Question

Match the following. \[ \begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline \begin{array}{l} \textbf{A.}\; \Delta_rH<0,\; \Delta_rS>0,\; \Delta_rG<0 \\ \textbf{B.}\; \Delta_rH<0,\; \Delta_rS<0,\; \Delta_rG<0 \\ \textbf{C.}\; \Delta_rH>0,\; \Delta_rS>0,\; \Delta_rG>0 \\ \textbf{D.}\; \Delta_rH>0,\; \Delta_rS<0,\; \Delta_rG>0 \end{array} & \begin{array}{l} \textbf{I.}\; \text{Non-spontaneous at low temperature} \\ \textbf{II.}\; \text{Spontaneous at high temperature} \\ \textbf{III.}\; \text{Non-spontaneous at all temperatures} \\ \textbf{IV.}\; \text{Spontaneous at low temperature} \end{array} \\ \hline \end{array} \]

• A. A-III, B-IV, C-II, D-I
• B. A-III, B-IV, C-I, D-II
• C. A-IV, B-III, C-II, D-I
• D. A-II, B-IV, C-I, D-III \bigskip

Hint:

Remember the four cases of \(\Delta G=\Delta H-T\Delta S\):

• \(\Delta H<0,\;\Delta S>0\): Spontaneous at all temperatures.
• \(\Delta H<0,\;\Delta S<0\): Spontaneous at low temperatures.
• \(\Delta H>0,\;\Delta S>0\): Spontaneous at high temperatures.
• \(\Delta H>0,\;\Delta S<0\): Never spontaneous.

Answer 1

The Correct Option is B

Concept: The spontaneity of a reaction depends on \[ \boxed{\Delta G=\Delta H-T\Delta S} \]

Step 1: Match each case. \[ \begin{array}{ll} \Delta H0 &\Rightarrow \text{Spontaneous at all temperatures (III)}[1mm] \Delta H[1mm] \Delta H>0,\;\Delta S>0 &\Rightarrow \text{Spontaneous at high temperature (II)}[1mm] \Delta H>0,\;\Delta S<0 &\Rightarrow \text{Non-spontaneous at all temperatures (I)} \end{array} \] Hence, \[ A\rightarrow III,\qquad B\rightarrow IV,\qquad C\rightarrow I,\qquad D\rightarrow II. \]

Step 2: Choose the correct option. The correct matching is \[ \boxed{A\text{-}III,\;B\text{-}IV,\;C\text{-}I,\;D\text{-}II} \] Hence, the correct option is \(\boxed{(B)}\).