Assertion: Current stops flowing when ECell = 0. Reason: Equilibrium of the cell reaction is attained. (i) Bot

NCERT Exemplar · Q66

E_{Cell} = 0

(i) Both assertion and reason are true and the reason is the correct explanation of assertion.

(ii) Both assertion and reason are true and the reason is not the correct explanation of assertion.

(iii) Assertion is true but the reason is false.

(iv) Both assertion and reason are false.

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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 key idea is that a cell stops producing current when it reaches equilibrium, where $E_{Cell} = 0$ and the reaction quotient $Q$ equals the equilibrium constant $K$ . Both the assertion and reason are true, and the reason correctly explains the assertion — so option (i) is correct.

Let’s start with the core concept. A galvanic cell works because there’s a difference in electrode potentials, which drives electrons through the external circuit. This potential difference is the cell potential $E_{Cell}$ . As the cell discharges, the concentrations of reactants and products change, and $E_{Cell}$ gradually falls. When the cell reaction reaches equilibrium, the forward and reverse rates become equal — no net reaction occurs, and no current flows. At equilibrium, the Nernst equation gives $E_{Cell} = 0$ , because the reaction quotient $Q$ equals the equilibrium constant $K$ .

Now, let’s break it down step by step.

What does $E_{Cell} = 0$ mean physically?

The cell potential is the driving force for electron flow. When $E_{Cell} = 0$ , there is no net driving force — electrons don’t flow spontaneously in either direction. So current stops. This is exactly what the assertion says.
Why does $E_{Cell}$ become zero?

The Nernst equation for a cell reaction $aA + bB \rightarrow cC + dD$ is:

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

where $Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ . As the reaction proceeds, $Q$ changes. At equilibrium, $Q = K$ (the equilibrium constant). Also, at equilibrium, $\Delta G = 0$ . The relation $\Delta G = -nFE_{Cell}$ then forces $E_{Cell} = 0$ . So the Nernst equation becomes:

0 = E^\circ_{Cell} - \frac{RT}{nF} \ln K

which is consistent — it just gives the standard relation $E^\circ_{Cell} = \frac{RT}{nF} \ln K$ .

Is the reason correct? …

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Common Mistakes & How to Avoid Them

Mistake 1: Thinking current completely stops at equilibrium

The error: Students assume $E_{Cell} = 0$ means zero current flow in the external circuit.
Why it's wrong: At equilibrium, the net current is zero, but microscopic equal and opposite currents (forward and reverse reactions) continue. The cell is not "dead" — it's balanced.
How to avoid: Remember: equilibrium is dynamic, not static. Use the analogy of a market — prices stop changing, but buying and selling still happen at equal rates.

Mistake 2: Confusing $E_{Cell} = 0$ with a "dead" battery

The error: Students think a cell with $E_{Cell} = 0$ is like a discharged battery where no reaction is possible.
Why it's wrong: A discharged battery has $E_{Cell} > 0$ but reactants are depleted. At $E_{Cell} = 0$ , the cell is at chemical equilibrium — reactants and products coexist with no net change.
How to avoid: Distinguish between:
- Dead battery: Reactants exhausted, $E_{Cell} > 0$ possible but no reaction.
- Equilibrium cell: $E_{Cell} = 0$ , reaction still occurs in both directions equally.

Mistake 3: Misapplying the Nernst equation

The error: Students write $E_{Cell} = E^\circ_{Cell} - \frac{0.059}{n} \log Q$ and forget that at equilibrium $Q = K$ , so $E_{Cell} = 0$ .
Why it's wrong: They may think $E_{Cell} = 0$ only when $Q = 1$ , not when $Q = K$ .
How to avoid: Always write:

E_{Cell} = E^\circ_{Cell} - \frac{0.059}{n} \log Q

At equilibrium: $Q = K$ and $E_{Cell} = 0$ , so:

E^\circ_{Cell} = \frac{0.059}{n} \log K

This is a direct consequence of equilibrium.

Mistake 4: Thinking the Reason is false

The error: Students reject "Equilibrium of the cell reaction is attained" as the reason.
Why it's wrong: The reason is true — $E_{Cell} = 0$ is the definition of electrochemical equilibrium.
How to avoid: Memorise the key link: …

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Q.Assertion: Current stops flowing when $E_{Cell} = 0$ .
Reason: Equilibrium of the cell reaction is attained.

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)

Method: Thermodynamic Equilibrium Analysis of Electrochemical Cells

Steps:

Common Mistakes & How to Avoid Them

Mistake 1: Thinking current completely stops at equilibrium

Mistake 2: Confusing $E_{Cell} = 0$ with a "dead" battery

Mistake 3: Misapplying the Nernst equation

Mistake 4: Thinking the Reason is false

Q.Assertion: Current stops flowing when ECell=0E_{Cell} = 0ECell​=0. Reason: Equilibrium of the cell reaction is attained.

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Q.Assertion: Current stops flowing when $E_{Cell} = 0$ .
Reason: Equilibrium of the cell reaction is attained.

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