The difference between the electrode potentials of two electrodes when no current is drawn through the cell is

NCERT Exemplar · Q4

Q. The difference between the electrode potentials of two electrodes when no current is drawn through the cell is called ___________.

(i) Cell potential

(ii) Cell emf

(iii) Potential difference

(iv) Cell voltage

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Concept understanding — Cell Representation Nernst Equation

Cell Representation and the Nernst Equation: From Intuition to Precision

Imagine you have a Daniell cell — a zinc rod in zinc sulphate solution connected by a salt bridge to a copper rod in copper sulphate solution. You know it produces a voltage. But what happens if you dilute the copper sulphate solution? Or if you change the temperature? The voltage changes. The Nernst equation is the tool that tells you exactly how much it changes.

The Intuition First

A battery works because the two half-cells "want" to react — zinc wants to lose electrons, copper ions want to gain them. This "want" is measured as a tendency, or potential. But the strength of that tendency depends on how crowded the ions are.

Think of it like this: If you have a room full of people who all want to leave (like zinc ions wanting to form), the push to get out is stronger when the room is packed. If the room is nearly empty, the push is weaker. Similarly, for copper ions wanting to enter the metal (gain electrons), the pull is stronger when there are many copper ions around, and weaker when there are few.

The Nernst equation quantifies this: the actual cell potential depends on the concentrations (or activities) of the ions involved.

The Precise Statement

For a general cell reaction:

aA + bB \rightarrow cC + dD

The cell potential $E$ under non-standard conditions is given by:

E = E^\circ - \frac{RT}{nF} \ln Q

Where:

$E$ = cell potential under the given conditions (in volts)
$E^\circ$ = standard cell potential (when all reactants/products are at 1 M, 1 atm, 25°C)
$R$ = universal gas constant (8.314 J/mol·K)
$T$ = temperature in Kelvin
$n$ = number of moles of electrons transferred in the balanced half-reactions
$F$ = Faraday constant (96,485 C/mol)
$Q$ = reaction quotient = $\frac{[C]^c [D]^d}{[A]^a [B]^b}$ (using concentrations for dilute solutions)

At 25°C (298 K), the equation simplifies to a very practical form:

E = E^\circ - \frac{0.0591}{n} \log_{10} Q

The 0.0591 comes from $\frac{2.303RT}{F}$ at 298 K. Notice it uses $\log_{10}$ (common log), not natural log.

Cell Representation: How We Write It

In electrochemistry, we represent a cell with a shorthand notation. For the Daniell cell:

\text{Zn(s)} \mid \text{Zn}^{2+}(\text{aq}) \parallel \text{Cu}^{2+}(\text{aq}) \mid \text{Cu(s)}

The single vertical line $\mid$ represents a phase boundary (solid electrode | solution). The double line $\parallel$ represents the salt bridge.

The anode (oxidation) is written on the left, the cathode (reduction) on the right. Electrons flow from left to right in the external circuit.

Applying the Nernst Equation to a Cell Representation

For the Daniell cell, the half-reactions are:

Anode (oxidation): $\text{Zn(s)} \rightarrow \text{Zn}^{2+}(\text{aq}) + 2e^-$
Cathode (reduction): $\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu(s)}$

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

Here $n = 2$ (two electrons transferred). The reaction quotient is:

Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

So the Nernst equation becomes:

E = E^\circ - \frac{0.0591}{2} \log_{10} \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

Note

Solids (Zn, Cu) do not appear in $Q$ because their concentrations are constant (activity = 1).

A Worked Example

Suppose you have a Daniell cell where $[\text{Zn}^{2+}] = 0.1$ M and $[\text{Cu}^{2+}] = 1.0$ M at 25°C. $E^\circ$ for the cell is 1.10 V.

$E = 1.10 - \frac{0.0591}{2} \log_{10} \frac{0.1}{1.0}$ …

Why this formula?

Cell Representation & the Nernst Equation: Why It Works

The Core Question

Why does a cell's voltage change when concentrations change? The Nernst equation answers this — but the reason lies in the link between chemical free energy and electrical work.

1. The Fundamental Link: Gibbs Free Energy & Cell Potential

A galvanic cell does electrical work. The maximum useful work a cell can do equals the change in Gibbs free energy ( $\Delta G$ ):

\Delta G = -nFE_{\text{cell}}

Where:

$n$ = moles of electrons transferred
$F$ = Faraday constant ( $96,485 \, \text{C mol}^{-1}$ )
$E_{\text{cell}}$ = cell potential (volts)

Why negative? A spontaneous reaction has $\Delta G < 0$ and $E_{\text{cell}} > 0$ — the negative sign makes this consistent.

2. The Chemical Side: $\Delta G$ Depends on Concentration

For a general redox reaction:

aA + bB \rightarrow cC + dD

The Gibbs free energy under non-standard conditions is:

\Delta G = \Delta G^\circ + RT \ln Q

Where $Q$ is the reaction quotient:

Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}

Why this form? It comes from the relationship between chemical potential and concentration — the entropy of mixing drives concentration dependence.

