N2(g) + 3 H2(g) ⇄ 2 NH3(g) ΔH°298 = −92 kJ/molrxn ; ΔG°298 = −33 kJ/molrxn Consider the reaction rep — Kinetics Chemistry Question

STEPS:

1. Analyze the thermodynamic properties given: We are given that the standard Gibbs free energy change of the reaction at room temperature is $\Delta G^\circ_{298} = -33\text{ kJ/mol}_{rxn}$. A negative Gibbs free energy value ($\Delta G^\circ < 0$) indicates that the synthesis of ammonia is thermodynamically favorable (spontaneous) at $298\text{ K}$.
2. Determine the equilibrium state of the reaction: Standard Gibbs free energy is related to the equilibrium constant ($K$) by the expression $\Delta G^\circ = -RT \ln K$. Because $\Delta G^\circ$ is negative, the equilibrium constant must be greater than 1 ($K > 1$). This indicates that at equilibrium, the system is highly favored to exist as products ($\text{NH}_3$) rather than reactants.
3. Address the conflict between thermodynamics and observation: Despite the reaction being thermodynamically favored to produce ammonia, no formation of $\text{NH}_3(g)$ is observed when the reactant gases are mixed at room temperature. This indicates that the reaction is under kinetic control, meaning that while the final product state is highly stable, the physical rate of the chemical reaction is incredibly slow.
4. Identify the molecular cause of the kinetic barrier: In order for a chemical reaction to occur, colliding reactant molecules must possess a minimum amount of kinetic energy to overcome the activation energy barrier ($E_a$). Nitrogen gas ($\text{N}_2$) is composed of nitrogen atoms held together by an exceptionally strong triple covalent bond ($\text{N}\equiv\text{N}$). Breaking or weakening this triple bond to initiate the reaction requires a massive input of energy, creating an extremely high activation energy barrier.
5. Conclude the temperature effect on the rate: At a room temperature of $298\text{ K}$, the average kinetic energy of the molecules is relatively low. Only an infinitesimally small fraction of the $\text{N}_2$ and $\text{H}_2$ collisions possess enough energy to clear this high activation energy barrier. As a result, the forward reaction is extremely slow and no product is observed, identifying Option B as the correct explanation.

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WHY_OTHERS_WRONG:

• Option A is incorrect: While the stoichiometry of the reaction requires a 1:3 ratio of $\text{N}_2$ to $\text{H}_2$ for complete conversion without excess reactants, chemical reactions do not require perfect stoichiometric ratios to initiate. Mixing them in a 1:1 ratio (equal volumes) would still allow a thermodynamically favorable reaction to proceed, with $\text{H}_2$ acting as the limiting reactant.
• Option C is incorrect: This option directly contradicts the given thermodynamic data. Since $\Delta G^\circ_{298} = -33\text{ kJ/mol}_{rxn}$ (a negative value) and $\Delta G^\circ = -RT \ln K$, the equilibrium constant $K$ at $298\text{ K}$ must be significantly greater than 1 ($K \approx 6 \times 10^5$). This indicates that a large amount of product would exist if the system actually reached equilibrium.
• Option D is incorrect: For an exothermic reaction ($\Delta H^\circ_{298} = -92\text{ kJ/mol}_{rxn} < 0$), the energy level of the products is lower than the energy level of the reactants. Consequently, the activation energy of the reverse reaction must be *higher* than that of the forward reaction ($E_{a,\text{rev}} = E_{a,\text{fwd}} + |\Delta H^\circ|$). Thus, the reverse reaction actually has a higher activation energy, making D factually false.