Question

Which of the following are the conditions for a reaction spontaneous at all temperatures?

• A. \( \Delta_r H>0 ; \Delta_r S>0 \)
• B. \( \Delta_r H<0 ; \Delta_r S>0 \)
• C. \( \Delta_r H<0 ; \Delta_r S<0 \)
• D. \( \Delta_r H = 0 ; \Delta_r S<0 \)
• E. \( \Delta_r H = 0 ; \Delta_r S = 0 \)

Hint:

For spontaneity at all temperatures, the enthalpy change (\( \Delta H \)) should be negative, and the entropy change (\( \Delta S \)) should be positive.

Answer 1

The Correct Option is B

For a reaction to be spontaneous at all temperatures, the change in Gibbs free energy (\( \Delta G \)) must be negative for all temperatures. 
The expression for \( \Delta G \) is: \[ \Delta G = \Delta H - T\Delta S \] For the reaction to be spontaneous at all temperatures, \( \Delta G \) should be negative. This will happen if: \[ \Delta_r H<0 \quad {and} \quad \Delta_r S>0 \] Thus, option (B) is the correct answer.