How to Calculate the EMF (Ecell) of a Galvanic Cell
The Nernst Equation is one of the most critical formulas in the Electrochemistry chapter. It allows us to calculate the cell potential (Ecell) under non-standard conditions—meaning when the concentration of the electrolyte solutions is not exactly 1 Molar or the temperature is not 298K.
While the formula itself is straightforward, students frequently make a critical error when formulating the reaction quotient. Let's learn the foolproof way to solve these numericals for JEE Main, JEE Advanced, and NEET.
Video Tutorial: Solving a Copper-Silver Cell
Watch Abhishek Sengar sir from CHEMCA break down a standard Galvanic cell problem involving Copper and Silver electrodes. Pay close attention to the second step!
The 3-Step Strategy
Step 1: Find Standard Cell Potential (E°cell)
Identify the Cathode (Right Side / Reduction) and the Anode (Left Side / Oxidation). Then apply:
E°cell = E°cathode - E°anode
Do NOT jump straight to the Nernst Equation. You must write the balanced cell reaction to find the correct number of transferred electrons (n) and the correct stoichiometric coefficients to square/cube your concentration terms. If you skip this, your answer will likely be wrong.
Step 3: Apply the Nernst Equation (at 298K)
Where Q is the Reaction Quotient: [Products] / [Reactants] raised to their stoichiometric powers.
Solved Example from the Video
Given: A cell with Cu | Cu2+(0.01M) || Ag+(0.1M) | Ag.
E°Cu2+/Cu = 0.34 V, E°Ag+/Ag = 0.80 V.
-
Calculate E°cell:
E°cell = 0.80 - 0.34 = 0.46 V -
Balanced Equation:
Cu gives 2 electrons, but Ag accepts 1. We must multiply Ag by 2.
Cu(s) + 2Ag+(aq) → Cu2+(aq) + 2Ag(s)
Electrons transferred (n) = 2. -
Nernst Equation:
Ecell = 0.46 - (0.0591 / 2) × log( [Cu2+] / [Ag+]2 )
Ecell = 0.46 - (0.0591 / 2) × log( 0.01 / (0.1)2 )
Since (0.1)2 = 0.01, the log term becomes log(0.01 / 0.01) = log(1) = 0.
Final Answer: Ecell = 0.46 V
Practice Questions for JEE & NEET
Try these hand-picked numericals. Remember to balance the equation first!
Question 1: Calculate the EMF of the Daniel Cell at 298K: Zn(s) | Zn2+(0.1M) || Cu2+(0.01M) | Cu(s).
Given: E°Zn2+/Zn = -0.76 V, E°Cu2+/Cu = 0.34 V.
Step-by-step Solution:
- Standard EMF: E°cell = 0.34 - (-0.76) = 1.10 V
- Balanced Equation: Zn + Cu2+ → Zn2+ + Cu. Here, n = 2.
- Nernst Equation: Ecell = 1.10 - (0.0591 / 2) × log( [Zn2+] / [Cu2+] )
- Ecell = 1.10 - 0.0295 × log( 0.1 / 0.01 )
- Ecell = 1.10 - 0.0295 × log(10)
- Since log(10) = 1: Ecell = 1.10 - 0.0295 = 1.0705 V
- Answer: 1.07 V
Question 2: Calculate the EMF of the following cell at 298K: Mg(s) | Mg2+(10-3 M) || Ag+(10-4 M) | Ag(s).
Given: E°cell = 3.16 V.
Step-by-step Solution:
- Balanced Equation: Mg + 2Ag+ → Mg2+ + 2Ag. Here, n = 2.
- Nernst Equation: Ecell = 3.16 - (0.0591 / 2) × log( [Mg2+] / [Ag+]2 )
- Ecell = 3.16 - 0.0295 × log( 10-3 / (10-4)2 )
- Simplify log term: log( 10-3 / 10-8 ) = log(105) = 5
- Ecell = 3.16 - 0.0295 × 5
- Ecell = 3.16 - 0.1475 = 3.0125 V
- Answer: 3.01 V
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