17.3 Electrode and Cell Potentials

Electrochemistry Fundamentals

Electrode and cell potentials let you predict whether a redox reaction will happen on its own and how much voltage an electrochemical cell can produce. These concepts are the foundation for understanding batteries, corrosion, and electroplating.

Electrode and Cell Potentials

Electrode potential measures how strongly a chemical species tends to gain electrons (be reduced). There's no way to measure a single electrode's potential in isolation, so all values are measured relative to the standard hydrogen electrode (SHE), which is assigned a potential of exactly 0 V.

• A species with a more positive reduction potential has a stronger tendency to gain electrons.
• A species with a more negative reduction potential would rather lose electrons (be oxidized).

Cell potential ($E_{cell}$) is the voltage produced by an electrochemical cell. You calculate it by subtracting the anode's standard reduction potential from the cathode's:

$E_{cell} = E_{cathode} - E_{anode}$

Both values in this equation are standard reduction potentials from a reference table. You don't need to flip the sign of the anode value before plugging it in; the subtraction handles that for you.

• A positive $E_{cell}$ means the reaction is spontaneous.
• A negative $E_{cell}$ means it's non-spontaneous.

Parts of an Electrochemical Cell

An electrochemical cell has two half-cells, each with an electrode sitting in an electrolyte solution.

• Anode: where oxidation occurs (electrons leave)
• Cathode: where reduction occurs (electrons arrive)
• Electrons flow from anode to cathode through an external wire.
• A salt bridge connects the two solutions and allows ions to migrate, keeping each half-cell electrically neutral.

A galvanic (voltaic) cell is the type that produces electricity from a spontaneous redox reaction. This is how a standard battery works.

Oxidant vs. Reductant Strengths

The standard reduction potential table doubles as a ranking of oxidizing and reducing strength.

• Stronger oxidizing agents have more positive reduction potentials. For example, $F_2$ sits near the top of the table because fluorine very readily gains electrons.
• Stronger reducing agents have more negative reduction potentials. Alkali metals like lithium and sodium sit near the bottom because they easily give up electrons.

The key prediction rule: a species with a higher reduction potential will oxidize a species with a lower reduction potential. The species being oxidized acts as the reducing agent and becomes the anode in a galvanic cell.

Calculating Cell Potentials and Predicting Spontaneity

Standard Cell Potential Calculations

Standard conditions means 25°C, all solution concentrations at 1 M, and all gas pressures at 1 atm. Under these conditions, you use standard reduction potentials ($E°$) from a table.

Step-by-step method:

1. Write out the two half-reactions in their reduction form (as they appear in the table).
2. Identify which species gets reduced (cathode) and which gets oxidized (anode). The one with the higher reduction potential is the cathode.
3. Plug both standard reduction potentials into the formula:

$E°_{cell} = E°_{cathode} - E°_{anode}$

Example: Suppose you have a cell with $Cu^{2+}/Cu$ ($E°= +0.34 \text{ V}$) and $Zn^{2+}/Zn$ ($E° = -0.76 \text{ V}$).

• Copper has the higher reduction potential, so it's the cathode.
• Zinc is the anode.
• $E°_{cell} = (+0.34) - (-0.76) = +1.10 \text{ V}$

The positive result confirms this reaction is spontaneous.

Interpreting the sign of $E°_{cell}$:

• $E°_{cell} > 0$: spontaneous under standard conditions
• $E°_{cell} < 0$: non-spontaneous under standard conditions
• $E°_{cell} = 0$: the system is at equilibrium

The Nernst Equation

Real cells rarely operate under perfect standard conditions. The Nernst equation adjusts the cell potential for non-standard concentrations and temperatures:

$E_{cell} = E°_{cell} - \frac{RT}{nF} \ln Q$

• $R$ = gas constant (8.314 J/mol·K)
• $T$ = temperature in Kelvin
• $n$ = number of electrons transferred in the balanced equation
• $F$ = Faraday's constant (96,485 C/mol)
• $Q$ = reaction quotient (same form as the equilibrium expression, but using current concentrations)

At 25°C, this simplifies to a form you'll often see:

$E_{cell} = E°_{cell} - \frac{0.0257}{n} \ln Q$

As $Q$ increases (more products accumulate), the cell potential decreases. When $Q = K$ (equilibrium), $E_{cell} = 0$ and the cell is "dead."

Electrochemistry Applications

These principles show up in real-world technology:

• Batteries are galvanic cells. The cell potential determines the voltage rating. A higher $E°_{cell}$ means a higher-voltage battery.
• Fuel cells continuously convert chemical energy (often from hydrogen) into electrical energy.
• Electroplating uses an external voltage to force a non-spontaneous reaction, depositing a thin metal coating onto a surface.

Understanding electrode potentials helps you predict which reactions will generate useful energy and which ones require energy input to proceed.