Chemistry · Ch 2 — Electrochemistry

Electrochemical Cells

2.1

Electrochemical Cells

Turning a Redox Reaction into Electricity

A redox reaction always has an oxidation half and a reduction half, and if those two halves are forced to happen in separate compartments — connected only by a wire and a salt bridge — the electron transfer between them can be tapped as an electric current. A device built this way is called an electrochemical cell. The reaction driving it does not have to be invented; it is the very same spontaneous reaction you would otherwise write down for a metal displacing a less reactive metal's ion from solution.

The reference example is the Daniell cell, built on the reaction

$\mathrm{Zn(s) + Cu^{2+}(aq) \longrightarrow Zn^{2+}(aq) + Cu(s)}$

Here a zinc rod is dipped in a solution containing a zinc salt (ZnSO₄) and a copper rod is dipped in a solution containing a copper salt (CuSO₄). The two solutions are kept in separate vessels and linked by a salt bridge, while the two metal rods are joined externally by a wire. Left to itself, this arrangement lets the reaction above proceed while forcing the electrons it releases to travel through the external wire rather than jump directly between the metal and the ions in solution — and that travelling electron flow is what we experience as an electric current.

Which Electrode Does What

The two metal rods do not behave identically:

At the zinc rod, zinc atoms lose electrons and go into solution as Zn²⁺ ions — this is oxidation.
At the copper rod, Cu²⁺ ions from the solution gain electrons and deposit as metallic copper — this is reduction.

Because oxidation happens at the zinc rod, it is the anode, and it carries a negative sign here; because reduction happens at the copper rod, it is the cathode, carrying a positive sign. Electrons leave the zinc rod, travel through the external wire, and arrive at the copper rod — so electron flow is from zinc to copper, while the conventional current, being opposite to electron flow, flows from copper to zinc through the external circuit. The salt bridge completes the circuit internally, letting ions migrate between the two solutions so that each compartment stays electrically neutral as the reaction proceeds.

Galvanic (or Voltaic) Cells

A cell of this kind — one that converts the chemical energy released by a spontaneous redox reaction directly into electrical energy — is called a galvanic cell or a voltaic cell. When the concentration of both Zn²⁺ and Cu²⁺ in the two solutions is held at unity (1 mol dm⁻³), the Daniell cell delivers a fixed electrical potential:

$E_{\text{cell}} = 1.1\ \text{V}$

This 1.1 V is simply a measure of how strongly this particular redox reaction "wants" to happen; it is what the cell can deliver when nothing is opposing it.

Pushing Back: An External Opposing Voltage

Instead of letting the Daniell cell drive current on its own, imagine connecting an external source that applies a voltage $E_{\text{ext}}$ in the opposite direction to the cell's own voltage, and slowly turning it up. Three distinct regimes appear:

Applied external voltage	What happens
$E_{\text{ext}} < E_{\text{cell}}$ (i.e., below 1.1 V)	The original reaction still goes forward: electrons keep flowing from zinc to copper, current keeps flowing from copper to zinc. Zinc keeps dissolving at the anode and copper keeps depositing at the cathode — just as in the unopposed cell.
$E_{\text{ext}} = E_{\text{cell}}$ (exactly 1.1 V)	The external push exactly balances the cell's own tendency to react. No electrons flow, no current flows, and — since there is no net electron transfer — the chemical reaction itself stops.
$E_{\text{ext}} > E_{\text{cell}}$ (above 1.1 V)	The external source now overpowers the cell and drives everything in reverse: electrons flow from copper to zinc, and current flows from zinc to copper — the opposite of the original directions. Zinc is now deposited at the zinc electrode while copper dissolves at the copper electrode, i.e., the reaction $\mathrm{Zn^{2+}(aq) + Cu(s) \rightarrow Zn(s) + Cu^{2+}(aq)}$ is being forced to occur even though it is non-spontaneous on its own.

