Electrochemistry Formulas For JEE 2026, Download PDF Now

Rules for Assigning Oxidation Numbers

• Free elements have oxidation number = 0 (e.g., Na, O$$_2$$, P$$_4$$, S$$_8$$)
• For monoatomic ions, oxidation number = charge on the ion (e.g., Na$$^+$$ = $$+1$$, Cl$$^-$$ = $$-1$$)
• Hydrogen is $$+1$$ in most compounds; $$-1$$ in metal hydrides (NaH, CaH$$_2$$)
• Oxygen is $$-2$$ in most compounds; $$-1$$ in peroxides (H$$_2$$O$$_2$$, Na$$_2$$O$$_2$$); $$-\frac{1}{2}$$ in superoxides (KO$$_2$$); $$+2$$ in OF$$_2$$
• Fluorine is always $$-1$$ (most electronegative element)
• Alkali metals are always $$+1$$; alkaline earth metals are always $$+2$$
• Sum of oxidation numbers = 0 for a neutral compound; = charge for a polyatomic ion

Half-Reaction Method Steps

• Step 1: Identify oxidation and reduction half-reactions
• Step 2: Balance atoms other than O and H in each half-reaction
• Step 3: Balance oxygen by adding H$$_2$$O
• Step 4: Balance hydrogen by adding H$$^+$$ (acidic medium) or OH$$^-$$ (basic medium)
• Step 5: Balance charge by adding electrons (e$$^-$$)
• Step 6: Multiply half-reactions so that electrons cancel
• Step 7: Add the two half-reactions together

Components of a Galvanic Cell

• Anode: The electrode where oxidation occurs (negative terminal in galvanic cell)
• Cathode: The electrode where reduction occurs (positive terminal in galvanic cell)
• Salt bridge: Provides ionic contact between half-cells (usually KCl or KNO$$_3$$ in agar)
• Electron flow: From anode to cathode through the external wire
• Ion flow: Anions move toward anode, cations move toward cathode through salt bridge

Cell Notation Convention

$$$\text{Anode} \,|\, \text{Anode solution} \,||\, \text{Cathode solution} \,|\, \text{Cathode}$$$

Example — Daniell Cell:

$$$\text{Zn}(s) \,|\, \text{Zn}^{2+}(aq) \,||\, \text{Cu}^{2+}(aq) \,|\, \text{Cu}(s)$$$

Anode (left): $$\text{Zn} \rightarrow \text{Zn}^{2+} + 2\text{e}^-$$ (oxidation)

Cathode (right): $$\text{Cu}^{2+} + 2\text{e}^- \rightarrow \text{Cu}$$ (reduction)

Overall: $$\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$$

Cell EMF

$$$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$$

For a spontaneous reaction: $$E^\circ_{\text{cell}} > 0$$

Note: Standard reduction potentials are used. The more positive the $$E^\circ$$, the stronger the oxidizing agent (greater tendency to be reduced).

Electrochemical Series (Selected Values)

Uses of the Electrochemical Series

• Predicting spontaneity: A species higher in the series (more negative $$E^\circ$$) can reduce a species lower in the series. Metal higher up displaces metal lower down from its salt solution.
• Strength of oxidizing/reducing agents: Higher $$E^\circ$$ = stronger oxidizing agent; lower $$E^\circ$$ = stronger reducing agent.
• Reactivity with water/acids: Metals above hydrogen can displace H$$_2$$ from dilute acids.

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

At 298 K (converting to log base 10):

$$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log Q$$$

where:

• $$n$$ = number of electrons transferred in the balanced equation
• $$F$$ = Faraday constant = 96485 C/mol $$\approx$$ 96500 C/mol
• $$Q$$ = reaction quotient
• $$R$$ = 8.314 J/(mol·K)

Gibbs Energy and EMF

$$$\Delta G = -nFE_{\text{cell}}$$$

Under standard conditions:

$$$\Delta G^\circ = -nFE^\circ_{\text{cell}}$$$

• If $$E^\circ_{\text{cell}} > 0$$: $$\Delta G^\circ < 0$$ (spontaneous — galvanic cell)
• If $$E^\circ_{\text{cell}} < 0$$: $$\Delta G^\circ > 0$$ (non-spontaneous — electrolytic cell needed)

Faraday's First Law of Electrolysis

The mass of substance deposited or dissolved at an electrode is directly proportional to the quantity of electricity (charge) passed:

$$$m = \frac{M \times I \times t}{n \times F} = \frac{M \times Q}{n \times F}$$$

where:

• $$m$$ = mass deposited (g)
• $$M$$ = molar mass (g/mol)
• $$I$$ = current (A), $$t$$ = time (s), $$Q = It$$ = charge (C)
• $$n$$ = number of electrons transferred per ion
• $$F$$ = 96500 C/mol (charge of 1 mol of electrons)

Faraday's Second Law of Electrolysis

When the same quantity of electricity passes through different electrolytes in series, the masses deposited are proportional to their equivalent weights:

$$$\frac{m_1}{m_2} = \frac{E_1}{E_2}$$$

where $$E = M/n$$ is the equivalent weight (molar mass divided by number of electrons exchanged per atom/ion).

