Cell Potential (Standard Conditions)

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Core Concept

Cell potential (EcellE_{\text{cell}}Ecell​) is the voltage produced by a voltaic cell due to the spontaneous redox reaction occurring in the cell.

Unit: Volts (V\text{V}V).

Standard Conditions:

  • Temperature: 25∘C25^\circ \text{C}25∘C (298 K298 \, \text{K}298K).

  • Pressure: 1 atm1 \, \text{atm}1atm for gases.

  • Concentration: 1.0 M1.0 \, \text{M}1.0M for solutions.

Practice Tips

  • Ecell°​ determines whether a redox reaction is spontaneous.

  • Use the standard reduction potential table to calculate Ecell°​.

  • A positive Ecell°​ indicates a reaction that can generate electric current, while a negative value means it requires external energy.

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The Standard Cell Potential (Ecell∘E^\circ_{\text{cell}}Ecell∘​)

  • Represents the cell potential under standard conditions.

  • Calculated using the reduction potentials of the half-reactions at the cathode and anode: Ecell∘=Ecathode∘−Eanode∘E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}Ecell∘​=Ecathode∘​−Eanode∘​

  • Ecathode∘E^\circ_{\text{cathode}}Ecathode∘​: Standard reduction potential of the reduction half-reaction.

  • Eanode∘E^\circ_{\text{anode}}Eanode∘​: Standard reduction potential of the oxidation half-reaction.

Interpreting Cell Potential

  • Ecell∘>0E^\circ_{\text{cell}} > 0Ecell∘​>0: The reaction is spontaneous, and the cell can generate an electric current.

  • Ecell∘=0E^\circ_{\text{cell}} = 0Ecell∘​=0: The cell is at equilibrium, and no net current flows.

  • Ecell∘<0E^\circ_{\text{cell}} < 0Ecell∘​<0: The reaction is non-spontaneous, and an external voltage is required for it to occur (as in an electrolytic cell).

Significance of Standard Reduction Potentials

  • The standard reduction potential (E∘E^\circE∘) measures the tendency of a species to gain electrons (be reduced).

  • Higher E∘E^\circE∘: Stronger oxidizing agent (e.g., F2\text{F}_2F2​, +2.87 V+2.87 \, \text{V}+2.87V).

  • Lower E∘E^\circE∘: Stronger reducing agent (e.g., Li (s)\text{Li (s)}Li (s), −3.04 V-3.04 \, \text{V}−3.04V).

Steps to Calculate Ecell∘E^\circ_{\text{cell}}Ecell∘​

  1. Write the Half-Reactions:

    • Identify the oxidation and reduction half-reactions.

  2. Find Standard Reduction Potentials (E∘E^\circE∘):

    • Use a standard reduction potential table.

  3. Assign Electrode Roles:

    • Cathode: The site of reduction (Ecathode∘E^\circ_{\text{cathode}}Ecathode∘​).

    • Anode: The site of oxidation (Eanode∘E^\circ_{\text{anode}}Eanode∘​).

  4. Apply the Formula:

    Ecell∘=Ecathode∘−Eanode∘E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}Ecell∘​=Ecathode∘​−Eanode∘​

Example Calculation

Reaction:

Zn (s)+Cu2+(aq)→Zn2+(aq)+Cu (s)\text{Zn (s)} + \text{Cu}^{2+} (aq) \rightarrow \text{Zn}^{2+} (aq) + \text{Cu (s)}Zn (s)+Cu2+(aq)→Zn2+(aq)+Cu (s)

Steps:

  1. Write Half-Reactions:

    • Oxidation (Anode): Zn (s)→Zn2+(aq)+2e−\text{Zn (s)} \rightarrow \text{Zn}^{2+} (aq) + 2e^-Zn (s)→Zn2+(aq)+2e−, E∘=−0.76 VE^\circ = -0.76 \, \text{V}E∘=−0.76V.

    • Reduction (Cathode): Cu2+(aq)+2e−→Cu (s)\text{Cu}^{2+} (aq) + 2e^- \rightarrow \text{Cu (s)}Cu2+(aq)+2e−→Cu (s), E∘=+0.34 VE^\circ = +0.34 \, \text{V}E∘=+0.34V.

  2. Calculate Ecell∘E^\circ_{\text{cell}}Ecell∘​:

    Ecell∘=Ecathode∘−Eanode∘E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}Ecell∘​=Ecathode∘​−Eanode∘​ Ecell∘=+0.34 V−(−0.76 V)=+1.10 VE^\circ_{\text{cell}} = +0.34 \, \text{V} - (-0.76 \, \text{V}) = +1.10 \, \text{V}Ecell∘​=+0.34V−(−0.76V)=+1.10V

Conclusion:

  • The positive Ecell∘E^\circ_{\text{cell}}Ecell∘​ indicates a spontaneous reaction.

Significance of Standard Reduction Potentials

  • The standard reduction potential (E∘E^\circE∘) measures the tendency of a species to gain electrons (be reduced).

  • Higher E∘E^\circE∘: Stronger oxidizing agent (e.g., F2\text{F}_2F2​, +2.87 V+2.87 \, \text{V}+2.87V).

  • Lower E∘E^\circE∘: Stronger reducing agent (e.g., Li (s)\text{Li (s)}Li (s), −3.04 V-3.04 \, \text{V}−3.04V).

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