Li3N(s) + 2 H2(g) <-> LiNH2(s) + 2 LiH(s) dH° = -192 kJ/mol_rxn Because pure H2 is a hazardous subst — Kinetics Chemistry Question

STEPS:

1. Distinguish between kinetics and thermodynamics:
The question asks why the reaction occurs at a "significant rate" only at elevated temperatures (above 200°C). Rate is a kinetic property that describes how fast a chemical reaction occurs. In contrast, properties like enthalpy ($\Delta H^\circ$), entropy ($\Delta S^\circ$), and free energy ($\Delta G^\circ$) are thermodynamic properties that describe the net energy changes and spontaneity of a process. This means the correct explanation must be rooted in kinetics rather than thermodynamics.

2. Apply collision theory to explain reaction rates:
According to collision theory, for a reaction to occur, reactant particles must collide with sufficient energy to break existing chemical bonds and form new ones. The minimum kinetic energy that colliding molecules must possess for a reaction to occur is called the activation energy ($E_a$).

3. Analyze the kinetic effect of increasing temperature:
* At lower temperatures, the average kinetic energy of the molecules is low. Only an extremely small fraction of reactant collisions have enough energy to equal or exceed the activation energy.
* When the temperature is increased, the average kinetic energy and speed of the reactant particles increase, shifting their Maxwell^-Boltzmann distribution to higher speeds.
* This significantly increases both the frequency of collisions and, more importantly, the fraction of collisions that possess energy greater than or equal to the activation energy.

4. Conclude why the high temperature is necessary:
Because this solid-gas storage reaction requires a high temperature (greater than 200°C) to occur at a useful, significant rate, the barrier preventing reactant molecules from transforming into product molecules must be high. This indicates that the reaction has a high activation energy under standard conditions. This directly corresponds to Option C.

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WHY_OTHERS_WRONG:

• Option A is incorrect: Although the reaction is highly exothermic ($\Delta H^\circ = -192\text{ kJ/mol}_{\text{rxn}}$), exothermicity is a thermodynamic property. A highly exothermic reaction can still be kinetically trapped and occur at an imperceptibly slow rate at room temperature if it has a high activation energy barrier (for example, the combustion of paper is highly exothermic, but paper does not spontaneously burn at room temperature).
• Option B is incorrect: The entropy change ($\Delta S^\circ$) for this reaction is indeed negative because two moles of highly disordered gas ($\text{H}_2$) are converted into highly ordered solid products ($\text{LiNH}_2$ and $\text{LiH}$). However, entropy is a thermodynamic state function that influences chemical spontaneity, not kinetics; a negative entropy change does not dictate or explain the rate of a reaction.
• Option D is incorrect: The condition $\Delta G^\circ < 0$ means that the reaction is thermodynamically favorable (spontaneous). Because the reaction is highly exothermic, $\Delta G^\circ$ is negative at lower temperatures where the unfavorable $T\Delta S^\circ$ term does not dominate. However, thermodynamically favored reactions can still have a rate of practically zero if the kinetic barrier (activation energy) is too high to overcome.