Calculating EMF of a Cell from Electrode Potentials

Chemistry · Redox Equilibrium · NEET

The EMF (electromotive force) of a cell is found with one formula: E°cell = E°cathode - E°anode, where both values are standard reduction potentials. The electrode with the higher (more positive) reduction potential becomes the cathode. Memory hook: "Cathode minus Anode" - always bigger E° minus smaller E°, and a positive answer means the cell reaction happens on its own.
E°cell = E°cathode - E°anodeCATHODE (higher E°)Reduction happensCu2+ + 2e- -> CuE° = +0.34 VANODE (lower E°)Oxidation happensZn -> Zn2+ + 2e-E° = -0.76 V-E°cell = 0.34 - (-0.76) = +1.10 V (positive -> spontaneous)
The electrode with the higher reduction potential is the cathode; subtract anode from cathode. For the Daniell cell, E°cell = 0.34 - (-0.76) = +1.10 V, and being positive it runs on its own.

Your doubts, answered

Do I add or subtract the two electrode potentials?

You subtract. The formula is E°cell = E°cathode - E°anode. A common wrong habit is adding the two numbers. Adding only works if you deliberately flipped one electrode into an oxidation potential first and changed its sign. To avoid mistakes, always keep both values as standard reduction potentials and just subtract.

Should I use reduction potential or oxidation potential?

Use standard reduction potentials for both electrodes. NEET tables and NCERT give reduction potentials. Oxidation potential is just the reduction value with the opposite sign. If you mix the two types, your answer will be wrong. Rule: keep everything as reduction potential, then E°cell = E°cathode - E°anode.

How do I know which electrode is the cathode?

The electrode with the higher (more positive) standard reduction potential is the cathode (reduction happens there). The one with the lower value is the anode (oxidation happens there). Example: Cu (+0.34 V) and Zn (-0.76 V) - copper is the cathode, zinc is the anode. This choice makes E°cell come out positive, which is what a real galvanic cell needs.

Do I multiply the potential by the number of electrons?

No. Electrode potential is an intensive property - it does not depend on how many electrons or how you balance the equation. So even if one half-reaction has 5 electrons and the other has 2, you do NOT scale the E° value. You only balance electrons when finding delta-G or using the Nernst equation, not for E°cell itself.

What does a negative E°cell tell me?

A negative E°cell means the reaction as written is non-spontaneous - it will not run on its own (delta-G is positive). The reverse reaction is the spontaneous one. In NEET, a negative E°cell is your signal that the metal or ion you picked as the oxidiser is actually too weak, so the reaction does not proceed.

⚠️ The NEET trap
Given E°(MnO4-/Mn2+) written as -1.510 V, students plug it straight in and get E°cell = -1.510 - 1.223 = -2.733 V, then answer 'No'.
That -1.510 V was quoted for the reverse (oxidation) direction. The standard REDUCTION potential is +1.510 V. So E°cell = +1.510 - 1.223 = +0.287 V (positive), and MnO4- DOES liberate O2.
🧠 Before subtracting, force both numbers to be reduction potentials. A sign flip hidden in the question is NTA's favourite trap.

Real NEET questions

NEET 2022

Half-cell reactions: MnO4- + 8H+ + 5e- -> Mn2+ + 4H2O, E°(MnO4-/Mn2+) = -1.510 V (quoted for the oxidation direction); 1/2 O2 + 2H+ + 2e- -> H2O, E°(O2/H2O) = +1.223 V. Will MnO4- liberate O2 from water in acid?

A · Yes, because E°cell = +0.287 V
B · No, because E°cell = -0.287 V
C · Yes, because E°cell = +2.733 V
D · No, because E°cell = -2.733 V
Solution: Convert to reduction potentials: E°(MnO4-/Mn2+) = +1.510 V. Here MnO4- is reduced (cathode) and water is oxidised (anode). E°cell = E°cathode - E°anode = 1.510 - 1.223 = +0.287 V. Positive E°cell means delta-G < 0, so the reaction is spontaneous and O2 is liberated. Answer (a). Note: you do NOT scale the potentials by the 5 vs 2 electrons.

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Frequently asked

What is the exact formula for EMF of a cell?

E°cell = E°cathode - E°anode, using standard reduction potentials for both electrodes. It can also be written as E°(right) - E°(left) when the cell is drawn in standard convention (anode on the left, cathode on the right).

Why must E°cell be positive for a galvanic cell?

A positive E°cell means delta-G° = -nFE°cell is negative, so the reaction releases energy and runs spontaneously. That is how a galvanic (voltaic) cell produces current. A negative E°cell would need an outside power source (electrolytic cell).

Is electrode potential affected by the number of electrons?

No. Standard electrode potential is intensive, so it stays the same no matter how you multiply the half-reaction. You never multiply E° by n when finding E°cell.

Can I use oxidation potentials instead?

Yes, but be consistent. If you use oxidation potentials, E°cell = E°ox(anode) + E°red(cathode). Most NEET students find it safer to keep only reduction potentials and use E°cathode - E°anode.

How does EMF connect to feasibility of a reaction?

If E°cell comes out positive, the reaction as written is feasible (spontaneous). If negative, it is not - the reverse runs instead. This links directly to the feasibility topic tested every year in NEET.