Question

The signs of $\Delta$H and $\Delta$s for a reaction to be spontaneous at all temperatures respectively are

• A. Positive , positive
• B. Positive , negative
• C. Negative , negative
• D. Negative , positive

Hint:

Think of it this way: Nature favors lower energy ($-\Delta H$) and higher disorder ($+\Delta S$). When both conditions are met, the reaction has no choice but to be spontaneous!

Answer 1

The Correct Option is D

Concept: The spontaneity of a chemical reaction is determined by the Gibbs free energy change ($\Delta G$). A reaction is spontaneous only when $\Delta G < 0$. The relationship is given by the Gibbs-Helmholtz equation: \[ \Delta G = \Delta H - T\Delta S \] Where:
• $\Delta H$ is the change in enthalpy.
• $T$ is the absolute temperature (always positive in Kelvin).
• $\Delta S$ is the change in entropy.

Step 1: Determine the conditions for spontaneity at all temperatures.
To ensure $\Delta G$ is always negative regardless of the value of $T$:
• The enthalpy term ($\Delta H$) should be negative (exothermic).
• The term $-T\Delta S$ should also be negative. Since $T$ is always positive, $\Delta S$ must be positive.

Step 2: Evaluate the mathematical result.
If $\Delta H$ is negative ($-$) and $\Delta S$ is positive ($+$), then the equation becomes: \[ \Delta G = (-) - T(+) \] \[ \Delta G = (-) - (+) = \text{Always Negative} \] Thus, based on the problem, the reaction will be spontaneous at any temperature.