Electrochemistry – NEET UG ChemistryPractice Questions & PYQs

The mass of an element deposited during electrolysis is directly proportional to the total electricity passed through the cell, following the relationship $m = \frac{M I t}{n F}$. The total charge is obtained by multiplying the current of 5 amperes by the duration of 2400 seconds. Since zinc ions require two moles of electrons for complete reduction, the equivalent charge of $2 \times 96500$ coulombs deposits one molar mass of zinc. Applying this stoichiometric equivalence to the calculated charge yields a deposited mass of 4.065 grams of zinc.

Metals exhibit high thermal conductivity because their crystal lattices contain a vast population of delocalized valence electrons that are free to move throughout the structure. When thermal energy is supplied to one region of the metal, these mobile electrons absorb kinetic energy and rapidly diffuse toward cooler regions. As these energized electrons collide with atoms and other electrons down the length of the metal, they efficiently transfer their thermal energy across the entire piece.

The potential of a hydrogen half-cell under non-standard conditions is determined using the Nernst equation, expressed as $E = E^{\circ} - \frac{2.303RT}{nF} \log \frac{[\mathrm{H}^{+}]^2}{P_{\mathrm{H}_2}}$. Substituting the given values where the hydrogen ion concentration is 0.02, the partial pressure is 2, the number of electrons is 2, and the temperature factor is 0.059 gives the logarithmic term for the cell reaction. Squaring the hydrogen ion concentration and dividing by the pressure yields two times ten to the negative fourth power. Evaluating the logarithm and multiplying by the coefficient results in a half-cell emf of 0.109 volts.

An electrochemical cell develops a non-zero potential when a gradient in ion concentration exists between its compartments, characteristic of a concentration cell. Although both $\mathrm{HCl}$ and $\mathrm{CH}_{3}\mathrm{COOH}$ share an initial concentration of 0.1 M, the former is a strong electrolyte that fully dissociates while the latter is a weak acid undergoing only partial ionization. As a result, the hydrogen ion availability and the resulting $\text{pH}$ levels differ across the compartments, creating a persistent chemical potential difference that keeps the cell voltage above zero.

The standard electromotive force of a galvanic cell is determined by combining the reduction potentials of the half-cells using the equation $E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}$. In the given reaction, zinc undergoes oxidation while iron ions undergo reduction, identifying iron as the cathode and zinc as the anode. Given the reduction potential of iron is -0.44 V and that of zinc is -0.76 V, substituting these values into the formula gives -0.44 minus -0.76. This calculation results in a standard cell EMF of +0.32 V.

The variation of molar conductivity with concentration for a strong electrolyte follows the linear relationship $\Lambda_{\mathrm{m}} = \Lambda_{\mathrm{m}}^0 - A\sqrt{c}$, where the slope represents $-A$. Substituting the given slope of -90.0 and the square root of the concentration, which is 0.1 for a 0.01 M solution, allows us to calculate the limiting molar conductivity as 145.0 plus 9.0, yielding 154.0. Applying Kohlrausch's law, the limiting molar conductivity of the salt equals the sum of the limiting molar conductivities of its constituent ions. Subtracting the given cationic contribution of 74.0 from this total gives the ionic value of 80.0.

The cell constant is related to specific conductance ($\kappa$) and resistance ($R$) through the equation $\text{Cell Constant} = \kappa \times R$. Substituting the given specific conductance of 0.012 ohm^-1 cm^-1 and resistance of 55 ohm into the relation yields the calculation $0.012 \times 55$. This multiplication directly results in a cell constant value of 0.66 cm^-1.

During the electrolysis of aqueous electrolytes using inert electrodes, the species with the more favorable discharge potential undergoes oxidation at the anode. In dilute $\mathrm{H}_2\mathrm{SO}_4$, $\mathrm{H}_2\mathrm{O}$ molecules are preferentially oxidized over $\mathrm{SO}_4^{2-}$ ions because water has a lower discharge potential than the sulphate ion. This anodic oxidation process on the platinum surface results in the decomposition of water to yield oxygen gas according to the equation $2\mathrm{H}_2\mathrm{O} \rightarrow \mathrm{O}_2 + 4\mathrm{H}^+ + 4\mathrm{e}^-$.

At electrochemical equilibrium, the cell potential drops to zero, establishing a logarithmic relationship between standard cell potential and the equilibrium constant through the equation $E^{\circ} = \frac{0.059}{n} \log K$. For the given zinc-copper cell, two electrons are transferred in the redox reaction, making $n = 2$, and the standard cell potential is 1.10 V. Substituting these values into the rearranged equation yields $\log K = \frac{2 \times 1.10}{0.059}$, which leads to an equilibrium constant on the order of 10^-37.

Faraday's laws of electrolysis dictate that the mass of a substance deposited at an electrode is directly proportional to the total electrical charge passed through the solution, governed by the formula $W = \frac{M I t}{n F}$. Multiplying the current of 1.5 amperes by the time of 600 seconds gives a total charge of 900 coulombs. For the deposition of copper from cupric ions, two electrons are involved, making the value of $n$ equal to 2. Substituting the molar mass of 63, the total charge, and Faraday's constant of 96487 into the relation yields a deposited mass of 0.2938 grams.