E_{\text{ext}} = E_{\text{cell}} \;\Longrightarrow\; I = 0

From Galvanic to Electrolytic

That reversal is the key idea separating the two kinds of electrochemical cells:

A galvanic (voltaic) cell lets a spontaneous redox reaction run and collects the electrical energy it produces.
An electrolytic cell is the same physical set-up used the opposite way — an external electrical energy source is used to force a non-spontaneous chemical reaction to occur.

Note

The Daniell cell demonstrates both faces of the same apparatus: with $E_{\text{ext}} < 1.1\ \text{V}$ (or no external source at all) it behaves as a galvanic cell doing spontaneous chemistry for free; with $E_{\text{ext}} > 1.1\ \text{V}$ the very same set-up becomes an electrolytic cell, consuming electrical energy to push the reaction backward.

Both kinds of cells are practically important — galvanic cells are how batteries generate usable electrical energy, while electrolytic cells are how electrical energy is used to carry out reactions (such as electroplating or extracting reactive metals) that would never happen on their own.

Figure 2.1Daniell cell having electrodes of zinc and copper dipping in the solutions of their respective salts.

Fig. 2.1 — Daniell cell having electrodes of zinc and copper dipping in the solutions of their respective salts.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

The figure shows a Daniell cell built from two separate beakers. The left beaker contains a zinc electrode (marked –) immersed in a solution of zinc sulphate ( $\text{ZnSO}_4$ ). The right beaker contains a copper electrode (marked +) immersed in a solution of copper sulphate ( $\text{CuSO}_4$ ). An inverted-U salt bridge connects the two solutions, completing the internal circuit. An external wire connects the two electrodes through a voltmeter and a switch; the wire is labelled with an arrow showing electron flow from Zn to Cu, and an opposite arrow showing current from Cu to Zn. Curved arrows inside the solutions indicate zinc ions leaving the zinc electrode (dissolving) and copper ions depositing onto the copper electrode.

What the figure teaches

The diagram illustrates the spontaneous redox reaction that powers the cell:

$\text{Zn(s)} + \text{Cu}^{2+}(\text{aq}) \rightarrow \text{Zn}^{2+}(\text{aq}) + \text{Cu(s)}$

This overall reaction is the sum of two half-reactions:

Oxidation (at the anode, Zn electrode):

$\text{Zn(s)} \rightarrow \text{Zn}^{2+}(\text{aq}) + 2e^-$

The zinc electrode loses mass as $\text{Zn}^{2+}$ ions enter the solution; the electrons left behind make the electrode negative.
Reduction (at the cathode, Cu electrode):

$\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu(s)}$

Copper ions from the solution gain electrons and deposit as solid copper on the electrode, making it positive.

The salt bridge allows ions to flow between the two half-cells, maintaining electrical neutrality. Without it, charge buildup would stop the reaction.

Key formula developed from this figure

The cell potential (electromotive force, emf) of the Daniell cell under standard conditions is:

$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

where:

$E^\circ_{\text{cell}}$ is the standard cell potential (measured when all species are at 1 M concentration, 1 bar pressure, 298 K). For the Daniell cell, $E^\circ_{\text{cell}} = 1.1\ \text{V}$ .
$E^\circ_{\text{cathode}}$ is the standard reduction potential of the copper half-cell: $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu(s)}$ , $E^\circ = +0.34\ \text{V}$ .
$E^\circ_{\text{anode}}$ is the standard reduction potential of the zinc half-cell: $\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn(s)}$ , $E^\circ = -0.76\ \text{V}$ .

Substituting:

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

The figure also introduces the Nernst equation (developed later in the chapter) that relates the cell potential to concentrations:

$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log Q$

where $n$ is the number of electrons transferred (here $n=2$ ) and $Q$ is the reaction quotient.

