Galvanic Cells and Cell Electromotive Force

The displacement reactions of the previous chapter all shared one feature: the oxidising and reducing species were in direct physical contact, so electrons transferred straight from one particle to the other with no possibility of capturing that transfer as useful electrical work. This chapter asks what happens if the two half-reactions are physically separated, forced to communicate only through an external wire. The answer is the galvanic cell (also called a voltaic cell): a device that converts the chemical energy of a spontaneous redox reaction directly into electrical energy, and the ancestor, in miniature, of every battery in practical use.

This chapter builds the vocabulary and the physical picture of a galvanic cell — its two half-cells, its salt bridge, its standard cell notation, and the electromotive force (EMF) that drives the whole device — using the zinc-copper displacement reaction of the previous chapter as the worked example throughout. The next chapter extends this picture with exact, tabulated numbers: the standard electrode potentials that let the EMF of any cell be calculated without building it.

1. From a Displacement Reaction to a Galvanic Cell

Recall the spontaneous displacement reaction $\text{Zn}(s) + \text{Cu}^{2+}(aq) \longrightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$: zinc metal dropped directly into copper(II) sulfate solution. The electron transfer here happens at the instant of contact between a zinc atom and a copper(II) ion, releasing the reaction's energy entirely as heat, with none of it available to do electrical work.

A galvanic cell achieves the same net chemistry while physically separating the two half-reactions into two half-cells, connected only by an external wire (through which the transferred electrons must travel) and an internal salt bridge (Section 4). Forcing the electrons through an external circuit is precisely what allows a measurable voltage and a usable current to be drawn from the reaction.

Definition. A galvanic (voltaic) cell is a device in which a spontaneous redox reaction is used to generate an electric current, by physically separating the oxidation and reduction half-reactions into two half-cells connected by an external circuit and a salt bridge.

2. The Structure of a Half-Cell

A simple half-cell consists of a metal electrode immersed in a solution containing its own ions — for example, a strip of zinc metal dipped in zinc sulfate solution, $\text{Zn}(s) \mid \text{Zn}^{2+}(aq)$. At the electrode surface, the half-equation for that metal's oxidation or reduction can, in principle, proceed in either direction; which direction actually happens in the working cell is decided by connecting two different half-cells together (Section 3).

A complete galvanic cell joins two such half-cells: in the classic example, the Daniell cell, a zinc half-cell ($\text{Zn}(s) \mid \text{ZnSO}_4(aq)$) is connected to a copper half-cell ($\text{Cu}(s) \mid \text{CuSO}_4(aq)$).

3. Anode and Cathode

Each electrode is named by the half-reaction occurring at its surface, using the same mnemonic from the half-equation method of an earlier chapter:

Definition. The anode is the electrode at which oxidation occurs. The cathode is the electrode at which reduction occurs. (Mnemonic: AN OX, RED CAT.)

In the Daniell cell, zinc is the more reactive metal (higher in the activity series of the previous chapter), so it is oxidised: zinc is the anode. Copper(II) is reduced at the copper electrode, which is therefore the cathode.

Because the anode releases electrons into the external wire and the cathode consumes them, electrons flow through the external circuit from the anode to the cathode. In a galvanic cell, this makes the anode the negative electrode (the source of electrons) and the cathode the positive electrode (where electrons are consumed, pulled by the externally connected circuit).

Warning. This polarity — anode negative, cathode positive — is specific to a galvanic cell, which generates current spontaneously. Two chapters from now, the electrolytic cell, which consumes an external electrical supply to force a non-spontaneous reaction, has the opposite polarity convention at its electrodes, even though "anode = oxidation" and "cathode = reduction" remain true in both cases. Confusing the two is one of the most common and consequential errors in this entire topic.

4. The Salt Bridge

If the two half-cell solutions were simply poured into the same beaker, the zinc and copper(II) ions would react directly on contact, exactly as in the original displacement reaction, and no useful current could be drawn. Keeping the solutions physically apart, however, creates a different problem: as electrons leave the zinc half-cell (building up positive charge there, as $\text{Zn}^{2+}$ accumulates) and arrive in the copper half-cell (building up negative charge there, as $\text{Cu}^{2+}$ is consumed), the resulting charge imbalance would rapidly halt the reaction.

