Finding the half-cell potential involves understanding the concept of electrochemical cells and standard reduction potentials. Here's a breakdown of the process:
Understanding Half-Cell Potentials
A half-cell potential is the voltage generated by a single half-cell, which is essentially one half of an electrochemical cell. It represents the tendency of a chemical species to be reduced (gain electrons) or oxidized (lose electrons). Since you can only measure the difference in potential between two half-cells, we use a standard reference point: the Standard Hydrogen Electrode (SHE).
Using Standard Reduction Potentials
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Standard Reduction Potential Tables: The foundation for finding half-cell potentials lies in standard reduction potential tables. These tables list half-reactions and their corresponding standard reduction potentials (E°), measured under standard conditions (298 K, 1 atm pressure, 1 M concentration). These potentials are relative to the SHE, which is assigned a value of 0.00 V. You can find these tables in chemistry textbooks or online. A good resource is the one provided by LibreTexts: LibreTexts Chemistry.
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Identifying the Half-Reactions: Determine the half-reactions occurring in the electrochemical cell. One half-reaction will involve oxidation (loss of electrons), and the other will involve reduction (gain of electrons).
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Looking Up Standard Reduction Potentials: Find the standard reduction potential (E°) for each half-reaction in the standard reduction potential table. Remember that standard reduction potentials are always written as reduction half-reactions.
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Reversing the Oxidation Half-Reaction: If a half-reaction is an oxidation (electrons are on the product side), you need to reverse the reaction as it appears in the table (which lists reduction potentials). When you reverse the reaction, you also change the sign of the standard reduction potential. So, if the reduction potential is +X V, the oxidation potential becomes -X V.
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Calculating the Cell Potential: The overall cell potential (E°cell) is calculated using the following equation:
E°cell = E°reduction - E°oxidation
Where:
- E°reduction is the standard reduction potential of the reduction half-cell.
- E°oxidation is the standard reduction potential of the oxidation half-cell (after reversing the sign).
Example:
Let's say you have an electrochemical cell with a silver (Ag) half-cell and a tin (Sn) half-cell.
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Identify Half-Reactions:
- Ag+(aq) + e- → Ag(s) (Reduction)
- Sn(s) → Sn2+(aq) + 2e- (Oxidation)
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Look Up Standard Reduction Potentials:
- E°(Ag+/Ag) = +0.80 V
- E°(Sn2+/Sn) = -0.14 V
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Reverse the Oxidation Half-Reaction: We are oxidizing Sn, so we look up the reduction half-reaction for Sn, and then reverse it and change the sign.
- Sn(s) → Sn2+(aq) + 2e- E° = +0.14 V (note the sign change)
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Calculate the Cell Potential:
E°cell = E°reduction - E°oxidation = 0.80 V - (-0.14 V) = 0.94 V
Therefore, the overall cell potential for this electrochemical cell is 0.94 V.
Important Considerations:
- Standard Conditions: Standard reduction potentials are measured under standard conditions. Changes in temperature, pressure, or concentration will affect the half-cell potential. The Nernst equation is used to calculate cell potentials under non-standard conditions.
- Nernst Equation: The Nernst equation relates the half-cell potential to the standard half-cell potential and the activities of the reactants and products. This equation is crucial for calculating cell potentials under non-standard conditions.
Summary:
Finding half-cell potentials involves using standard reduction potential tables, identifying the oxidation and reduction half-reactions, reversing the oxidation half-reaction (and changing the sign of its potential), and then calculating the overall cell potential using the formula: E°cell = E°reduction - E°oxidation. Remember to consider standard conditions and the Nernst equation for non-standard conditions.
