If the cell reaction is spontaneous then — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Define the Universal Thermodynamic Criterion for Spontaneity Under the conditions of constant temperature ($T$) and pressure ($P$), which represent the typical working environment for most chemical reactions and electrochemical systems, the spontaneity of a process is determined by the change in the Gibbs free energy ($\Delta G$). According to the Second Law of Thermodynamics: * If $\Delta G < 0$ (negative), the reaction is spontaneous and can proceed in the forward direction. * If $\Delta G > 0$ (positive), the reaction is non-spontaneous in the forward direction (but spontaneous in the reverse direction). * If $\Delta G = 0$, the system has reached a state of dynamic chemical equilibrium. Thus, the absolute, non-negotiable criterion for spontaneity under general experimental conditions is: $$\Delta G < 0 \quad \text{(negative)}$$ Step 2 - Relate Gibbs Free Energy to Cell Potential ($E_{\text{cell}}$) For an electrochemical cell, the change in Gibbs free energy ($\Delta G$) is directly coupled to the actual electrical work done by the cell. This relation is mathematically described by the equation: $$\Delta G = -n F E_{\text{cell}}$$ Where: * $n$ is the number of moles of electrons transferred in the balanced redox equation. * $F$ is Faraday's constant ($\approx 96500\text{ C mol}^{-1}$). * $E_{\text{cell}}$ is the actual (non-standard) cell potential. Since both $n$ and $F$ are positive constants, the sign of $\Delta G$ is opposite to that of $E_{\text{cell}}$: $$\text{For Spontaneity: } \Delta G < 0 \implies -n F E_{\text{cell}} < 0 \implies E_{\text{cell}} > 0 \quad \text{(positive)}$$ Thus, a spontaneous cell reaction must have a negative actual Gibbs free energy change ($\Delta G < 0$) and a positive actual cell potential ($E_{\text{cell}} > 0$). Step 3 - Contrast Standard vs. Non-Standard State Parameters It is a crucial pedagogical distinction to separate standard state parameters ($\Delta G^\circ$, $E^\circ_{\text{cell}}$) from actual state parameters ($\Delta G$, $E_{\text{cell}}$): 1. **Standard Parameters ($\Delta G^\circ$, $E^\circ_{\text{cell}}$):** These describe the reaction only when all participating chemical species are at their standard states (concentrations of exactly $1.0\text{ M}$ for solutes, partial pressures of exactly $1.0\text{ bar}$ for gases, and pure solids or liquids in their most stable forms). 2. **Actual Parameters ($\Delta G$, $E_{\text{cell}}$):** These describe the reaction under the actual, prevailing experimental concentrations and pressures, which can be determined using the Nernst equation: $$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q$$ A reaction with a negative standard cell potential ($E^\circ_{\text{cell}} < 0$) and a positive standard Gibbs free energy ($\Delta G^\circ > 0$) can still be made spontaneous ($\Delta G < 0$ and $E_{\text{cell}} > 0$) by adjusting the concentrations of reactants and products such that the reaction quotient ($Q$) is extremely small. Therefore, standard parameters are not the universal criteria for spontaneity. Step 4 - Evaluate and Explain the Options * **Option (A) is incorrect:** While $\Delta G^\circ = \text{-ve}$ ensures spontaneity under standard conditions, it is not a requirement for spontaneity under non-standard conditions. * **Option (B) is incorrect:** $E^\circ_{\text{red}} = \text{-ve}$ represents a negative standard reduction potential of a single half-cell electrode. A single half-cell cannot undergo a spontaneous reaction on its own, and a negative reduction potential simply indicates that the electrode is a stronger reducing agent than hydrogen. * **Option (C) is incorrect:** $E^\circ_{\text{cell}} = \text{+ve}$ is the standard cell potential. Similar to Option (A), this only guarantees spontaneity if the system is maintained strictly at standard conditions. * **Option (D) is correct:** $\Delta G = \text{-ve}$ is the universal thermodynamic criterion for a spontaneous process at constant temperature and pressure, regardless of standard or non-standard concentration states. $$\text{Correct Option: } \boxed{\text{D}}$$