question_answer

(i) For a reaction both \[\Delta H\] and \[\Delta S\]are negative. Under what conditions does the reaction occur spontaneously? (ii) For a reaction both \[\Delta H\] and \[\Delta S\] are positive. Under what conditions does the reaction occur spontaneously?

Answer:

                (i) Here,  \[\Delta H=-ve\] and \[\Delta S=-ve\] According to Gibbs Helmholtz equation, change in free energy \[\Delta G=\Delta H-T\Delta S=(-ve)-(+ve)\,(-ve)\](Temperature, T on Kelvin scale is always + ve) \[=(-ve\,)\,-(-ve)\] For a reaction to be spontaneous, \[\Delta G\] should be negative. Therefore, the reaction can be made spontaneous by decreasing the magnitude of \[T\Delta S\]. This can be done by decreasing the temperature T. Thus, the reaction can occur spontaneously only at low temperature. (ii) Here, \[\Delta H\,=\,+\,ve\] and \[\Delta S\,=\,+\,ve\] According to Gibbs-Helmholtz equation change in free energy ; \[\Delta G=\Delta H-T\Delta S=(+\,ve)\,-\,(+\,ve)\,(+\,ve)\] \[=(+\,ve)\,-\,(+\,ve)\] For a reaction to be spontaneous, \[\Delta G\] should be negative. Therefore, the reaction can be made spontaneous by increasing the magnitude of \[T\Delta S\]. This can be done by increasing the temperature, T. Thus, the reaction can occur spontaneously only at high temperature.