EMF of a Cell — Revision Notes

⚡ 30-Second Revision

EMF (E): — Max potential difference, open circuit, no current. Unit: Volts (V). \n- **Standard EMF ($E_{\text{cell}}^\circ$): At 298 K, 1 M conc., 1 atm pressure. \n- Formula for $E_{\text{cell}}^\circ$:** $E_{\text{cell}}^\circ = E_{\text{cathode}}^\circ - E_{\text{anode}}^\circ$ \n- Nernst Equation (298 K): $E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.0592}{n} \log Q$ \n- Gibbs Free Energy: $\Delta G = -nFE_{\text{cell}}$ (Spontaneous if $E_{\text{cell}} > 0$, $\Delta G < 0$) \n- Equilibrium Constant: $E_{\text{cell}}^\circ = \frac{0.0592}{n} \log K$ (At equilibrium, $E_{\text{cell}} = 0$) \n- Faraday's Constant (F): $96485 \text{ C mol}^{-1}$

2-Minute Revision

EMF (Electromotive Force) is the maximum voltage an electrochemical cell can produce when no current is flowing, representing the driving force of the redox reaction. It's an intensive property, depending on the nature of electrodes, electrolyte concentrations, and temperature, but not electrode size.

Standard EMF ($E_{\text{cell}}^\circ$) is calculated from standard reduction potentials: $E_{\text{cell}}^\circ = E_{\text{cathode}}^\circ - E_{\text{anode}}^\circ$, where the cathode has the more positive reduction potential.

For non-standard conditions, the Nernst equation, $E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.0592}{n} \log Q$ (at 298 K), is used, where $n$ is the number of electrons transferred and $Q$ is the reaction quotient.

EMF is directly related to Gibbs free energy change ($\Delta G = -nFE_{\text{cell}}$), meaning a positive EMF signifies a spontaneous reaction (negative $\Delta G$). At equilibrium, $E_{\text{cell}} = 0$, and $E_{\text{cell}}^\circ$ relates to the equilibrium constant K.

Remember to distinguish EMF from terminal potential difference, which is always lower when current is drawn due to internal resistance.

5-Minute Revision

The Electromotive Force (EMF) of an electrochemical cell is the maximum potential difference generated between its electrodes under open-circuit conditions (no current flow). It quantifies the cell's ability to drive a spontaneous redox reaction and is measured in Volts.

The standard EMF ($E_{\text{cell}}^\circ$) is determined under standard conditions (298 K, 1 M concentrations, 1 atm pressure) using standard reduction potentials. The formula is $E_{\text{cell}}^\circ = E_{\text{cathode}}^\circ - E_{\text{anode}}^\circ$, where the cathode is the half-cell with the more positive standard reduction potential (undergoes reduction), and the anode is the half-cell with the less positive (or more negative) standard reduction potential (undergoes oxidation).

\n\nFor non-standard conditions, the Nernst equation is indispensable: \n

$$E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{RT}{nF} \ln Q$$

\nAt 298 K, this simplifies to: \n$$E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.

0592}{n} \log Q$$\nHere,$n$is the number of electrons transferred in the balanced redox reaction, and$Q$ is the reaction quotient, similar to the equilibrium constant expression but with current concentrations/pressures.

\n\nExample: For the cell Zn(s) | Zn$^{2+}$(0.1 M) || Cu$^{2+}$(0.01 M) | Cu(s), given $E^\circ_{\text{Zn}^{2+}/\text{Zn}} = -0.76 \text{ V}$ and $E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34 \text{ V}$.

\n1. **Calculate $E_{\text{cell}}^\circ$:** Cu is cathode, Zn is anode. \n $E_{\text{cell}}^\circ = (+0.34) - (-0.76) = +1.10 \text{ V}$. \n2. Determine 'n' and 'Q': The reaction is Zn(s) + Cu$^{2+}$(aq) $\rightarrow$ Zn$^{2+}$(aq) + Cu(s).

