IB Chemistry: Electrochemistry HL

Electrochemistry sits at the powerful intersection of chemistry, physics, and engineering, explaining how chemical energy becomes electrical energy and vice versa. Mastering this topic is crucial for the IB Chemistry HL exam and provides the foundation for understanding everything from smartphone batteries to industrial metal extraction.

Standard Electrode Potentials: The Language of Tendency

Every redox reaction involves two halves: an oxidation and a reduction. A standard electrode potential ($E^{\theta }$) is a quantitative measure of the inherent tendency of a half-cell to undergo reduction under standard conditions. These conditions are a 1.00 mol dm⁻³ solution concentration, a gas pressure of 100 kPa, and a temperature of 298 K.

The key to using these values is the Standard Hydrogen Electrode (SHE), which is arbitrarily assigned a potential of $0.00\text{ V}$. All other half-cell potentials are measured relative to it. A positive $E^{\theta }$ indicates a stronger tendency to gain electrons (be reduced) compared to the hydrogen half-cell, while a negative value indicates a weaker tendency. It's vital to remember that these are reduction potentials. When writing a half-equation for a species with a high positive $E^{\theta }$, such as $F_2$, you write it as a reduction: $F_2(g)+2e^{-}\to 2F^{-}(aq)$ with $E^{\theta }=+2.87\text{ V}$.

Constructing and Interpreting the Electrochemical Series

By arranging half-cells in order of their standard electrode potentials, from most negative to most positive, you create the electrochemical series. This is not just a list; it's a powerful predictive tool. The series allows you to:

• Identify oxidizing and reducing agents: Species on the left (with more negative $E^{\theta }$) are stronger reducing agents (they get oxidized). Species on the right (with more positive $E^{\theta }$) are stronger oxidizing agents (they get reduced).
• Predict reaction feasibility: A redox reaction is feasible if the half-cell with the more positive (or less negative) $E^{\theta }$ undergoes reduction, and the half-cell with the more negative (or less positive) $E^{\theta }$ undergoes oxidation. In other words, the oxidizing agent must be higher on the right-hand side of the series than the reducing agent.

For example, consider zinc ($E^{\theta }(Z{n}^{2+}/Zn)=-0.76\text{ V}$) and copper ($E^{\theta }(C{u}^{2+}/Cu)=+0.34\text{ V}$). Copper(II) ions have a more positive potential, so they will act as the oxidizing agent and be reduced. Zinc has a more negative potential, so it will act as the reducing agent and be oxidized. The reaction $Zn(s)+C{u}^{2+}(aq)\to Z{n}^{2+}(aq)+Cu(s)$ is therefore feasible.

Calculating Standard Cell Potentials

A galvanic (voltaic) cell generates electrical energy from a spontaneous redox reaction. Its voltage under standard conditions is the standard cell potential ($E_{cell}^{\theta }$). The calculation is straightforward but requires careful attention to sign.

The standard cell potential is calculated by subtracting the standard electrode potential of the half-cell where oxidation occurs (the anode) from the standard electrode potential of the half-cell where reduction occurs (the cathode).

$$E_{cell}^{\theta }=E_{cathode}^{\theta }-E_{anode}^{\theta }$$

Since the cathode has the more positive $E^{\theta }$, this formula always yields a positive value for a spontaneous cell. Using the zinc-copper example: Cathode (reduction): $C{u}^{2+}(aq)+2e^{-}\to Cu(s)$ $E^{\theta }=+0.34\text{ V}$ Anode (oxidation): $Zn(s)\to Z{n}^{2+}(aq)+2e^{-}$ $E^{\theta }=-0.76\text{ V}$ $$E_{cell}^{\theta }=(+0.34)-(-0.76)=+1.10\text{ V}$$

This +1.10 V is the maximum potential difference the cell can produce under standard conditions.

Thermodynamic Feasibility and the Link to Gibbs Free Energy

The electrochemical series gives a qualitative prediction of feasibility. Cell potential provides a quantitative link to thermodynamics through the relationship with Gibbs free energy change ($\Delta G^{\theta }$). The key equation is:

$$\Delta G^{\theta }=-nF{E}_{cell}^{\theta }$$

Where:

• $\Delta G^{\theta }$ = standard Gibbs free energy change (J mol⁻¹)
• $n$ = number of moles of electrons transferred in the balanced redox equation
• $F$ = the Faraday constant ($96,500{\text{ C mol}}^{-1}$)
• $E_{cell}^{\theta }$ = standard cell potential (V)

This equation is profound:

• If $E_{cell}^{\theta }>0$, then $\Delta G^{\theta }<0$, and the reaction is spontaneous (thermodynamically feasible).
• If $E_{cell}^{\theta }<0$, then $\Delta G^{\theta }>0$, and the reaction is non-spontaneous.
• If $E_{cell}^{\theta }=0$, the system is at equilibrium ($\Delta G^{\theta }=0$).

