Electrochemical Cells

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; 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:

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:

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:

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

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 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).

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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.

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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:

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) …