Faraday's law of electrolysis fails when — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Recall Faraday's Laws of Electrolysis and their Physical Basis Faraday's laws of electrolysis establish the fundamental quantitative relationship between the quantity of electric charge passed through an electrolytic cell and the mass of chemical substances reacted or deposited at the electrodes: 1. **Faraday's First Law:** The mass ($m$) of a substance liberated or deposited at any electrode during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte: $$m = z \cdot Q = z \cdot I \cdot t$$ where $z$ is the electrochemical equivalent of the substance, $I$ is the electric current, and $t$ is the time duration. 2. **Faraday's Second Law:** When the same quantity of electricity is passed through multiple electrolytes connected in series, the masses ($m_1, m_2$) of different substances liberated or deposited are directly proportional to their respective chemical equivalent weights ($E_1, E_2$): $$\frac{m_1}{m_2} = \frac{E_1}{E_2}$$ At the microscopic scale, these laws are a direct consequence of the **quantization of electric charge** and the **law of conservation of charge**. Since each individual electron carries a fundamental, invariant charge ($e \approx 1.602 \times 10^{-19}\text{ C}$), a precise stoichiometric number of electrons must be transferred to reduce or oxidize a given amount of an ionic species. For example, $1\text{ Faraday}$ of charge ($1\text{ F} \approx 96,500\text{ C}$, representing the charge of $1\text{ mole}$ of electrons) will always reduce exactly $1\text{ equivalent}$ of any substance. Because Faraday's laws are rooted in the fundamental conservation of charge, they are absolute physical laws and do not depend on the kinetics or mechanisms of the electrolytic processes. Step 2 - Analyze Option (A): Effect of Increasing Temperature When the temperature of an electrolytic solution is increased: * The kinetic energy of the ions increases and the viscosity of the solvent decreases, leading to an increase in ionic mobility. * The degree of dissociation ($\alpha$) of weak electrolytes increases. * Consequently, the electrical conductivity ($\kappa$) increases, allowing more current to flow for a given applied voltage. * However, the stoichiometric relationship remains strictly valid: $1\text{ Faraday}$ of electricity still transfers exactly $1\text{ mole}$ of electrons and deposits exactly $1\text{ equivalent}$ of a substance, regardless of how fast or slow the ions migrate. Therefore, Faraday's laws **do not fail** when the temperature is increased. Step 3 - Analyze Option (B): Effect of Using Inert Electrodes When inert electrodes (such as platinum, graphite, or gold) are used: * The electrodes do not participate chemically in the oxidation or reduction reactions; they merely act as a source or sink for electrons. * The electrochemical reactions that take place on their surfaces involve the active ionic species or water molecules in the electrolyte with the most favorable standard potentials. * The mass of the products formed (e.g., gaseous oxygen or hydrogen) is still determined strictly by the number of electrons passed through the circuit according to the stoichiometric half-reaction: $$\ce{2H^+ + 2e^- -> H2(g)}$$ Therefore, Faraday's laws **do not fail** when inert electrodes are used. Step 4 - Analyze Option (C): Effect of Using a Mixture of Electrolytes When a mixture of different electrolytes is electrolyzed: * Multiple competitive reduction reactions can occur simultaneously at the cathode, and multiple competitive oxidation reactions can occur simultaneously at the anode. * For example, in a mixture of $\ce{Cu^2+}$ and $\ce{Ag^+}$ ions, both metals may deposit together on the cathode. * However, the total number of equivalents of all substances deposited or reacted at any electrode remains strictly equal to the total number of Faradays of charge passed through the cell: $$\text{Total Equivalents} = \text{Equivalents of Cu} + \text{Equivalents of Ag} = \frac{Q}{F}$$ Thus, the conservation of charge is maintained, and Faraday's laws **do not fail** when a mixture of electrolytes is used. Step 5 - Conclusion Faraday's laws of electrolysis are fundamental physical laws that hold strictly correct under all physical conditions, temperatures, and choices of electrolytes or electrodes. They do not fail in any of these cases. $$\text{Correct Option: } \boxed{\text{D}}$$