Assertion: ECell should have a positive value for – Class 12 Chemistry

NCERT Exemplar · Q60

E_{Cell}

(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 assertion is true (a cell needs positive $E_{cell}$ to function spontaneously), but the reason is false (the correct condition is $E_{cathode} > E_{anode}$ , not the reverse). So the correct option is (iii).

Let’s understand why. A galvanic (voltaic) cell works by converting chemical energy into electrical energy spontaneously. The driving force is the difference in reduction potentials of the two half-cells.

The cell potential is defined as:

E_{cell} = E_{cathode} - E_{anode}

where $E_{cathode}$ and $E_{anode}$ are the reduction potentials of the cathode and anode respectively.

For the cell to function spontaneously (i.e., produce a positive voltage and drive current), $E_{cell}$ must be positive. This is the assertion — and it is correct.

Now, what does a positive $E_{cell}$ imply about the relative values of $E_{cathode}$ and $E_{anode}$ ? From the equation:

E_{cell} > 0 \quad \Rightarrow \quad E_{cathode} - E_{anode} > 0 \quad \Rightarrow \quad E_{cathode} > E_{anode}

The reason given says $E_{cathode} < E_{anode}$ , which is exactly the opposite. That condition would give a negative $E_{cell}$ , meaning the cell would not function spontaneously — it would need an external voltage to force the reaction. …

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Common Mistakes & How to Avoid Them

Mistake 1: Confusing the sign convention for $E_{Cell}$

The error: Students often think $E_{Cell}$ must be positive for any cell to function. This is partially true — a spontaneous (functioning) galvanic cell does have a positive $E_{Cell}$ . However, the reason given is wrong, which leads students to incorrectly mark option (i) or (ii).

How to avoid:

Remember the correct formula:

E_{Cell} = E_{cathode} - E_{anode}

For a spontaneous cell:

E_{cathode} > E_{anode} \quad \Rightarrow \quad E_{Cell} > 0

The reason says $E_{cathode} < E_{anode}$ , which would give $E_{Cell} < 0$ — that describes a non-spontaneous (electrolytic) cell.

Mistake 2: Thinking the reason correctly explains the assertion

The error: Students see "Assertion is true" and "Reason mentions cathode & anode" and assume the reason is correct and explains the assertion.

How to avoid:

Check the inequality in the reason carefully.
The assertion says $E_{Cell} > 0$ (true for a functioning galvanic cell).
The reason says $E_{cathode} < E_{anode}$ (false for a spontaneous cell).
Since the reason is false, options (i) and (ii) are eliminated immediately.

Mistake 3: Forgetting that a "functioning cell" in this context means a galvanic (voltaic) cell

The error: Students think of electrolytic cells (which require external voltage) and get confused about sign conventions.

How to avoid:

In Indian board exams, "cell" in such assertion-reason questions usually refers to a galvanic cell (spontaneous).
For a galvanic cell:
- $E_{Cell} > 0$ (spontaneous)
- $E_{cathode} > E_{anode}$
For an electrolytic cell:
- $E_{Cell} < 0$ (non-spontaneous, needs external energy)
- $E_{cathode} < E_{anode}$ (but this is not the "functioning" case meant here)

Mistake 4: Overthinking the assertion into electrolytic-cell territory

The error: Some students reason: "An electrolytic cell also 'functions', and it runs on a negative $E_{Cell}$ (it needs an external source to force the reaction) — so the assertion, read as a universal statement about any cell, must be false. Both statements are false → option (iv)."

Why it's wrong: In this chapter, "cell" (without qualification) means a galvanic/voltaic cell — the device this whole topic of $E_{Cell} = E_{cathode} - E_{anode}$ and spontaneity is built around. Within that intended scope, the assertion is correct exactly as stated: a galvanic cell only drives current spontaneously when $E_{Cell} > 0$ . Reading "cell" as also covering electrolytic cells is over-interpreting a straightforward statement — the actual factual error lies in the reason, not the assertion (the reason reverses $E_{cathode}$ and $E_{anode}$ ). …

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Q.Assertion: $E_{Cell}$ should have a positive value for the cell to function.
Reason: $E_{cathode} < E_{anode}$

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: Conceptual Verification of Assertion-Reason Statements

Relevant Concept: Cell Potential and Spontaneity

Step-by-Step Verification

Common Mistakes & How to Avoid Them

Mistake 1: Confusing the sign convention for $E_{Cell}$

Mistake 2: Thinking the reason correctly explains the assertion

Mistake 3: Forgetting that a "functioning cell" in this context means a galvanic (voltaic) cell

Mistake 4: Overthinking the assertion into electrolytic-cell territory

Q.Assertion: ECellE_{Cell}ECell​ should have a positive value for the cell to function. Reason: Ecathode<EanodeE_{cathode} < E_{anode}Ecathode​<Eanode​

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Q.Assertion: $E_{Cell}$ should have a positive value for the cell to function.
Reason: $E_{cathode} < E_{anode}$

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