3. Combining Both Sides: The Derivation

Set the electrical work equal to the chemical free energy change:

-nFE_{\text{cell}} = -nFE^\circ_{\text{cell}} + RT \ln Q

Divide both sides by $-nF$ :

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

This is the Nernst equation.

4. The "Why" in Plain Terms

Concept	Physical Meaning
$E^\circ_{\text{cell}}$	Voltage when all species are at 1 M (standard state)
$-\frac{RT}{nF} \ln Q$	Correction factor — adjusts voltage for real concentrations
$Q$	Tells you how far the reaction is from equilibrium

Key insight: When $Q = K$ (equilibrium), $E_{\text{cell}} = 0$ — the battery is dead because no net reaction occurs.

5. The Common Form (log base 10)

At $25^\circ \text{C}$ ( $298 \, \text{K}$ ):

\frac{RT}{F} \ln 10 \approx 0.0592 \, \text{V}

So:

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log_{10} Q

Why convert to log? Exam convenience — most concentration values are powers of 10.

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The difference between the electrode potentials of two electrodes when no current is drawn is the electromotive force (emf) of the cell. The correct option is (ii).

This question tests a fundamental distinction in electrochemistry: the difference between the voltage you measure when the cell is doing work (current flowing) and the voltage it can produce when it's at rest (no current). The key is the phrase "when no current is drawn."

When a cell is connected to a load and current flows, the measured voltage drops due to internal resistance. That measured value is the cell potential or cell voltage under load. But when no current flows — the cell is in an open-circuit condition — the measured voltage is the maximum possible voltage the cell can deliver. This maximum, no-load voltage is the electromotive force (emf) of the cell.

Let's walk through the options:

Cell potential — This is a general term for the voltage of a cell, but it's often used interchangeably with the voltage under operating conditions (when current is flowing). The question specifically says "when no current is drawn," so this isn't the precise term.
Cell emf — This is the exact term. EMF stands for electromotive force. It is defined as the potential difference between the two electrodes of a cell when no current is flowing through the external circuit. It represents the driving force of the cell.
Potential difference — This is a broader physics term for the difference in electric potential between two points. In a cell, the potential difference across the terminals changes when current flows (due to internal resistance). So it's not specific to the no-current condition. …

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Here is the breakdown of the common mistakes students make on this specific question, along with the precise conceptual understanding required to avoid them.

The Correct Answer

The blank is correctly filled by (ii) Cell emf.

Why: The definition explicitly states "when no current is drawn." This is the defining condition for Electromotive Force (emf). It represents the maximum potential difference the cell can produce under zero-current conditions.

Common Mistake #1: Confusing "Cell emf" with "Cell potential" / "Cell voltage"

The Mistake: Students often treat these terms as perfectly interchangeable synonyms. They see "potential difference" and "voltage" and assume they mean the same thing as "emf" in all contexts.
Why it happens: In everyday conversation, we use "voltage" loosely. However, in electrochemistry, the distinction is critical.
How to Avoid It: Memorize the operational definition:
- EMF ( $\mathcal{E}$ ): The potential difference when $I = 0$ (no current). It is the "driving force" of the cell.
- Cell potential / Voltage ( $V$ ): The potential difference when $I \neq 0$ (current is flowing). This is always less than the emf due to internal resistance ( $V = \mathcal{E} - Ir$ ).
- Key Exam Trick: If the question mentions "no current," the answer is almost always emf.

Common Mistake #2: Ignoring the "No Current" Condition

The Mistake: Students read the question quickly, see "difference between electrode potentials," and immediately select "Potential difference" (Option C) because that's the most literal reading.
Why it happens: They fail to register the crucial qualifier: "when no current is drawn."
How to Avoid It: Underline the condition. In any electrochemistry question, the presence or absence of current changes the definition entirely.
- No current $\rightarrow$ EMF (the cell is at equilibrium, or open circuit).
- Current flowing $\rightarrow$ Terminal voltage / Cell potential (the cell is doing work).

Common Mistake #3: Thinking "Cell potential" is the same as "EMF"

The Mistake: Students believe "Cell potential" is the umbrella term that includes emf. …

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Q.The difference between the electrode potentials of two electrodes when no current is drawn through the cell is called ___________.

Concept understanding — Cell Representation Nernst Equation

Cell Representation and the Nernst Equation: From Intuition to Precision

The Intuition First

The Precise Statement

Cell Representation: How We Write It

Applying the Nernst Equation to a Cell Representation

A Worked Example

Why this formula?

Cell Representation & the Nernst Equation: Why It Works

The Core Question

1. The Fundamental Link: Gibbs Free Energy & Cell Potential

2. The Chemical Side: $\Delta G$ Depends on Concentration

3. Combining Both Sides: The Derivation

4. The "Why" in Plain Terms

5. The Common Form (log base 10)

Concept: Electrochemical Cell Potential Under Zero Current

Method: Definition-Based Elimination

The Correct Answer

Common Mistake #1: Confusing "Cell emf" with "Cell potential" / "Cell voltage"

Common Mistake #2: Ignoring the "No Current" Condition

Common Mistake #3: Thinking "Cell potential" is the same as "EMF"

Q.The difference between the electrode potentials of two electrodes when no current is drawn through the cell is called ___________.

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