The strength of an oxidizing agent is directly proportional to its standard reduction potential, where a higher or less negative value indicates a greater tendency to undergo reduction. Comparing the given values, the reduction potential of $\mathrm{Mg}^{2+} | \mathrm{Mg}$ is $-2.37$ volt, which is the highest among the listed species compared to $\mathrm{Na}^+ | \mathrm{Na}$ at $-2.71$ volt, $\mathrm{Ba}^{2+} | \mathrm{Ba}$ at $-2.90$ volt, and $\mathrm{Li}^+ | \mathrm{Li}$ at $-3.05$ volt. Because it possesses the least negative reduction potential, $\mathrm{Mg}^{2+}$ accepts electrons most readily from its surroundings.

Since electrode potential is an intensive property, free energy changes must be used to combine half-cell reactions because $\Delta G^{\circ} = -nFE^{\circ}$ is an extensive property. The reduction of $\mathrm{Fe}^{3+}$ to $\mathrm{Fe}$ involves three electrons with a free energy change of $-3F(-0.04)$, while the reduction of $\mathrm{Fe}^{2+}$ to $\mathrm{Fe}$ involves two electrons with $-2F(-0.44)$. Subtracting the second reaction's free energy from the first yields $+0.12F - (+0.88F)$, which equals $-0.76F$ for the single-electron reduction to $\mathrm{Fe}^{2+}$. Dividing this by $-1F$ results in a standard electrode potential of +0.76 V.

The standard Gibbs free energy change and standard cell potential are related through the expression $\Delta_r G^{\ominus} = -nFE_{\text{cell}}^{\ominus}$, where $n$ represents the total number of electrons transferred in the redox process. From the balanced ionic equation, two electrons are exchanged as zinc is oxidized and iron ions are reduced, making $n$ equal to two. Substituting these values along with $F = 96487$ C and $E_{\text{cell}}^{\ominus} = 0.32$ V yields $-61751.68$ J mol$^{-1}$, which directly converts to $-61.75$ kJ mol$^{-1}$.

The quantity of electricity in Faradays required for any electrochemical conversion directly corresponds to the total moles of electrons involved in the balanced redox half-reaction. For the conversion of water, the underlying stoichiometry shows that two moles of $\mathrm{H_2O}$ yield oxygen via a four-electron pathway, meaning a single mole of $\mathrm{H_2O}$ demands two Faradays of charge. When permanganate is reduced to $\mathrm{Mn^{2+}}$, the manganese center undergoes a five-unit decrease in its oxidation state, requiring five Faradays per mole of reactant.

The electrodeposition of calcium from molten $\mathrm{CaCl_2}$ proceeds through the reduction of divalent calcium ions, where each ion accepts two electrons, bringing the total requirement for one and a half moles of the metal to three Faradays. Similarly, transforming iron(II) oxide into $\mathrm{Fe_2O_3}$ involves oxidizing iron from the plus two to the plus three state, a single-electron change per formula unit that consumes exactly one Faraday for every mole of FeO processed.

The mass of a substance deposited during electrolysis is determined by Faraday's law using the relation $w = \frac{M i t}{n F}$, where $M$ is the molar mass, $i$ is the current, $t$ is the time, $n$ is the valence change, and $F$ is the Faraday constant. For copper deposition from a copper sulfate solution, the divalent copper ion gains two electrons, setting $n$ equal to two. Substituting the molar mass of 63 g mol$^{-1}$, current of 9.6487 A, time of 100 s, and $F = 96487$ C into the formula results in a deposited mass of 0.315 g.

Corrosion is a natural redox process where metals are slowly degraded and coated with oxides, carbonates, or sulphides through environmental exposure. Processes like the rusting of iron, the tarnishing of silver, and the formation of a green patina on copper and bronze ornaments are classic examples of this spontaneous chemical degradation. In contrast, the production of hydrogen through the electrolysis of water is an artificial, non-spontaneous process driven by an external electrical supply in an electrolytic cell. Therefore, this electrolytic decomposition stands apart as it does not involve the environmental weathering characteristic of metallic corrosion.

Gibbs free energy change is an extensive thermodynamic property whose magnitude scales directly with the amount of chemical species reacting, making it dependent on the stoichiometric electron count $n$ in the relation $\Delta_r G = -nFE_{\text{cell}}$. In contrast, cell potential is an intensive property that remains invariant regardless of the system's scale or the number of electrons transferred. Therefore, while both statements are scientifically accurate, the extensive versus intensive nature of these thermodynamic variables does not serve as the direct cause for why free energy depends on $n$.

The Debye-Hückel-Onsager parameter depends explicitly on the viscosity and dielectric constant of the solvent medium, as well as the stoichiometry and charges of the constituent ions. Because this constant varies with the nature of the solvent and the valence type of the electrolyte, ions of identical charge configurations yield matching values. Consequently, barium chloride and magnesium hydroxide share the same electrolyte charge type, making their corresponding constant values identical.

The cell constant of an electrolytic cell is determined by the product of its conductivity and electrical resistance, following the relationship $G^* = k \times R$. Inserting the provided conductivity of 0.0210 ohm$^{-1}$ cm$^{-1}$ and the resistance of 60 ohm into this equation gives the product $0.0210 × 60$, which directly evaluates to 1.26 cm$^{-1}$.

The overall standard cell potential is determined by subtracting the standard reduction potential of the anode from that of the cathode using the formula $E_{\text{cell}}^{\circ} = E_{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ}$. The dichromate half-reaction possesses a higher positive reduction potential, designating it as the cathode, whereas the iron half-reaction acts as the anode. Substituting the respective cathode and anode potentials of 1.33 V and -0.44 V into the equation results in 1.33 minus negative 0.44, which evaluates to +1.77 V.