An electrochemical cell can behave like an electro – Class 12 Chemistry

NCERT Exemplar · Q6

Q. An electrochemical cell can behave like an electrolytic cell when ____________.

(i)

E_{cell} = 0

(ii)

E_{cell} > E_{ext}

(iii)

E_{ext} > E_{cell}

(iv)

E_{cell} = E_{ext}

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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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An electrochemical cell behaves like an electrolytic cell when an external voltage greater than the cell’s emf is applied in opposition — forcing the cell reaction to reverse. The correct condition is $E_{ext} > E_{cell}$ , which corresponds to option (iii).

The key idea is simple: an electrochemical cell normally produces electricity spontaneously. But if you connect it to a stronger external battery in the opposite direction, you can overpower it and force the current to flow backwards — turning the cell into an electrolytic cell where the reaction is driven non-spontaneously.

This is exactly how electrolysis works: you apply an external voltage larger than the cell’s natural emf to reverse the redox reaction. The Nernst equation for cell potential tells us the driving force for the spontaneous direction. When $E_{ext}$ exceeds $E_{cell}$ , the net potential becomes negative for the spontaneous direction, meaning the reaction now runs in reverse.

Let’s walk through each option carefully.

Option (i): $E_{cell} = 0$

This means the cell is at equilibrium — no net reaction occurs. It’s neither a galvanic nor an electrolytic cell in action. So this is not the condition.
Option (ii): $E_{cell} > E_{ext}$

Here the cell’s own emf is larger than the opposing external voltage. The cell still wins — current flows in the spontaneous (galvanic) direction. No reversal happens.
Option (iii): $E_{ext} > E_{cell}$

The external voltage overpowers the cell. The net driving force is now opposite to the spontaneous direction. The cell reaction is forced to go backwards — exactly what happens in an electrolytic cell. This is the correct condition.
Option (iv): $E_{cell} = E_{ext}$ …

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Common Mistakes & How to Avoid Them

Concept First: What the Question Tests

An electrochemical cell (galvanic/voltaic cell) produces electricity spontaneously. An electrolytic cell consumes electricity to drive a non-spontaneous reaction.

The key condition for a cell to behave like an electrolytic cell is when an external voltage ( $E_{ext}$ ) is applied greater than the cell's own emf ( $E_{cell}$ ), forcing the reverse reaction.

Mistake #1: Confusing the direction of inequality

The error: Students often pick option (ii) $E_{cell} > E_{ext}$ , thinking "if the cell is stronger, it will behave like an electrolytic cell."

Why it's wrong: A larger $E_{cell}$ means the spontaneous reaction is even more favoured — it remains an electrochemical cell, not an electrolytic one.

How to avoid:

Remember: Electrolytic = external source overpowers the cell.
Visualise a tug-of-war:
- $E_{cell}$ pulls one way (spontaneous).
- $E_{ext}$ pulls the opposite way (forced).
- Only when $E_{ext}$ is larger does the direction reverse.

Correct choice: (iii) $E_{ext} > E_{cell}$

Mistake #2: Thinking $E_{cell} = 0$ means electrolytic behaviour

The error: Some students associate $E_{cell} = 0$ with "no reaction" and assume that's when an external source is needed.

Why it's wrong: $E_{cell} = 0$ means equilibrium — the cell is dead (no net reaction). An external voltage can indeed drive a reaction, but the cell is not "behaving like an electrolytic cell" at $E_{cell}=0$ ; it's simply at equilibrium.

How to avoid:

$E_{cell} = 0$ → equilibrium, not electrolytic mode.
Electrolytic behaviour requires overcoming the cell's emf, not being at zero.

Mistake #3: Picking $E_{cell} = E_{ext}$ (option D)

The error: Students think "equal voltages cancel out, so the cell becomes electrolytic." …

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Q.An electrochemical cell can behave like an electrolytic cell when ____________.

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 vs. Electrolytic Cell Behaviour

Method: Comparison of Cell EMF and External Voltage

Common Mistakes & How to Avoid Them

Concept First: What the Question Tests

Mistake #1: Confusing the direction of inequality

Mistake #2: Thinking $E_{cell} = 0$ means electrolytic behaviour

Mistake #3: Picking $E_{cell} = E_{ext}$ (option D)

Q.An electrochemical cell can behave like an electrolytic cell when ____________.

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