The salt bridge — typically a tube of gel containing a concentrated solution of an unreactive, soluble ionic compound, such as potassium nitrate or potassium chloride — solves this by allowing ions, but not bulk solution, to migrate between the two half-cells, maintaining electrical neutrality in each without letting the two solutions mix and react directly.

Key distinction. The salt bridge carries the circuit's current internally, by the physical migration of ions, while the external wire carries the current by the flow of electrons. Cations in the salt bridge migrate toward the cathode (where positive charge is being consumed as $\text{Cu}^{2+}$ is removed from solution); anions migrate toward the anode (where positive charge is building up as $\text{Zn}^{2+}$ accumulates). Together, electron flow through the wire and ion flow through the salt bridge form one single, complete circuit.

A salt bridge's ionic compound must be chosen so that neither its cation nor its anion reacts with, or precipitates with, either half-cell solution — potassium salts are popular precisely because $\text{K}^+$ is not easily reduced and rarely interferes.

5. Standard Cell Notation

A galvanic cell is represented compactly using a standardised shorthand, the cell diagram, read left to right exactly as the physical circuit is conventionally drawn, anode first:

• A single vertical line, $\mid$, marks a phase boundary (here, solid metal electrode against its aqueous ion solution).
• The double vertical line, $\parallel$, represents the salt bridge, separating the two half-cells.
• The anode half-cell is always written on the left, the cathode half-cell on the right — the same left-to-right order as the direction of electron flow through the external circuit (from the negative anode terminal, through the external load, to the positive cathode terminal).

Worked example. Write the cell diagram for a galvanic cell built from a silver half-cell and an iron half-cell, given that iron is oxidised and silver(I) is reduced.

Since iron is oxidised, it is the anode (written first, on the left); silver is the cathode (written last, on the right):

6. Electromotive Force (EMF)

The electromotive force, $E_{\text{cell}}$, of a galvanic cell is the maximum potential difference it can produce between its two electrodes, measured under conditions of zero current flow (using a voltmeter of very high resistance, so that essentially no charge actually passes while the reading is taken).

Definition. The electromotive force (EMF) of a cell, $E_{\text{cell}}$, is the potential difference between its two electrodes measured when no current is drawn, representing the maximum electrical "push" the cell's spontaneous reaction can provide. It is measured in volts ($\text{V}$).

The word "force" here is a historical holdover — EMF is a potential difference (energy per unit charge), not a mechanical force — but the term persists throughout electrochemistry. A positive EMF indicates that the cell reaction, as written, is spontaneous: electrons genuinely do flow from anode to cathode of their own accord, without any external push. If the two half-cells were connected the other way around, with the labelled anode and cathode reversed, the measured EMF would simply be the same magnitude with the opposite sign, indicating that this direction is non-spontaneous.

6.1 The link to Gibbs free energy

The EMF of a cell is directly related to the Gibbs free energy change of its overall reaction:

where $n$ is the number of moles of electrons transferred per mole of reaction (read directly from the balanced half-equations, exactly as in the half-equation method of an earlier chapter) and $F$ is the Faraday constant, the charge on one mole of electrons ($F \approx 96\,500~\text{C}\,\text{mol}^{-1}$). A positive $E_{\text{cell}}$ therefore corresponds to a negative $\Delta G$ — confirming, from thermodynamics, that a positive-EMF cell reaction is indeed spontaneous as written. This relationship is stated here as a forward link; its full use in calculations is developed once standard electrode potentials, which allow $E_{\text{cell}}$ to be calculated rather than only measured, are introduced in the next chapter.

7. Worked Example: The Complete Daniell Cell

Setup. A zinc strip is placed in $1~\text{mol}\,\text{dm}^{-3}$ zinc sulfate solution; a copper strip is placed in $1~\text{mol}\,\text{dm}^{-3}$ copper(II) sulfate solution. The two half-cells are connected by a salt bridge of potassium nitrate solution, and the two metal strips are connected by an external wire through a voltmeter.