You can use this to calculate $\Delta G^{\theta }$ from electrochemical data. For our zinc-copper cell with $E_{cell}^{\theta }=+1.10\text{ V}$ and $n=2$: $$\Delta G^{\theta }=-(2)(96500)(1.10)=-212,300{\text{ J mol}}^{-1}=-212.3{\text{ kJ mol}}^{-1}$$ The large negative value confirms the high thermodynamic feasibility of the reaction.

Practical Applications of Electrochemical Principles

Electrochemistry is not confined to the lab; its applications are ubiquitous. Two major categories are electrolysis and batteries.

• Electrolysis: This uses electrical energy to drive a non-spontaneous redox reaction ($E_{cell}<0$, $\Delta G>0$). Key industrial applications include the extraction of reactive metals like aluminum from molten $A{l}_2{O}_3$ (Hall-Héroult process) and the electroplating of objects with a thin layer of metal like chrome or silver for protection or decoration.
• Batteries (Galvanic Cells): These are designed portable sources of electricity based on spontaneous reactions ($E_{cell}>0$). A simple Daniell cell uses the Zn/Cu²⁺ reaction. More advanced systems include lithium-ion batteries, where the high reactivity (very negative $E^{\theta }$) of lithium provides a high cell potential and energy density, making it ideal for portable electronics. The principles of cell potential and the electrochemical series guide the selection of electrode materials to maximize voltage and efficiency.

Common Pitfalls

1. Confusing Sign Conventions in $E_{cell}$ Calculations: The most common error is simply adding the two half-cell potentials without considering which is the anode. Always identify the cathode (reduction, higher $E^{\theta }$) and anode (oxidation, lower $E^{\theta }$) and use $E_{cell}^{\theta }=E_{cathode}^{\theta }-E_{anode}^{\theta }$. This automatically handles the signs correctly.

1. Misapplying the Electrochemical Series for Feasibility: Remember, feasibility is determined by the combination of two half-cells. A species with a very positive $E^{\theta }$ is a strong oxidizing agent, but it will only oxidize a species that is lower in the series (a stronger reducing agent). Do not look at single values in isolation.

1. Forgetting the Effect of Non-Standard Conditions: The Nernst equation (covered in more depth in the syllabus) shows that cell potential changes with concentration. A reaction predicted to be feasible under standard conditions ($1{\text{ mol dm}}^{-3}$) may not proceed if concentrations are drastically different. Always note that $E^{\theta }$ predictions assume standard conditions.

1. Neglecting the Role of n in $\Delta G$ Calculations: In the equation $\Delta G^{\theta }=-nF{E}_{cell}^{\theta }$, $n$ must be the moles of electrons transferred as written in the balanced redox equation for the cell reaction. Using an incorrect $n$ (e.g., using 1 for the Zn/Cu reaction when it should be 2) will give a $\Delta G$ value that is off by a factor of two.

Summary

• Standard electrode potential ($E^{\theta }$) measures the tendency of a half-cell to be reduced relative to the Standard Hydrogen Electrode (0.00 V). Positive values indicate a strong tendency for reduction.
• The electrochemical series orders half-cells by $E^{\theta }$ and allows you to predict the direction of redox reactions and identify strong oxidizing/reducing agents.
• Standard cell potential ($E_{cell}^{\theta }$) for a spontaneous galvanic cell is calculated using $E_{cell}^{\theta }=E_{cathode}^{\theta }-E_{anode}^{\theta }$, and always results in a positive voltage.
• Gibbs free energy and cell potential are directly linked by $\Delta G^{\theta }=-nF{E}_{cell}^{\theta }$. A positive $E_{cell}$ indicates a negative $\Delta G$ and a spontaneous reaction.
• Practical applications include electrolysis (forcing non-spontaneous reactions, e.g., aluminum extraction) and batteries (harnessing spontaneous reactions, e.g., lithium-ion cells).