Redox Chemistry and Electrochemical Cells

Redox chemistry is the foundation for understanding how batteries power our devices, how metals corrode, and how biological systems generate energy. It revolves around the transfer of electrons between substances, a process that can be harnessed to do electrical work. Mastering this topic allows you to predict which reactions are spontaneous, calculate the voltage a cell can produce, and understand the fundamental language of electron movement.

Oxidation States and Identifying Redox Reactions

An oxidation state is a hypothetical charge an atom would have if all bonds to atoms of different elements were 100% ionic. Assigning oxidation states is the first step in analyzing any redox process. You must remember a set of rules: the oxidation state of an atom in its elemental form is 0; for monatomic ions, it equals the ion charge; oxygen is usually -2 (except in peroxides); hydrogen is +1 (except in metal hydrides); and the sum of oxidation states in a neutral compound is zero, or equals the overall charge for a polyatomic ion.

For example, in $H_{2}S{O}_4$, hydrogen is +1 and oxygen is -2. To find sulfur's state (S), you solve: $2(+1)+S+4(-2)=0$, which gives $S=+6$. This systematic approach is non-negotiable for clear analysis.

A redox reaction is any reaction where a change in oxidation state occurs. Oxidation is defined as an increase in oxidation state (loss of electrons), while reduction is a decrease in oxidation state (gain of electrons). A useful mnemonic is "OIL RIG": Oxidation Is Loss, Reduction Is Gain. In the reaction of zinc with copper ions, $Zn(s)+C{u}^{2+}(aq)\to Z{n}^{2+}(aq)+Cu(s)$, zinc's state goes from 0 to +2 (it is oxidized), while copper's goes from +2 to 0 (it is reduced). The substance that causes oxidation (here, $C{u}^{2+}$) is the oxidizing agent, and it itself is reduced. Conversely, the reducing agent (Zn) is oxidized.

Balancing Redox Half-Equations

Because redox reactions involve electron transfer, they are best understood by splitting them into two half-equations: one for oxidation and one for reduction. Balancing these equations is a critical skill. You must balance atoms and charge, using $H^{+}$ (in acidic conditions), $O{H}^{-}$ (in basic conditions), and $H_{2}O$ as needed.

Let's balance the half-equation for the reduction of dichromate(VI) ions, $C{r}_2{O}_7^{2-}$, to chromium(III) ions, $C{r}^{3+}$, in acidic solution.

1. Balance atoms other than H and O: $C{r}_2{O}_7^{2-}\to 2C{r}^{3+}$
2. Balance oxygen atoms by adding $H_{2}O$: $C{r}_2{O}_7^{2-}\to 2C{r}^{3+}+7H_{2}O$
3. Balance hydrogen atoms by adding $H^{+}$: $C{r}_2{O}_7^{2-}+14H^{+}\to 2C{r}^{3+}+7H_{2}O$
4. Balance charge by adding electrons ($e^{-}$): Calculate the charge on each side.

• Left: $(-2)+14(+1)=+12$
• Right: $2(+3)+7(0)=+6$
• To balance, add 6 electrons to the more positive side: $C{r}_2{O}_7^{2-}+14H^{+}+6e^{-}\to 2C{r}^{3+}+7H_{2}O$

The final, balanced half-equation shows that the reduction of one dichromate ion requires six electrons. The oxidation half-equation is balanced using the same principles. To form the full ionic equation, you combine the half-equations, ensuring the electrons cancel.

Electrochemical Cells and Standard Electrode Potentials

An electrochemical cell converts chemical energy into electrical energy by harnessing a spontaneous redox reaction. It consists of two half-cells, each containing a species in different oxidation states (e.g., $Z{n}^{2+}/Zn$ or $F{e}^{3+}/F{e}^{2+}$). The half-cells are connected by a wire, through which electrons flow, and a salt bridge, which maintains electrical neutrality by allowing ion migration. In a voltaic (or galvanic) cell, the reaction is spontaneous and produces a voltage.

The tendency of a half-cell to gain electrons (be reduced) is measured by its electrode potential. To compare all half-cells, we measure them under standard conditions (298 K, 100 kPa, 1.00 mol dm${}^{-3}$ solutions) against a standard hydrogen electrode (SHE), which is arbitrarily assigned a potential of 0.00 V. The standard electrode potential, $E^{\theta }$, is the voltage measured when the half-cell is connected to the SHE. A positive $E^{\theta }$ indicates a greater tendency for reduction than the $H^{+}/H_2$ couple.

