The formula ΔG° = -nFE°cell is used with the value of E°cell = 0.03 V and n = 2, resulting in ΔG° = -5.7891 kJ.
Step-by-step explanation:
To calculate the standard free energy change (ΔG°) for the reaction 2Cr³+(aq) + Fe(s) → 2Cr²+(aq) + Fe²+(aq) using standard reduction potentials, we first need to write out the half-reactions and determine their respective standard potentials (E°) from a standard reduction potential table.
For the oxidation half-reaction (Fe(s) → Fe²+(aq) + 2e⁻), we would use the standard potential for the reduction of Fe²+ to Fe which needs to be reversed to reflect oxidation.
For the reduction half-reaction (Cr³+(aq) + e⁻ → Cr²+(aq)), we use the standard potential as is since it reflects the reduction.
If we are given the values:
- E°(Fe²+/Fe) = -0.44 V (must be reversed)
- E°(Cr³+/Cr²+) = -0.41 V
Then the total cell potential (E°cell) is calculated by subtracting the standard potential of the anode (oxidation) from the cathode (reduction):
E°cell = E°(cathode) - E°(anode)
E°cell = (-0.41 V) - (-0.44 V) = 0.03 V
Once E°cell is determined, we can use the formula ΔG° = -nFE°cell to find the standard free energy change, where n is the number of moles of electrons transferred (which is 2 in this case) and F is Faraday's constant (96485 C/mol).
ΔG° = -2 mol × 96485 C/mol × 0.03 V
ΔG° = -5789.1 J (which is 5.7891 kJ)
Therefore, the standard free energy change for the given reaction is -5.7891 kJ, indicating that the reaction is spontaneous at standard conditions.