Identifying anode and cathode. Zinc, higher in the activity series than copper, is the stronger reducing agent and is oxidised: zinc is the anode, the negative electrode. Copper(II) is reduced: copper is the cathode, the positive electrode.

Electron and ion flow. Electrons flow through the external wire from the zinc electrode (anode) to the copper electrode (cathode). Inside the salt bridge, $\text{NO}_3^{-}$ anions migrate toward the zinc half-cell (to balance the accumulating $\text{Zn}^{2+}$), while $\text{K}^{+}$ cations migrate toward the copper half-cell (to balance the $\text{Cu}^{2+}$ being removed from solution as it is reduced).

Half-equations and overall equation.

Cell diagram. $\text{Zn}(s) \mid \text{Zn}^{2+}(aq) \parallel \text{Cu}^{2+}(aq) \mid \text{Cu}(s)$.

EMF. A high-resistance voltmeter connected across this cell under standard conditions reads a positive value (its exact magnitude, $+1.10~\text{V}$, is calculated from tabulated data in the next chapter), confirming that the zinc-reduces-copper(II) direction, exactly as predicted by the activity series, is indeed the spontaneous one.

8. Common Exam Pitfalls

• Swapping anode/cathode polarity between galvanic and electrolytic cells. In a galvanic cell the anode is negative and the cathode is positive; in an electrolytic cell (two chapters ahead) the convention reverses. "Oxidation at the anode, reduction at the cathode" is always true; the sign of each electrode is not.
• Describing the salt bridge as the path for electron flow. Electrons travel only through the external wire; the salt bridge carries the circuit's current internally by the migration of ions, not electrons.
• Getting cation/anion migration direction backwards in the salt bridge. Cations migrate toward the cathode (where positive charge is being consumed); anions migrate toward the anode (where positive charge is accumulating as the metal dissolves).
• Reversing the order of half-cells in the cell diagram. The anode (oxidation) half-cell is always written on the left, the cathode (reduction) half-cell always on the right, matching the convention that electrons effectively flow left-to-right through the diagram.
• Confusing $\mid$ and $\parallel$. A single line marks a phase boundary within one half-cell; the double line specifically represents the salt bridge separating the two half-cells, and appears exactly once in a simple two-half-cell diagram.
• Forgetting that EMF is measured at zero current. Any current actually drawn from a real cell causes the measured voltage to drop below the true EMF, due to internal resistance — a complication met directly when a cell's voltage is used for calculation in later contexts.

Summary

• A galvanic cell generates an electric current from a spontaneous redox reaction by physically separating the oxidation and reduction half-reactions into two half-cells, connected by an external wire and a salt bridge.
• The anode is where oxidation occurs (negative electrode, source of electrons); the cathode is where reduction occurs (positive electrode) — this polarity is specific to galvanic cells and reverses for electrolytic cells.
• Electrons flow through the external wire from anode to cathode; the salt bridge completes the circuit internally, with cations migrating toward the cathode and anions migrating toward the anode, maintaining electrical neutrality in each half-cell.
• Cell notation writes the anode half-cell on the left and the cathode half-cell on the right, with $\mid$ for a phase boundary and $\parallel$ for the salt bridge: e.g. $\text{Zn}(s) \mid \text{Zn}^{2+}(aq) \parallel \text{Cu}^{2+}(aq) \mid \text{Cu}(s)$.
• The electromotive force (EMF), $E_{\text{cell}}$, is the maximum potential difference a cell can produce, measured at zero current; a positive EMF indicates the cell reaction, as written, is spontaneous.
• EMF links to thermodynamics through $\Delta G = -nFE_{\text{cell}}$, confirming that a positive-EMF reaction has a negative Gibbs free energy change — the exact numerical calculation of $E_{\text{cell}}$ from tabulated data is the subject of the next chapter, standard electrode potentials.