Nernst Equation Class 12 Derivation Easy Explanation | Formula, Numericals & Applications for CBSE 2025

Nernst Equation Class 12 Derivation Easy Explanation | Applications, Numericals & Board Questions 2025

Introduction

Electrochemistry is one of the most scoring yet conceptually challenging chapters in Class 12 Chemistry. Among its key topics, the Nernst Equation stands out because it connects chemistry and physics — explaining how electrical potential depends on ion concentration.
In this article, you’ll learn the Nernst Equation derivation, its applications, formula meaning, solved numericals, and board-based questions with clear explanations — all in one place.

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What Is the Nernst Equation?

Developed by German scientist Walther Nernst, this equation relates the electrode potential (E) of an electrochemical cell to the standard electrode potential (E°) and the concentrations (activities) of the reacting species.

In simple terms:

It tells us how the cell potential changes when the ionic concentrations are not standard (1 M).

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Basic Concept

Every redox reaction in an electrochemical cell tends to reach equilibrium.
At equilibrium, the Gibbs Free Energy (ΔG) is related to the cell potential (Ecell) by:

Where:

• = number of electrons transferred
• = Faraday constant (96,500 C mol⁻¹)

The Nernst Equation builds on this concept to include the effect of ion concentration.

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Derivation of Nernst Equation (Step-by-Step)

Let us derive it for a general redox reaction:

At standard conditions (1 M concentration, 1 atm, 298 K):

At non-standard conditions:

Substitute the ΔG relations:

Divide both sides by :

This is the Nernst Equation.

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 At 298 K Simplified Form

At temperature T = 298 K,

So,

Convert ln to log₁₀:

Therefore:

This is the form used in Class 12 CBSE calculations.

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 Understanding Each Term

Symbol	Meaning	Unit
E	Electrode potential under given conditions	Volt (V)
E°	Standard electrode potential (1 M, 1 atm, 298 K)	Volt (V)
R	Gas constant (8.314 J mol⁻¹ K⁻¹)	J mol⁻¹ K⁻¹
T	Temperature in Kelvin	K
n	Number of electrons transferred	–
F	Faraday constant (96500 C mol⁻¹)	C mol⁻¹
Q	Reaction quotient	Dimensionless

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Application of Nernst Equation

1. To Calculate EMF of a Cell

For the Daniell cell:

2. To Find Concentration of Ions

Given Ecell and E°, you can rearrange to compute unknown ion concentration.

3. To Determine pH

Using hydrogen electrode:

From measured E, find [H⁺] and then pH = −log[H⁺].

4. In Concentration Cells

In cells where both electrodes are the same but have different ion concentrations:

5. Understanding Corrosion and Battery Function

Battery potentials change as concentration of ions changes — Nernst Equation predicts that variation.

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Solved Numerical Example

Q1. Calculate the EMF of a Daniell cell at 298 K when

Solution:

✅ Final Answer: 1.13 V

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Common Mistakes to Avoid

1. Confusing log with ln – always use log₁₀ for the 0.0591 form.
2. Forgetting to balance n (number of electrons) – this changes the E value.
3. Using wrong concentration terms – only include aqueous species and gases.
4. Not converting temperature to Kelvin.
5. Misplacing Q – remember: .

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Important Board Questions (CBSE Pattern 2025)

 1-Mark Questions

• Write the Nernst Equation for a general redox reaction.
• Define the term electrode potential.
• What is the effect of temperature on cell potential?

 2-Mark Questions

• Derive the Nernst Equation from Gibbs Free Energy.
• Calculate Ecell for the cell: where E° = 0.77 V and .

 3-Mark Questions

• Explain any three applications of the Nernst Equation.
• Derive the simplified form E = E° − (0.0591/n) log Q for 298 K.

 Assertion-Reason Type

1. Assertion: Cell potential decreases as reaction proceeds.
   Reason: Concentration of reactants decreases, reducing Ecell as per Nernst Equation.
   ✅ Both Assertion and Reason are true, and Reason explains Assertion.

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💬 Competency-Based Question (Example 2025 Pattern)

The EMF of a Daniell cell at 298 K is found to be 1.12 V when and . Calculate x if E°_{cell} = 1.10 V.

Solution:

✅ [Cu²⁺] = 0.48 M

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Summary – Quick Revision Chart

Concept	Key Point
Relation between ΔG and E	ΔG = −nFE
Nernst Equation	E = E° − (RT/nF) ln Q
Simplified at 298 K	E = E° − (0.0591/n) log Q
Meaning of Q	(products)/(reactants)
Importance	Shows effect of ion concentration on Ecell
Used for	EMF calculation, pH, ion concentration, corrosion study

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Exam Tips for Full Marks

1. Always write the complete equation for the cell before substituting values.
2. Keep your logarithm calculation steps clear — board checkers give marks for method.
3. Include units and write answers to two decimal places.
4. Learn standard potentials for common electrodes (Zn, Cu, Fe, Ag).
5. Practice numericals daily — at least five problems from past papers.

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 Conclusion

The Nernst Equation is a cornerstone of Electrochemistry that explains how a cell’s potential changes with concentration and temperature. By mastering its derivation, understanding its physical meaning, and solving numerical questions, students can easily score full marks in this topic.

On Toppers Hub, we simplify complex Class 12 Chemistry topics into clear, exam-ready notes with previous-year patterns and competency-based practice — helping you learn smart, revise faster, and score better.

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