Conductance Formulas

Conductance (G) = reciprocal of resistance:

$$$G = \frac{1}{R} = \kappa \times \frac{A}{l}$$$

Cell constant: $$G^* = l/A$$ (where $$l$$ = distance between electrodes, $$A$$ = area)

$$$\kappa = G \times G^* = \frac{G^*}{R}$$$

Molar conductivity:

$$$\Lambda_m = \frac{\kappa \times 1000}{c}$$$

where $$c$$ = concentration in mol/L, $$\kappa$$ in S/cm, and $$\Lambda_m$$ in S·cm$$^2$$/mol.

Variation of $$\Lambda_m$$ with Dilution

For strong electrolytes (e.g., NaCl, KCl):

$$\Lambda_m$$ increases slightly with dilution and approaches a limiting value $$\Lambda_m^\circ$$ (molar conductivity at infinite dilution):

$$$\Lambda_m = \Lambda_m^\circ - A\sqrt{c} \quad \text{(Debye–Hückel–Onsager equation)}$$$

For weak electrolytes (e.g., CH$$_3$$COOH):

$$\Lambda_m$$ increases steeply with dilution because ionization increases. $$\Lambda_m^\circ$$ cannot be obtained by extrapolation — we use Kohlrausch's law instead.

Kohlrausch's Law Formula

$$$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$$

where $$\nu_+$$ and $$\nu_-$$ are the number of cations and anions per formula unit, and $$\lambda_+^\circ$$ and $$\lambda_-^\circ$$ are the limiting ionic conductivities.

Applications:

• Finding $$\Lambda_m^\circ$$ of weak electrolytes (which cannot be measured directly)
• Calculating degree of dissociation: $$\alpha = \dfrac{\Lambda_m}{\Lambda_m^\circ}$$
• Finding $$K_a$$ of a weak acid: $$K_a = \dfrac{c\alpha^2}{1 - \alpha} = \dfrac{c(\Lambda_m)^2}{\Lambda_m^\circ(\Lambda_m^\circ - \Lambda_m)}$$

Types of Batteries

Lead-Acid Battery Reactions

At anode (during discharge):

$$\text{Pb}(s) + \text{SO}_4^{2-}(aq) \rightarrow \text{PbSO}_4(s) + 2\text{e}^-$$

At cathode (during discharge):

$$\text{PbO}_2(s) + \text{SO}_4^{2-}(aq) + 4\text{H}^+ + 2\text{e}^- \rightarrow \text{PbSO}_4(s) + 2\text{H}_2\text{O}$$

Overall:

$$$\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O}$$$

During charging, the reactions are reversed.

Mechanism of Rusting

Iron rusting occurs in the presence of both water and oxygen:

At anodic region (Fe surface):

$$\text{Fe}(s) \rightarrow \text{Fe}^{2+}(aq) + 2\text{e}^-$$ (oxidation)

At cathodic region (near water droplet):

$$\text{O}_2(g) + 4\text{H}^+(aq) + 4\text{e}^- \rightarrow 2\text{H}_2\text{O}(l)$$ (reduction)

The Fe$$^{2+}$$ ions are further oxidized to Fe$$^{3+}$$, forming rust: $$\text{Fe}_2\text{O}_3 \cdot x\text{H}_2\text{O}$$ (hydrated iron(III) oxide).

Prevention methods:

• Galvanization (coating with Zn — Zn is more reactive, acts as sacrificial anode)
• Painting, oiling, or greasing the surface
• Electroplating with a less reactive metal (Cr, Ni)
• Cathodic protection (connecting to a more reactive metal like Mg)
• Alloying (e.g., stainless steel contains Cr which forms a protective oxide layer)

• $$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$
• Nernst: $$E = E^\circ - \dfrac{0.0591}{n}\log Q$$ (at 298 K)
• Gibbs–EMF: $$\Delta G^\circ = -nFE^\circ_{\text{cell}}$$
• Equilibrium: $$\log K = \dfrac{nE^\circ}{0.0591}$$
• Faraday's 1st law: $$m = \dfrac{MIt}{nF}$$
• Molar conductivity: $$\Lambda_m = \dfrac{\kappa \times 1000}{c}$$
• Kohlrausch: $$\Lambda_m^\circ = \nu_+\lambda_+^\circ + \nu_-\lambda_-^\circ$$
• Degree of dissociation: $$\alpha = \Lambda_m / \Lambda_m^\circ$$