Reduction potential quantifies a chemical species’ inherent inclination to acquire electrons. This tendency to be reduced is expressed in volts and indicates how strongly a substance acts as an oxidizing agent. Understanding this potential is foundational for predicting the direction and energy output of electrochemical processes, such as those that occur in batteries or biological electron transport chains. Calculating reduction potential allows scientists to determine which reactions are spontaneous.
Understanding Standard Reduction Potential
To establish a common point of reference, reduction potentials are measured under defined standard conditions. These conditions mandate that all dissolved species have a concentration of 1 molar (M), all gases are at a pressure of 1 atmosphere (atm), and the temperature is maintained at 25 degrees Celsius (298 Kelvin). The resulting value is known as the Standard Reduction Potential, symbolized as \(E^\circ\).
All measured \(E^\circ\) values are relative to the Standard Hydrogen Electrode (SHE), which is the universally accepted zero point. The SHE involves the reduction of hydrogen ions to hydrogen gas, and its standard potential is arbitrarily assigned a value of 0.00 volts.
Calculating Potential for Standard State Reactions
Calculating the potential for a complete electrochemical cell under standard conditions requires combining two half-reactions: one reduction (gain of electrons) and one oxidation (loss of electrons). The half-reaction with the more positive \(E^\circ\) value proceeds as the reduction, occurring at the cathode. The half-reaction with the less positive \(E^\circ\) value is reversed to become the oxidation process at the anode. The Standard Cell Potential (\(E^\circ_{cell}\)) is calculated by subtracting the standard potential of the oxidation half-reaction from the reduction half-reaction: \(E^\circ_{cell} = E^\circ_{reduction} – E^\circ_{oxidation}\).
For example, if one half-reaction has a potential of \(+0.80\) V and the other has \(+0.34\) V, the \(+0.80\) V reaction is the reduction (cathode). The cell potential is calculated as \(0.80 \text{ V} – 0.34 \text{ V}\), yielding an \(E^\circ_{cell}\) of \(+0.46\) V. A positive \(E^\circ_{cell}\) value indicates that the overall reaction is spontaneous and generates a current under standard conditions.
Determining Potential Under Non-Standard Conditions
In real-world applications, concentrations and temperatures rarely remain at standard state values, causing the cell potential to deviate from \(E^\circ_{cell}\). The Nernst Equation is used to calculate the actual cell potential (\(E_{cell}\)) under these non-standard conditions. This equation mathematically accounts for the changes in concentration and temperature that affect the cell’s driving force.
The full form of the Nernst Equation is \(E_{cell} = E^\circ_{cell} – \frac{RT}{nF} \ln Q\). The term \(\frac{RT}{nF} \ln Q\) represents the correction factor for non-standard conditions. \(R\) is the universal gas constant (\(8.314 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}\)), and \(T\) is the absolute temperature in Kelvin. \(n\) is the number of moles of electrons transferred, and \(F\) is Faraday’s constant (\(96,485 \text{ C} \cdot \text{mol}^{-1}\)).
The variable \(Q\) is the Reaction Quotient, calculated by taking the ratio of product concentrations to reactant concentrations, raised to their stoichiometric coefficients. If the temperature is \(25^\circ \text{C}\), the equation can be simplified to \(E_{cell} = E^\circ_{cell} – \frac{0.0592 \text{ V}}{n} \log Q\). This simplified form allows for a more direct calculation using the base-10 logarithm.
As a reaction progresses, reactant concentrations decrease and product concentrations increase, causing the value of \(Q\) to rise steadily. This increase in \(Q\) makes the subtraction term of the Nernst equation larger, which causes the cell potential (\(E_{cell}\)) to decrease. Eventually, when the system reaches equilibrium, \(E_{cell}\) becomes zero.
Relating Reduction Potential to Reaction Energy
The calculated cell potential (\(E_{cell}\)) has a direct link to the thermodynamics of the reaction through Gibbs Free Energy (\(\Delta G\)). Gibbs Free Energy measures the maximum amount of non-expansion work that can be extracted from a closed system. This relationship is defined by the equation \(\Delta G = -nFE_{cell}\).
The negative sign ensures that a positive cell potential (\(E_{cell} > 0\)) corresponds to a negative change in Gibbs Free Energy (\(\)\Delta G < 0[/latex]), which is the condition for a spontaneous process. Conversely, a non-spontaneous reaction requiring energy input will have a negative [latex]E_{cell}[/latex] and a positive [latex]\Delta G[/latex]. The [latex]\Delta G[/latex] value derived from the cell potential represents the theoretical maximum electrical work obtainable from the electrochemical cell.