So, $n=2$. \n $Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.1}{0.01} = 10$. \n3. Apply Nernst Equation: \n $E_{\text{cell}} = 1.10 - \frac{0.0592}{2} \log(10) = 1.10 - 0.0296 \times 1 = 1.

0704 \text{ V}$. \n\nEMF is also linked to the Gibbs free energy change ($\Delta G$) by$\Delta G = -nFE_{\text{cell}}$. A positive$E_{\text{cell}}$corresponds to a negative$\Delta G$, indicating a spontaneous reaction.

At equilibrium, $E_{\text{cell}} = 0$, and $E_{\text{cell}}^\circ = \frac{0.0592}{n} \log K$, where K is the equilibrium constant. Remember that EMF is an intensive property, independent of electrode size, and distinct from terminal potential difference ($V = E - Ir$), which is lower when current flows due to internal resistance.

Prelims Revision Notes

1
Definition of EMF: — Electromotive Force (EMF) is the maximum potential difference between the electrodes of an electrochemical cell when no current is drawn from it (open circuit). It is the driving force for the cell reaction. \n2. Units: EMF is measured in Volts (V). \n3. Nature: EMF is an intensive property; it does not depend on the size or amount of the electrodes or electrolytes. \n4. Electrode Potential: Potential difference between an electrode and its electrolyte. \n5. **Standard Electrode Potential ($E^\circ$):** Electrode potential measured under standard conditions (298 K, 1 M concentration for ions, 1 atm pressure for gases) relative to the Standard Hydrogen Electrode (SHE), which is assigned $0.00 \text{ V}$. \n6. **Calculation of Standard Cell EMF ($E_{\text{cell}}^\circ$):** \n * Identify the cathode (reduction, more positive $E^\circ$) and anode (oxidation, less positive $E^\circ$). \n * Formula: $E_{\text{cell}}^\circ = E_{\text{cathode}}^\circ - E_{\text{anode}}^\circ$. \n7. Nernst Equation (for non-standard conditions): \n * General form: $E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{RT}{nF} \ln Q$ \n * At 298 K: $E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.0592}{n} \log Q$ \n * $n$: number of electrons transferred in the balanced reaction. \n * $Q$: reaction quotient (products/reactants, excluding pure solids/liquids). \n8. **Relationship with Gibbs Free Energy ($\Delta G$):** \n * $\Delta G = -nFE_{\text{cell}}$ \n * For standard conditions: $\Delta G^\circ = -nFE_{\text{cell}}^\circ$ \n * Spontaneity: If $E_{\text{cell}} > 0$, then $\Delta G < 0$ (spontaneous). If $E_{\text{cell}} < 0$, then $\Delta G > 0$ (non-spontaneous). If $E_{\text{cell}} = 0$, then $\Delta G = 0$ (equilibrium). \n9. Relationship with Equilibrium Constant (K): \n * At equilibrium, $E_{\text{cell}} = 0$. \n * $E_{\text{cell}}^\circ = \frac{0.0592}{n} \log K$ (at 298 K) \n10. EMF vs. Terminal Potential Difference: \n * EMF: Maximum voltage, open circuit. \n * Terminal Potential Difference (V): Actual voltage when current (I) flows. $V = E - Ir$, where $r$ is internal resistance. $V \le E$. \n11. Salt Bridge: Maintains electrical neutrality and completes the internal circuit. \n12. Concentration Cells: $E_{\text{cell}}^\circ = 0$. EMF arises solely from concentration differences, calculated using the Nernst equation.

Vyyuha Quick Recall

Every Moment For Neet Gives Knowledge: \nEMF: Maximum Force (voltage) \nNernst Equation: $E = E^\circ - \frac{0.0592}{n} \log Q$ \nGibbs Free Energy: $\Delta G = -nFE$ \nK (Equilibrium Constant): $E^\circ = \frac{0.0592}{n} \log K$