For example, the $C{u}^{2+}/Cu$ half-cell has $E^{\theta }=+0.34V$. When connected to the SHE, the copper half-cell is reduced, drawing electrons from the hydrogen electrode. Conversely, the $Z{n}^{2+}/Zn$ half-cell has $E^{\theta }=-0.76V$; it has a lower tendency for reduction than $H^{+}$, so zinc is oxidized when paired with the SHE.

Using Standard Electrode Potentials

Predicting Reaction Feasibility: The feasibility of a redox reaction under standard conditions can be predicted. The half-cell with the more positive (or less negative) $E^{\theta }$ value has a greater tendency to gain electrons and undergo reduction. The other half-cell will undergo oxidation. For a reaction to be feasible (spontaneous), the electromotive force (EMF) of the cell, $E_{cell}^{\theta }$, must be positive. It is calculated as:

$$E_{cell}^{\theta }=E_{(reductionhalf-cell)}^{\theta }-E_{(oxidationhalf-cell)}^{\theta }$$

Where reduction half-cell is the one you have identified as being reduced.

Worked Example: Will acidified manganate(VII) ions oxidize chloride ions to chlorine under standard conditions?

• Reduction half-equation (Mn(VII) to Mn(II)): $Mn{O}_4^{-}+8H^{+}+5e^{-}\to M{n}^{2+}+4H_{2}O$; $E^{\theta }=+1.51V$
• Oxidation half-equation (Cl${}^{-}$ to $C{l}_2$): $2C{l}^{-}\to C{l}_2+2e^{-}$; $E^{\theta }=+1.36V$ (This is the reverse of the tabulated reduction potential for $C{l}_2/C{l}^{-}$).

The manganate(VII) half-cell has the more positive $E^{\theta }$, so it is the stronger oxidizing agent and will be reduced. The chloride half-cell will be oxidized. $$E_{cell}^{\theta }=E_{(Mn{O}_4^{-}/M{n}^{2+})}^{\theta }-E_{(C{l}_2/C{l}^{-})}^{\theta }=+1.51-(+1.36)=+0.15V$$ Since $E_{cell}^{\theta }$ is positive, the reaction is feasible. However, a crucial caveat is that standard electrode potentials indicate thermodynamic feasibility, not kinetic rate. A reaction with a positive EMF may be impractically slow without a catalyst or elevated temperature.

Common Pitfalls

1. Confusing Oxidizing/Reducing Agents: Remember, the oxidizing agent is reduced. If you see a species' oxidation state decrease, that species is the oxidizing agent. For example, in $2F{e}^{3+}+2I^{-}\to 2F{e}^{2+}+I_2$, $F{e}^{3+}$ is reduced to $F{e}^{2+}$, so it is the oxidizing agent, not the substance being oxidized.

1. Incorrectly Combining Half-Equations: A frequent error is failing to balance the number of electrons before adding half-equations. You must multiply one or both half-equations by a factor so that the electrons cancel completely. If the oxidation half produces 2 electrons and the reduction half requires 3, you need to find the lowest common multiple (6) and multiply accordingly.

1. Misinterpreting the Sign of $E^{\theta }$: A negative $E^{\theta }$ does not mean a species cannot be reduced; it means it is less likely to be reduced than $H^{+}$ under standard conditions. When predicting reactions, always use the more positive $E^{\theta }$ for reduction and the less positive (more negative) for oxidation. The formula $E_{cell}^{\theta }=E_{right}^{\theta }-E_{left}^{\theta }$ is also valid if you have correctly drawn the cell diagram.

1. Ignoring Non-Standard Conditions: $E^{\theta }$ values are for standard conditions. Changes in concentration (explained by the Nernst equation, beyond core A-Level) or pH can alter the observed EMF and even reverse the direction of a reaction's feasibility. For example, oxidizing power often increases with greater acidity.

Summary

• Oxidation states are assigned using a set of rules and are used to identify oxidation (increase in state) and reduction (decrease in state) within a reaction.
• Redox reactions are balanced by constructing and combining half-equations, ensuring both mass and charge are balanced, often using $H^{+}$, $O{H}^{-}$, and $H_{2}O$.
• An electrochemical cell consists of two half-cells connected by a wire and salt bridge; a spontaneous redox reaction generates an electrical current.
• The standard electrode potential ($E^{\theta }$) of a half-cell is measured against the Standard Hydrogen Electrode (SHE) and indicates its relative tendency to undergo reduction.
• The feasibility of a redox reaction under standard conditions is predicted by calculating the cell EMF: $E_{cell}^{\theta }=E_{(reduction)}^{\theta }-E_{(oxidation)}^{\theta }$. A positive value indicates a thermodynamically spontaneous reaction.