PCl\(_5\)\((_g\)) → PCl\(_3\)\((_s\)) + Cl\(_2\)\((_g\))
In the equation above, the reaction will be spontaneous if
The spontaneity of a reaction is determined by the Gibbs free energy change (\(\Delta G\)), given by the equation:\(\Delta G=\Delta H-T\Delta S\)For a reaction to be spontaneous, \(\Delta G\) must be negative (\(\Delta G<0\)). For the given reaction: Entropy Change (\(\Delta S\)): The reaction involves the conversion of one mole of gas into one mole of solid and one mole of gas. The formation of a highly ordered solid from a less ordered gas results in a decrease in entropy, so \(\Delta S\) is negative (\(\Delta S<0\)).Enthalpy Change (\(\Delta H\)): Since the entropy change is negative, the term \(-T\Delta S\) is positive. For \(\Delta G\) to be negative (spontaneous), the \(\Delta H\) term must be sufficiently negative to overcome the positive \(-T\Delta S\) term. Therefore, the reaction must be exothermic, meaning \(\Delta H\) is negative (\(\Delta H<0\)). Therefore, for this specific reaction to be spontaneous, the enthalpy change (\(\Delta H\)) must be negative.
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