Physical idea: Gibbs energy and electrical work

The spontaneous reaction in the Daniell cell has a negative Gibbs energy change ( $\Delta G < 0$ ). This chemical energy is converted into electrical work:

$\Delta G = -n F E_{\text{cell}}$

where $F$ is the Faraday constant ( $96\,485\ \text{C mol}^{-1}$ ). The figure shows that when the external voltage $E_{\text{ext}}$ is less than 1.1 V, electrons flow from Zn to Cu (spontaneous direction). When $E_{\text{ext}} = 1.1\ \text{V}$ , no net reaction occurs. When $E_{\text{ext}} > 1.1\ \text{V}$ , the cell is forced to run in reverse — zinc deposits and copper dissolves — demonstrating electrolysis.

Figure 2.2Functioning of Daniell cell when external voltage Eext opposing the cell potential is applied.

Fig. 2.2 — Functioning of Daniell cell when external voltage Eext opposing the cell potential is applied.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

The figure shows three states of a Daniell cell connected to an external voltage source $E_{\text{ext}}$ . The cell itself has a standard potential of 1.1 V (the voltage when no external source is applied). The three panels illustrate what happens as $E_{\text{ext}}$ is varied relative to this value.

Panel (a): $E_{\text{ext}} < 1.1\ \text{V}$

The external voltage is less than the cell’s natural potential.
Electrons flow from the zinc electrode (anode) to the copper electrode (cathode) through the external wire.
Current (conventional) flows in the opposite direction: from copper to zinc.
At the zinc electrode: $\text{Zn(s)} \rightarrow \text{Zn}^{2+}(\text{aq}) + 2e^-$ — zinc dissolves (oxidation).
At the copper electrode: $\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu(s)}$ — copper deposits (reduction).
The cell still acts as a galvanic cell (spontaneous reaction), but the net driving force is reduced because $E_{\text{ext}}$ opposes it.

Panel (b): $E_{\text{ext}} = 1.1\ \text{V}$

The external voltage exactly balances the cell’s potential.
The meter reads $I = 0$ — no current flows.
No net chemical reaction occurs. The system is at equilibrium.
This is the condition where the applied voltage equals the cell’s electromotive force (emf).

Panel (c): $E_{\text{ext}} > 1.1\ \text{V}$

The external voltage exceeds the cell’s natural potential.
Electrons now flow from copper to zinc (opposite to the spontaneous direction).
Current flows from zinc to copper.
The cell becomes an electrolytic cell — a non-spontaneous reaction is forced.
At the zinc electrode: $\text{Zn}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Zn(s)}$ — zinc is deposited (reduction).
At the copper electrode: $\text{Cu(s)} \rightarrow \text{Cu}^{2+}(\text{aq}) + 2e^-$ — copper dissolves (oxidation).

Physical Idea

The figure teaches that a galvanic cell can be reversed into an electrolytic cell by applying an external voltage greater than the cell’s own emf. The threshold is the cell’s standard potential $E^\circ_{\text{cell}} = 1.1\ \text{V}$ . Below this, the cell still discharges spontaneously; at exactly this value, it is at equilibrium; above it, the cell is forced to run backwards.

Key Formula Developed

The textbook uses this figure to introduce the concept of electromotive force (emf) and the condition for equilibrium in an electrochemical cell. The fundamental relation is:

$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q$

where:

$E_{\text{cell}}$ = cell potential under non-standard conditions (V)
$E^\circ_{\text{cell}}$ = standard cell potential (1.1 V for Daniell cell)
$R$ = universal gas constant ( $8.314\ \text{J mol}^{-1}\text{K}^{-1}$ )
$T$ = absolute temperature (K)
$n$ = number of electrons transferred in the balanced redox reaction (here $n=2$ )
$F$ = Faraday constant ( $96485\ \text{C mol}^{-1}$ )
$Q$ = reaction quotient (ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients)

When $E_{\text{ext}} = E_{\text{cell}}$ , the net driving force is zero — this is the equilibrium condition shown in panel (b). The figure thus grounds the idea that applying an external voltage equal to the cell’s emf stops the reaction, and exceeding it reverses the direction.

Next · 2.2 →Galvanic Cells

Electrochemical Cells

2.1