Question

What is the standard free energy change at 25∘C?

Cu₂⁺(aq)+Zn(s)⟶Cu(s)+Zn₂⁺(aq)
anode (oxidation): Zn(s)⟶Zn₂⁺(aq)+2e−E∘Zn₂⁺/Zn=−0.76
Vcathode (reduction): Cu₂⁺(aq)+2e⁻⟶Cu(s)E∘Cu₂⁺/Cu=0.34V

Select the correct answer below:
a. -106 kJ/mol
b. 106.1 kJ/mol
c. 213.3 kJ/mol
d. -212.3 kJ/mol

Answer 1

The standard free energy change (ΔG°) for the cell reaction at 25°C is calculated using the standard cell potential (E°cell) and the formula ΔG° = -nFE°cell, resulting in -212.3 kJ/mol.

Step-by-step explanation:

To calculate the standard free energy change (ΔG°) for the given cell reaction at 25°C, we first need to find the standard cell potential (E°cell). We do this by subtracting the standard reduction potential of the anode reaction, Zn(s) → Zn2+(aq) + 2e- (E°Zn2+/Zn = -0.76 V), from the standard reduction potential of the cathode reaction, Cu2+(aq) + 2e- → Cu(s) (E°Cu2+/Cu = 0.34 V).

E°cell = E°cathode - E°anode = 0.34 V - (-0.76 V) = 1.10 V

Now that we have E°cell, we use the following relationship to calculate ΔG°:

ΔG° = -nFΔE°cell

where n is the number of moles of electrons transferred in the reaction (n = 2 for this reaction) and F is the Faraday constant (F = 96485 C/mol).

ΔG° = -(2 mol)(96485 C/mol)(1.10 V)

ΔG° = -212,267 J/mol or -212.3 kJ/mol

Therefore, the correct answer is: d. -212.3 kJ/mol.