To calculate the "change in reduction potential" in the context of an electrochemical cell or reaction under standard conditions, you determine the overall standard potential difference by comparing the standard reduction potentials of the two half-reactions involved: one at the cathode (where reduction occurs) and one at the anode (where oxidation occurs).
Specifically, according to the standard definition:
The standard reduction potential for the overall reaction (or cell potential) is determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode.
This calculation gives you the standard cell potential ($E^\circ_{cell}$), which represents the potential difference between the two electrodes under standard conditions (usually 25 °C, 1 atm pressure for gases, and 1 M concentration for solutions).
Understanding the Calculation
Electrochemical reactions involve two main parts:
- Reduction: Gain of electrons, occurs at the cathode.
- Oxidation: Loss of electrons, occurs at the anode.
Each of these processes has an associated standard reduction potential ($E^\circ$). Tables of standard reduction potentials list the potential for various half-reactions written as reductions.
The overall standard cell potential ($E^\circ_{cell}$) is calculated using the formula:
$E^\circ{cell} = E^\circ{cathode} - E^\circ_{anode}$
Where:
- $E^\circ_{cell}$ is the standard cell potential (the "change" or difference in potential).
- $E^\circ_{cathode}$ is the standard reduction potential for the half-reaction occurring at the cathode.
- $E^\circ_{anode}$ is the standard reduction potential for the half-reaction occurring at the anode.
The reference explicitly states, "The minus sign is necessary because oxidation is the reverse of reduction." When you use the standard reduction potential value for the reaction at the anode, you are essentially reversing the tabulated reduction reaction to represent oxidation, and the subtraction correctly accounts for this reversal in potential sign relative to the reduction half-reaction.
Practical Steps for Calculation
Here’s how you typically perform this calculation:
- Identify the two half-reactions involved in the overall redox reaction.
- Determine which half-reaction is reduction (cathode) and which is oxidation (anode). Reduction involves gaining electrons (oxidation number decreases), while oxidation involves losing electrons (oxidation number increases).
- Look up the standard reduction potential ($E^\circ$) for both half-reactions in a standard table. Note that tables list potentials for reactions written as reductions.
- Identify $E^\circ{cathode}$ and $E^\circ{anode}$ from the values you looked up, based on which process occurs at each electrode.
- Calculate $E^\circ_{cell}$ using the formula: $E^\circ{cell} = E^\circ{cathode} - E^\circ_{anode}$.
Example
Let's consider a simple example: A cell involving Zinc (Zn) and Copper (Cu).
Suppose the reaction is: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$
- Half-reactions:
- $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
- $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
- Identify cathode and anode:
- Copper gains electrons ($Cu^{2+}$ is reduced): This is the cathode.
- Zinc loses electrons ($Zn$ is oxidized): This is the anode.
- Look up $E^\circ$ values:
- $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$ has $E^\circ = +0.34 \text{ V}$
- $Zn^{2+}(aq) + 2e^- \rightarrow Zn(s)$ has $E^\circ = -0.76 \text{ V}$
- Assign $E^\circ{cathode}$ and $E^\circ{anode}$:
- $E^\circ{cathode} = E^\circ{Cu^{2+}/Cu} = +0.34 \text{ V}$
- $E^\circ{anode} = E^\circ{Zn^{2+}/Zn} = -0.76 \text{ V}$
- Calculate $E^\circ_{cell}$:
- $E^\circ{cell} = E^\circ{cathode} - E^\circ_{anode} = (+0.34 \text{ V}) - (-0.76 \text{ V}) = +0.34 \text{ V} + 0.76 \text{ V} = +1.10 \text{ V}$
So, the standard cell potential (change in reduction potential for the system) is +1.10 V. A positive $E^\circ_{cell}$ indicates that the reaction is spontaneous under standard conditions.
Summary Table
| Component | Process | Standard Reduction Potential ($E^\circ$) Source | Role in Calculation |
|---|---|---|---|
| Cathode | Reduction | Value from table for the reduction half-reaction | $E^\circ_{cathode}$ |
| Anode | Oxidation | Value from table for the reduction half-reaction at the anode | $E^\circ_{anode}$ |
| Cell | Overall Rx | Calculated | $E^\circ{cathode} - E^\circ{anode}$ |
This method precisely calculates the standard potential difference between the reduction process at the cathode and the oxidation process at the anode, effectively quantifying the "change" in potential driving the electrochemical reaction under standard conditions.
