Nernst Equation — Revision Notes

⚡ 30-Second Revision

General Nernst Equation: — $E = E^{\circ} - \frac{RT}{nF}\ln Q$
Nernst Equation at $298, ext{K}$: — $E = E^{\circ} - \frac{0.0592}{n}\log Q$
For a half-cell (reduction): — $E_{red} = E^{\circ}_{red} - \frac{0.0592}{n}\log \frac{[Reduced,form]}{[Oxidized,form]}$
Reaction Quotient (Q): — For $aA + bB \rightleftharpoons cC + dD$, $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (exclude solids/pure liquids).
At Equilibrium: — $E_{cell} = 0$, $Q = K_{eq}$. Thus, $E^{\circ}_{cell} = \frac{0.0592}{n}\log K_{eq}$ (at $298,\text{K}$).
Constants: — $R = 8.314,\text{J/(mol\cdot K)}$, $F = 96485,\text{C/mol}$.
'n': — Number of electrons transferred in the balanced reaction.

2-Minute Revision

The Nernst equation is your go-to tool for calculating electrode or cell potentials under non-standard conditions, meaning when concentrations aren't $1,\text{M}$ or temperature isn't $298,\text{K}$. Remember its general form: $E = E^{\circ} - \frac{RT}{nF}\ln Q$.

For NEET, you'll most often use the simplified version at $298,\text{K}$: $E = E^{\circ} - \frac{0.0592}{n}\log Q$. Key steps for any problem: first, correctly identify 'n', the number of electrons transferred in the balanced reaction.

Second, accurately set up the reaction quotient 'Q', remembering to exclude pure solids and liquids and to use stoichiometric coefficients as exponents. Third, substitute values carefully and perform logarithmic calculations.

Don't forget that at equilibrium, $E_{cell} = 0$, which allows you to link $E^{\circ}_{cell}$ to the equilibrium constant $K_{eq}$ via $E^{\circ}_{cell} = \frac{0.0592}{n}\log K_{eq}$. Always check if the temperature is $298,\text{K}$ before using the $0.

0592$ constant.

5-Minute Revision

The Nernst equation is fundamental for understanding how electrochemical cells function outside of ideal standard conditions. It quantifies the deviation of cell potential ($E_{cell}$) from standard cell potential ($E^{\circ}_{cell}$) due to changes in reactant/product concentrations and temperature.

The core equation is $E_{cell} = E^{\circ}_{cell} - \frac{RT}{nF}\ln Q$. Here, $R$ is the gas constant, $T$ is absolute temperature, $n$ is the moles of electrons transferred, $F$ is Faraday's constant, and $Q$ is the reaction quotient.

For most NEET problems at $298,\text{K}$, this simplifies to $E_{cell} = E^{\circ}_{cell} - \frac{0.0592}{n}\log Q$.

Example 1: Half-cell potential. Calculate the potential of a $Ni^{2+}/Ni$ electrode in $0.001,\text{M}$ $NiSO_4$ at $298,\text{K}$, given $E^{\circ}_{Ni^{2+}/Ni} = -0.25,\text{V}$. Reaction: $Ni^{2+}(aq) + 2e^- \rightleftharpoons Ni(s)$. So, $n=2$. $Q = \frac{[Ni(s)]}{[Ni^{2+}]} = \frac{1}{0.001} = 1000$. $E_{Ni^{2+}/Ni} = -0.25 - \frac{0.0592}{2}\log(1000) = -0.25 - 0.0296 \times 3 = -0.25 - 0.0888 = -0.3388,\text{V}$.

Example 2: Equilibrium Constant. If $E^{\circ}_{cell} = 0.1184,\text{V}$ for a reaction with $n=2$ at $298,\text{K}$, find $K_{eq}$. At equilibrium, $E_{cell} = 0$, so $E^{\circ}_{cell} = \frac{0.0592}{n}\log K_{eq}$. $0.1184 = \frac{0.0592}{2}\log K_{eq}$. $0.1184 = 0.0296\log K_{eq}$. $\log K_{eq} = \frac{0.1184}{0.0296} = 4$. $K_{eq} = 10^4$.

Always ensure you correctly determine 'n' by balancing the redox reaction and correctly set up 'Q' by including only aqueous species and gases with their proper stoichiometric exponents. Remember that pure solids and liquids are excluded from $Q$. Pay attention to the temperature given in the problem.

Prelims Revision Notes

The Nernst equation is vital for NEET, allowing calculation of electrode and cell potentials under non-standard conditions. The general form is $E = E^{\circ} - \frac{RT}{nF}\ln Q$. For most NEET problems, assume $T=298,\text{K}$ and use the simplified form: $E = E^{\circ} - \frac{0.0592}{n}\log Q$. Here, $E$ is the non-standard potential, $E^{\circ}$ is the standard potential, $n$ is the number of electrons transferred in the balanced reaction, and $Q$ is the reaction quotient.

Key Points for Recall:

'n' determination: — Always balance the redox reaction to find 'n'. For example, in $Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu$, $n=2$. In $2Al + 3Ni^{2+} \rightarrow 2Al^{3+} + 3Ni$, $n=6$.
Reaction Quotient (Q): — For a general reaction $aA + bB \rightleftharpoons cC + dD$, $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$. Remember to exclude pure solids and pure liquids, as their activities are considered 1. For gases, use partial pressures.
Half-cell potential: — For a reduction $Ox^{n+} + ne^- \rightleftharpoons Red$, $E_{red} = E^{\circ}_{red} - \frac{0.0592}{n}\log \frac{[Red]}{[Ox^{n+}]}$. Note that $[Red]$ refers to the concentration of the reduced species if it's aqueous, otherwise it's 1 for a solid.
Cell potential: — $E_{cell} = E_{cathode} - E_{anode}$, where both are reduction potentials calculated using the Nernst equation for their respective half-cells, or directly using the overall $E^{\circ}_{cell}$ and $Q$ for the full reaction.
Equilibrium Constant ($K_{eq}$): — At equilibrium, $E_{cell} = 0$ and $Q = K_{eq}$. This leads to $E^{\circ}_{cell} = \frac{0.0592}{n}\log K_{eq}$ (at $298,\text{K}$). A positive $E^{\circ}_{cell}$ means $K_{eq} > 1$, favoring products.
Temperature Effect: — If $T \neq 298,\text{K}$, use the full equation with $\ln Q$ and calculate $\frac{RT}{nF}$ with the given $T$. Increasing $T$ generally decreases $E_{cell}$ if $Q > 1$.
pH Calculation: — For a standard hydrogen electrode (SHE), $E_{H^+/H_2} = -0.0592\text{pH}$ (at $P_{H_2} = 1,\text{atm}$).

Vyyuha Quick Recall

Nernst's Equation: 'E' for 'E'verything, 'E-naught' for 'E'xactly standard, 'R'eally 'T'ough 'n' 'F'actors, 'ln Q'uickly changes!