Relationship Between E°cell and the Equilibrium Constant (K)
What happens mathematically when a Galvanic cell battery completely dies? In the language of chemistry, the reaction has reached Equilibrium. At this exact moment, the driving force of the reaction drops to zero.
In JEE and NEET Electrochemistry, questions frequently test your ability to connect the Standard Cell Potential (E°cell) to the Equilibrium Constant (K). Let's see how the Nernst Equation transforms under these conditions.
Video Tutorial: Deriving the Equilibrium Formula
Watch Abhishek Sengar sir from CHEMCA break down the derivation and explain all three spontaneity cases that commonly appear in statement-based MCQs.
The Equilibrium Condition
We start with the standard Nernst Equation at any given time:
1. The battery stops working, so the cell potential drops to zero: Ecell = 0.
2. The Reaction Quotient (Q) is now perfectly balanced and becomes the Equilibrium Constant: Q = K.
Substituting these two conditions into the Nernst Equation:
-
0 = E°cell − (RT / nF) · ln(K)
-
E°cell = (RT / nF) · ln(K)
- Converting Natural Log (ln) to Base 10 Log (log) by multiplying by 2.303:
The Three Cases Cheat Sheet (Highly Tested!)
Because ΔG° = -nFE°cell, the values of K, E°cell, and ΔG° are inextricably linked. Memorize this table to solve theoretical MCQs in seconds.
| Value of K | Value of log(K) | Sign of E°cell | Sign of ΔG° | Reaction Status |
|---|---|---|---|---|
| K = 1 | 0 | 0 | 0 | At Equilibrium |
| K > 1 | Positive (+) | Positive (+) | Negative (-) | Spontaneous (Forward) |
| K < 1 | Negative (-) | Negative (-) | Positive (+) | Non-Spontaneous |
Practice Questions for JEE & NEET
Apply the equilibrium formulas to solve these standard examination numericals.
Question 1: Calculate the equilibrium constant (Kc) for the reaction Zn(s) + Cu2+(aq) ⇌ Zn2+(aq) + Cu(s) at 298 K.
Given: E°cell = 1.10 V. (Assume 2.303 RT / F = 0.059 V).
Answer: Kc ≈ 2 × 1037
Step-by-step Solution:
- Number of electrons exchanged (n) = 2.
- Formula at 298 K: E°cell = (0.059 / n) · log(Kc)
- 1.10 = (0.059 / 2) · log(Kc)
- log(Kc) = (1.10 × 2) / 0.059
- log(Kc) = 2.20 / 0.059 ≈ 37.288
- Taking antilog: Kc = 1037.288. Since 10^{0.288} \approx 2, the answer is approximately 2 × 10^{37}.
Question 2: A hypothetical electrochemical cell has a standard cell potential of -0.45 V. Which of the following is true about its equilibrium constant (K)?
A) K = 1
B) K > 1
C) K < 1
D) Cannot be determined
Answer: C) K < 1
Reasoning:
As per the cheat sheet table in the notes, if the Standard Cell Potential (E°cell) is negative (-0.45 V), it indicates that the reaction is non-spontaneous in the forward direction. Consequently, the equilibrium heavily favors the reactants over the products, meaning the value of the equilibrium constant (K) must be less than 1.
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