Question

Calculate the standard free-energy change at 25°C for the given reaction using standard reduction electrode potentials:

3Cu(s)+2NO₃−​(aq)+8H+(aq)→3Cu₂⁺(aq)+2NO(g)+4H₂​O(l).

Answer 1

To calculate the standard free-energy change for the electrolysis reaction involving copper and nitrate ions at 25°C, the standard cell potential needs to be determined using the standard electrode potentials for the half-reactions from provided reference data, then ΔG° can be calculated using the formula ΔG° = -nFE°cell.

Step-by-step explanation:

To calculate the standard free-energy change (ΔG°) for the given reaction at 25°C, we need to use the standard reduction electrode potentials. The reaction in question is:

3Cu(s) + 2NO₃−​(aq) + 8H+(aq) → 3Cu²+​(aq) + 2NO(g) + 4H₂​O(l)

This reaction is a redox reaction involving the oxidation of copper and the reduction of nitrate ions. To find the standard cell potential (E°), we need to construct the half-reactions for oxidation and reduction and then balance them:

1. Oxidation (x3): Cu(s) → Cu²+​(aq) + 2e−
2. Reduction (x2): NO₃−​(aq) + 4H+(aq) + 3e− → NO(g) + 2H₂O(l)

To calculate E° for the full reaction, we must know the standard electrode potentials for both half-reactions. Unfortunately, the standard electrode potential data for these specific half-reactions was not provided in your question. Assuming that you can find these values in Appendix L, you would apply the following formula to find the E° for the overall reaction:

E°cell = E°cathode - E°anode

Once you have E°cell, you can calculate the ΔG° using the following equation:

ΔG° = -nFE°cell

Where 'n' is the number of moles of electrons transferred in the balanced equation, and 'F' is the Faraday constant (approximately 96485 C/mol). The negative sign indicates that a positive E°cell corresponds to a spontaneous reaction under standard conditions. If ΔG° is negative, the reaction is spontaneous; if it is positive, the reaction is non-spontaneous.