Calculate E°_cell for each balanced redox reaction and determine if the reaction is spontaneous as written. a. 2 Cu(s) + Mn²⁺(aq) → 2 Cu⁺(aq) + Mn(s)

Verified step by step guidance

1. Identify the oxidation and reduction half-reactions. For the given reaction, copper (Cu) is oxidized from 0 to +1, and manganese (Mn) is reduced from +2 to 0.
2. Write the half-reactions separately. For oxidation: Cu(s) → Cu+(aq) + e-. For reduction: Mn2+(aq) + 2e- → Mn(s).
3. Look up the standard reduction potentials (E°) for each half-reaction in a standard reduction potential table. You will find E° for Cu+(aq) + e- → Cu(s) and Mn2+(aq) + 2e- → Mn(s).
4. Calculate the standard cell potential (Ec°ell) using the formula: Ec°ell = E°(cathode) - E°(anode). Here, the cathode is the reduction half-reaction and the anode is the oxidation half-reaction.
5. Determine if the reaction is spontaneous. If Ec°ell is positive, the reaction is spontaneous as written; if it is negative, the reaction is non-spontaneous.

Key Concepts

Standard Electrode Potential (Ec°ell)

The standard electrode potential, Ec°ell, is a measure of the tendency of a chemical species to be reduced, expressed in volts. It is determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). The overall cell potential for a redox reaction can be calculated by subtracting the reduction potential of the anode from that of the cathode.

Balancing Redox Reactions

Balancing redox reactions involves ensuring that both mass and charge are conserved. This is achieved by identifying the oxidation and reduction half-reactions, balancing the number of electrons transferred, and then combining the half-reactions to form a balanced overall equation. This step is crucial for accurately calculating the standard electrode potential.

Spontaneity of Reactions

A redox reaction is considered spontaneous if the cell potential (Ec°ell) is positive. This indicates that the reaction can occur without external energy input. The relationship between the cell potential and spontaneity is governed by the Gibbs free energy change, where a negative Gibbs free energy corresponds to a positive cell potential, confirming the reaction's spontaneity.