Question

\(\Delta H\) and \(\Delta S\) value of a reaction which is non-spontaneous at high T and spontaneous at low T is:

• A. \(\Delta H>0, \Delta S<0\)
• B. \(\Delta H<0, \Delta S>0\)
• C. \(\Delta H>0, \Delta S>0\)
• D. \(\Delta H<0, \Delta S<0\)

Hint:

For reactions that are non-spontaneous at high T and spontaneous at low T, \(\Delta H>0\) and \(\Delta S<0\).

Answer 1

The Correct Option is A

The spontaneity of a reaction is determined by the Gibbs free energy (\(\Delta G\)), which is given by the equation: \[ \Delta G = \Delta H - T\Delta S \] For the reaction to be non-spontaneous at high temperatures and spontaneous at low temperatures, the following conditions must hold: - \(\Delta H>0\): The reaction is endothermic at high temperatures. - \(\Delta S<0\): The reaction leads to a decrease in entropy (i.e., a more ordered state). At high temperatures, the term \(-T\Delta S\) becomes large and negative, making \(\Delta G>0\), making the reaction non-spontaneous. At low temperatures, the \(\Delta H\) term dominates, making \(\Delta G<0\), which leads to spontaneity. Thus, the correct answer is \(\Delta H>0, \Delta S<0\).