17.2 Galvanic Cells

Galvanic cells convert chemical energy into electrical energy through spontaneous redox reactions. They're one of the most practical topics in electrochemistry because they explain how batteries work. This section covers the components of a galvanic cell, how to read and write cell notation, and the difference between active and inert electrodes.

A galvanic cell has two half-cells, each containing an electrode dipped in an electrolyte solution. The two half-cells are connected by a salt bridge, and electrons flow from the anode to the cathode through an external wire. The key thing to remember: oxidation always happens at the anode, and reduction always happens at the cathode.

Galvanic Cell Components and Function

Components of galvanic cells

Each part of a galvanic cell has a specific job. Here's a breakdown using the classic zinc-copper cell as an example:

• Anode (negative electrode): Where oxidation occurs. The electrode loses electrons. In a Zn-Cu cell, zinc metal is oxidized: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
• Cathode (positive electrode): Where reduction occurs. The electrode gains electrons. Copper ions in solution are reduced: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
• Salt bridge: A tube filled with an inert salt solution (like $KCl$ or $KNO_3$) that connects the two half-cells. It allows ions to migrate between solutions, which keeps the charge balanced in each half-cell. Without it, charge would build up and electron flow would stop almost immediately.
• External circuit (wire): Electrons flow from the anode to the cathode through this wire. A voltmeter placed in the circuit measures the potential difference (voltage) between the two electrodes. The Zn-Cu cell produces about 1.1 V under standard conditions.
• Half-cells: Each half-cell pairs an electrode with an electrolyte solution containing its ions. The oxidation half-cell has the Zn electrode sitting in a $Zn^{2+}$ solution, and the reduction half-cell has the Cu electrode sitting in a $Cu^{2+}$ solution.

A quick memory trick: An Ox, Red Cat. Anode = Oxidation, Reduction = Cathode.

Cell notation for galvanic cells

Cell notation is a shorthand way to describe a galvanic cell on paper without drawing the whole diagram. The format follows a set of rules:

1. Write the anode (oxidation) on the left and the cathode (reduction) on the right.
2. Use a single vertical line ( | ) to separate an electrode from its electrolyte solution (this represents a phase boundary).
3. Use a double vertical line ( || ) to represent the salt bridge between the two half-cells.

The general format looks like this:

For the zinc-copper cell:

$Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$

Reading left to right, this tells you: solid zinc is oxidized to $Zn^{2+}$ ions in solution, the salt bridge separates the half-cells, and $Cu^{2+}$ ions in solution are reduced to solid copper.

Active vs inert electrodes

Not all electrodes behave the same way. The distinction matters for how you set up and interpret a cell.

Active electrodes actually participate in the reaction. The electrode material is either consumed (at the anode) or built up (at the cathode). In the Zn-Cu cell, both electrodes are active: the zinc anode slowly dissolves as it's oxidized, and copper metal deposits onto the cathode as $Cu^{2+}$ ions are reduced. Other common active electrode metals include $Ag$ and $Mg$.

Inert electrodes don't react at all. They just provide a surface where electron transfer can happen. You need inert electrodes when the reacting species are all in solution or are gases and can't serve as electrodes themselves. Common inert electrode materials include $Pt$ (platinum), $Au$ (gold), and graphite. For example, in a cell where $Fe^{2+}$ is oxidized to $Fe^{3+}$, both species are dissolved ions, so you'd use a platinum electrode to give the reaction a surface to occur on.

Electrochemical Potentials and Calculations

Every half-reaction has a standard electrode potential ($E°$), which measures how strongly that half-reaction tends to occur as a reduction under standard conditions (1 M concentration, 25°C, 1 atm). These values are measured relative to the standard hydrogen electrode (SHE), which is assigned a potential of 0.00 V.

The electrochemical series is a table that ranks half-reactions from most negative $E°$ (least tendency to be reduced) to most positive $E°$ (greatest tendency to be reduced). Species higher on the table are stronger reducing agents; species lower on the table are stronger oxidizing agents.

To calculate the standard cell potential for a galvanic cell:

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

For the Zn-Cu cell, using standard reduction potentials:

• $E°$ for $Cu^{2+}/Cu = +0.34 \text{ V}$
• $E°$ for $Zn^{2+}/Zn = -0.76 \text{ V}$

$E°_{cell} = (+0.34) - (-0.76) = +1.10 \text{ V}$

A positive $E°_{cell}$ tells you the reaction is spontaneous, which is exactly what you expect for a galvanic cell. If you ever calculate a negative value, either the reaction isn't spontaneous or you've mixed up the anode and cathode.

The Nernst equation extends this by letting you calculate cell potential under non-standard conditions (when concentrations aren't 1 M or temperature isn't 25°C), but at the intro level, the standard cell potential calculation above is the one you'll use most.