Gibbs Energy and Cell EMF: ΔG° = −nFE°cell Explained
Chemistry · Thermodynamics · NEET
The equation ΔG° = −nFE°cell connects the Gibbs free energy of a reaction to the EMF (voltage) of a cell. Here n is the number of electrons transferred, F is the Faraday constant (96500 C/mol), and E°cell is the standard cell voltage. Remember the minus sign: if E°cell is positive, ΔG° is negative, so the reaction is spontaneous. Memory hook: "Positive volts, negative G, reaction runs free."
The sign of E°cell decides everything: a positive voltage gives negative ΔG° (spontaneous, K greater than 1), while a negative voltage gives positive ΔG° (non-spontaneous, K less than 1). The minus sign in the formula flips the sign.
Your doubts, answered
Why is there a minus sign in ΔG° = −nFE°cell?
The minus sign fixes the direction rule. A cell that works on its own (spontaneous) has a positive voltage, E°cell > 0. But a spontaneous reaction must have negative Gibbs energy, ΔG° < 0. The minus sign flips the positive voltage into a negative ΔG°, so both signs agree with each other. Without the minus sign the two rules would clash.
What does 'n' mean in the nFE°cell formula?
n is the number of moles of electrons that move from the anode to the cathode in the balanced cell reaction. You find n by balancing the half-reactions and seeing how many electrons cancel out. For example, if the reaction transfers 2 electrons, n = 2. In NEET, always read the balanced equation carefully to get n right, because a wrong n doubles or halves your answer.
If E°cell is negative, is ΔG° positive or negative?
If E°cell is negative, then ΔG° is positive. Look at the formula: ΔG° = −nFE°cell. Since n and F are always positive, a negative E°cell makes the whole right side positive. A positive ΔG° means the reaction is non-spontaneous (it will not run on its own). This exact idea was tested in NEET 2016.
What is the value of F (Faraday constant) I should use?
Use F = 96500 C/mol (coulombs per mole of electrons). Some books round it to 96487, but for NEET 96500 is standard. When E°cell is in volts and F is in C/mol, ΔG° comes out in joules per mole. Divide by 1000 to get kJ/mol.
How do ΔG°, E°cell, and K all connect?
Three formulas describe the same thing. ΔG° = −nFE°cell links Gibbs energy to voltage. ΔG° = −RT ln K links Gibbs energy to the equilibrium constant K. Setting them equal gives nFE°cell = RT ln K. So a positive E°cell means large K (products favoured) and a negative E°cell means small K (reactants favoured). Knowing one value lets you find the other two.
⚠️ The NEET trap ✗ E°cell is negative, so ΔG° must also be negative and the reaction is spontaneous. ✓ E°cell negative makes ΔG° positive (because of the minus sign), so the reaction is non-spontaneous and K < 1. 🧠 The minus sign FLIPS the sign of E°cell. Negative volts give positive G, never negative.
Real NEET questions
NEET 2016 Phase 2
If the E°cell for a given reaction has a negative value, which of the following gives the correct relationships for the values of ΔG° and K_eq?
A · ΔG° > 0; K_eq < 1 ✓
B · ΔG° > 0; K_eq > 1
C · ΔG° < 0; K_eq < 1
D · ΔG° < 0; K_eq > 1
Solution: Use ΔG° = −nFE°cell. E°cell is negative, and n, F are positive, so ΔG° = −(positive)(negative) = positive, meaning ΔG° > 0. Now use ΔG° = −RT ln K_eq. A positive ΔG° forces ln K_eq to be negative, so K_eq < 1. Answer: ΔG° > 0 and K_eq < 1, option A.
NEET 2019
For the cell reaction 2Fe³⁺(aq) + 2I⁻(aq) → 2Fe²⁺(aq) + I₂(aq), E°cell = 0.24 V at 298 K. The standard Gibbs energy (ΔrG°) of the cell reaction is:
A · −46.32 kJ/mol
B · −23.16 kJ/mol ✓
C · 46.32 kJ/mol
D · 23.16 kJ/mol
Solution: ΔrG° = −nFE°cell. The official NEET key uses n = 1, so ΔrG° = −1 × 96500 × 0.24 = −23160 J = −23.16 kJ/mol, option B. Note: if you count the balanced equation as transferring 2 electrons (n = 2), you get −46.32 kJ/mol (option A). NEET accepted B as per the official key, so match n to what the answer key uses. The negative sign confirms the reaction is spontaneous, as expected for a positive E°cell.
NEET 2019
For a cell involving one electron, E°cell = 0.59 V at 298 K. The equilibrium constant for the cell reaction is: (Given 2.303RT/F = 0.059 V at 298 K)
A · 1.0 × 10²
B · 1.0 × 10⁵
C · 1.0 × 10¹⁰ ✓
D · 1.0 × 10³⁰
Solution: At equilibrium ΔG° = −nFE°cell = −RT ln K. Rearranging gives log K = nE°cell / 0.059. With n = 1 and E°cell = 0.59 V: log K = (1 × 0.59) / 0.059 = 10. So K = 1.0 × 10¹⁰, option C. This shows how a moderate positive voltage gives a huge equilibrium constant.
Solved Thermodynamics NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the unit of ΔG° when using ΔG° = −nFE°cell?
When n has no unit, F is in C/mol, and E°cell is in volts, ΔG° comes out in J/mol (joules per mole). Divide by 1000 to convert to kJ/mol, which is the common NEET answer unit.
Does the sign of E°cell decide if a cell is a galvanic cell?
Yes. A galvanic (voltaic) cell produces electricity on its own, so it has a positive E°cell and a negative ΔG°. If E°cell is negative, the reaction is non-spontaneous and would need an external voltage (electrolysis).
How do I quickly find n for a cell reaction?
Write the two half-reactions, balance the electrons so they are equal in both halves, and n is that balanced number of electrons. For example, Zn → Zn²⁺ + 2e⁻ gives n = 2.
Why does NEET love this formula?
It links three big ideas in one line: thermodynamics (ΔG°), electrochemistry (E°cell), and equilibrium (K). One question can test all three, so learning ΔG° = −nFE°cell gives you fast marks across chapters.
