Electrochemistry

Electrochemistry studies the relationship between chemical reactions and electrical energy. A galvanic (voltaic) cell converts the energy of a spontaneous redox reaction directly into electricity — the principle behind every battery. The classic example is the Daniell cell, in which zinc is oxidised and copper ions are reduced, with the two half-reactions separated into half-cells connected by a salt bridge.

In any electrochemical cell, oxidation occurs at the anode and reduction at the cathode. A vital NEET point is the sign convention: in a galvanic cell the anode is negative and the cathode is positive, and electrons flow through the external wire from anode to cathode while ions move through the salt bridge to maintain electrical neutrality. (In electrolysis the signs are reversed.)

The tendency of an electrode to gain or lose electrons is measured by its electrode potential. Since a single electrode potential cannot be measured in isolation, all values are quoted relative to the standard hydrogen electrode (SHE), whose potential is defined as exactly $0\ \text{V}$. The standard electrode potential $E^{\circ}$ is measured at $298\ \text{K}$, $1\ \text{M}$ concentration and $1\ \text{bar}$ pressure.

Arranging electrodes in order of their standard reduction potentials gives the electrochemical series. An electrode with a more negative $E^{\circ}$ has a greater tendency to be oxidised (it is a stronger reducing agent), while one with a more positive $E^{\circ}$ is more easily reduced (a stronger oxidising agent). The series lets you predict which metal displaces another, whether a reaction is feasible, and which electrode acts as anode or cathode — all recurring NEET applications.

The driving force of a galvanic cell is its electromotive force (EMF) or cell potential. Under standard conditions, $E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}$, using standard reduction potentials for both. A positive $E^{\circ}_{cell}$ means the cell reaction is spontaneous as written — a check NEET asks for constantly.

Real cells rarely operate at standard concentrations, so the Nernst equation gives the potential under any conditions: $E = E^{\circ} - \dfrac{RT}{nF}\ln Q$, which at $298\ \text{K}$ simplifies to $E = E^{\circ} - \dfrac{0.059}{n}\log Q$, where $n$ is the number of electrons transferred and $Q$ the reaction quotient. The equation shows how potential rises when reactant concentration increases and falls as products build up; for a single electrode it relates the potential to ion concentration. Nernst-equation numericals are a NEET staple.

Electrochemistry connects directly to thermodynamics. The maximum electrical work a cell can do equals the decrease in Gibbs free energy, giving $\Delta G^{\circ} = -nFE^{\circ}_{cell}$, where $F = 96500\ \text{C mol}^{-1}$ is the Faraday constant. So a positive $E^{\circ}_{cell}$ corresponds to a negative $\Delta G^{\circ}$ (spontaneous) — the same conclusion reached in thermodynamics, now from a different angle.

Combining $\Delta G^{\circ} = -nFE^{\circ}_{cell}$ with $\Delta G^{\circ} = -RT\ln K$ links cell potential to the equilibrium constant: $E^{\circ}_{cell} = \dfrac{RT}{nF}\ln K$, or at $298\ \text{K}$, $E^{\circ}_{cell} = \dfrac{0.059}{n}\log K$. A large positive $E^{\circ}_{cell}$ therefore implies a large $K$ (reaction goes nearly to completion). When the cell reaches equilibrium, $Q = K$, the EMF falls to zero, and the battery is 'dead'. Holding these three relations — Nernst, $\Delta G^{\circ} = -nFE^{\circ}$, and $E^{\circ}$–$K$ — together covers nearly every quantitative NEET question in this chapter.

Solutions of electrolytes conduct electricity by the movement of ions. The conducting ability is described by several related quantities. Conductance is the reciprocal of resistance; conductivity (specific conductance) $\kappa$ is the conductance of a unit cube of solution. More useful is the molar conductivity $\Lambda_m$, the conductivity of a solution containing one mole of electrolyte between electrodes a unit distance apart: $\Lambda_m = \dfrac{\kappa \times 1000}{C}$, where $C$ is molarity. Knowing how each quantity changes with dilution is a NEET favourite.

On dilution, conductivity $\kappa$ decreases (fewer ions per unit volume), but molar conductivity $\Lambda_m$ increases (the same moles of ions move more freely and dissociate more fully). The behaviour differs between electrolyte types: for strong electrolytes, $\Lambda_m$ rises only slightly and linearly with dilution, extrapolating cleanly to a limiting value $\Lambda_m^{\circ}$ at infinite dilution. For weak electrolytes, $\Lambda_m$ is low at higher concentration and rises steeply on dilution as more molecules ionise, so $\Lambda_m^{\circ}$ cannot be found by direct extrapolation.

This is where Kohlrausch's law of independent migration of ions comes in: at infinite dilution, each ion contributes a fixed, independent amount to the molar conductivity, so $\Lambda_m^{\circ} = \nu_+ \lambda_+^{\circ} + \nu_- \lambda_-^{\circ}$ — the limiting molar conductivity is the sum of the limiting conductivities of the constituent ions. This lets us calculate $\Lambda_m^{\circ}$ for a weak electrolyte indirectly from the values of strong electrolytes, a classic NEET calculation.

Kohlrausch's law has practical uses: it allows the calculation of the degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^{\circ}$) and the dissociation constant of a weak electrolyte, and underlies conductometric titrations. Understanding the dilution trends and applying Kohlrausch's law to find $\Lambda_m^{\circ}$ and $\alpha$ are the high-yield skills from this topic.

Electrolysis is the opposite of a galvanic cell: an external source of electricity drives a non-spontaneous redox reaction. In an electrolytic cell the anode is connected to the positive terminal and the cathode to the negative terminal (the reverse of a galvanic cell), but oxidation still occurs at the anode and reduction at the cathode. Electrolysis is used industrially to extract reactive metals, refine copper, and produce chlorine, sodium hydroxide and aluminium.

The amount of product formed is governed by Faraday's laws of electrolysis. The first law states that the mass $m$ of a substance deposited or liberated at an electrode is proportional to the quantity of charge $Q$ passed: $m = Z\,Q = Z\,I\,t$, where $Z$ is the electrochemical equivalent, $I$ the current and $t$ the time. The second law states that for the same quantity of charge, the masses of different substances liberated are proportional to their equivalent weights. NEET numericals usually apply these directly.

One Faraday ($1\ F = 96500\ \text{C}$) is the charge on one mole of electrons. Depositing one mole of a substance requires $n$ Faradays, where $n$ is the number of electrons in its electrode half-reaction — so depositing one mole of $\text{Cu}$ from $\text{Cu}^{2+}$ needs $2\ F$, while one mole of $\text{Ag}$ from $\text{Ag}^+$ needs $1\ F$. Recognising the value of $n$ for each ion is a frequent NEET trap.

The chapter's applications include batteries and fuel cells: primary cells (the dry Leclanché cell, mercury cell) are used once; secondary cells (the lead storage battery, nickel–cadmium cell) are rechargeable; and fuel cells (such as the hydrogen–oxygen fuel cell) convert the energy of fuel combustion directly into electricity with high efficiency and little pollution. Finally, corrosion — especially the rusting of iron — is an unwanted electrochemical (galvanic) process, prevented by barrier coatings, galvanising and cathodic (sacrificial) protection. These applications are favourite NEET assertion-reason topics.