Question

If an endothermic reaction occurs spontaneously at constant temperature \(T\) and pressure \(P\), then which of the following is true?

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

Hint:

Endothermic spontaneous reactions require large positive entropy so that \(T\Delta S > \Delta H\).

Answer 1

The Correct Option is C

Step 1: Condition for spontaneity at constant \(T, P\).
A process is spontaneous if:
\[ \Delta G<0 \]
Step 2: Gibbs free energy equation.
\[ \Delta G = \Delta H - T\Delta S \]
Step 3: Endothermic reaction means.
For endothermic process:
\[ \Delta H>0 \]
Step 4: For spontaneity, \(\Delta G\) must be negative.
\[ \Delta H - T\Delta S<0 \Rightarrow T\Delta S>\Delta H \]
Step 5: Hence \(\Delta S\) must be positive.
Since \(\Delta H\) is positive, \(\Delta S\) must be sufficiently positive so that \(T\Delta S\) is greater than \(\Delta H\).
Final Answer:
\[ \boxed{\Delta S>0} \]