Question

The reaction \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) proceeds spontaneously at \(25^{\circ} \mathrm{C}\) even though there is a decrease in the number of microstates of the system (gases are converted to a solid). Explain.

Short answer

Despite the decrease in the number of microstates, the reaction occurs spontaneously because it may still have a negative Gibbs free energy change due to the decrease in enthalpy from the exothermic reaction.

Step-by-step solution

Understand the Concept of Spontaneity

The spontaneity of a reaction doesn't depend only on the number of microstates or entropy change, but also on the Gibbs free energy change \(\Delta G\). A reaction can proceed spontaneously if the Gibbs free energy change is negative.

The Reaction Details

The reaction given is \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\). Even though there is a decrease in the number of microstates (going from gases to a solid), the reaction is exothermic, releasing heat.

Conclusion

The decrease in enthalpy (exothermic reaction) along with the decrease in entropy (from gas molecules to solid) might still result in a negative Gibbs free energy change \((\Delta G = \Delta H - T\Delta S)\), allowing the reaction to proceed spontaneously.