Calculate E°_cell for each balanced redox reaction and determine if the reaction is spontaneous as written. b. MnO₂(aq) + 4 H⁺(aq) + Zn(s) → Mn²⁺(aq) + 2H₂O(l) + Zn²⁺(aq) c. Cl₂(g) + 2 F^–(aq) → F₂(g) + 2 Cl^–(aq)

Verified step by step guidance

1. Identify the half-reactions involved in the redox process. For the given reaction, the half-reactions are: \( \text{MnO}_2 + 4\text{H}^+ + 2e^- \rightarrow \text{Mn}^{2+} + 2\text{H}_2\text{O} \) and \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \).
2. Look up the standard reduction potentials (\( E^\circ \)) for each half-reaction from a standard reduction potential table. The reduction potential for \( \text{MnO}_2 + 4\text{H}^+ + 2e^- \rightarrow \text{Mn}^{2+} + 2\text{H}_2\text{O} \) and the oxidation potential for \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \) are needed.
3. Calculate the standard cell potential (\( E^\circ_{\text{cell}} \)) using the formula: \( E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \). Here, the cathode is the reduction half-reaction and the anode is the oxidation half-reaction.
4. Determine the spontaneity of the reaction. If \( E^\circ_{\text{cell}} > 0 \), the reaction is spontaneous as written. If \( E^\circ_{\text{cell}} < 0 \), the reaction is non-spontaneous as written.
5. Summarize the findings: State the calculated \( E^\circ_{\text{cell}} \) and whether the reaction is spontaneous or not based on the sign of \( E^\circ_{\text{cell}} \).

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). A positive Ec°ell indicates a spontaneous reaction, while a negative value suggests non-spontaneity. The overall cell potential is 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 in the reaction. This is achieved by identifying the oxidation and reduction half-reactions, balancing the atoms involved, and adjusting the electrons transferred. The balanced equation allows for accurate calculations of the standard electrode potentials and helps in determining the spontaneity of the reaction.

Spontaneity of Reactions

A reaction is considered spontaneous if it occurs without external intervention, which can be determined by the sign of the standard cell potential (Ec°ell). If Ec°ell is positive, the reaction is spontaneous as written; if negative, it is non-spontaneous. This concept is crucial in electrochemistry, as it helps predict the feasibility of redox reactions and their practical applications in batteries and electrolysis.