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:

To remember this conceptually: nature favors lower energy (negative enthalpy, exothermicity) and higher disorder (positive entropy). When both driving forces favor the reaction, it will occur spontaneously at any temperature.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Spontaneity refers to whether a chemical reaction or physical process occurs naturally under a given set of conditions without being driven by an external power source.
The criterion for spontaneity at constant temperature and pressure is the change in Gibbs Free Energy (\( \Delta G \)).
A reaction is spontaneous if \( \Delta G \) is negative (\(<0 \)).
A reaction is non-spontaneous if \( \Delta G \) is positive (\(>0 \)).
The value of \( \Delta G \) depends on the interplay between two driving forces: Enthalpy (\( \Delta H \)) and Entropy (\( \Delta S \)).
Step 2: Key Formula or Approach:
The relationship is defined by the Gibbs-Helmholtz equation:
\[ \Delta G = \Delta H - T\Delta S \]
Where:
\( \Delta H \) is the change in enthalpy (energy factor).
\( T \) is the absolute temperature in Kelvin (always positive, \( T>0 \)).
\( \Delta S \) is the change in entropy (disorder factor).
Step 3: Detailed Explanation:
To make \( \Delta G \) negative at "all temperatures" (\( T \)), we need both terms in the equation to contribute negatively.
1. Enthalpy Factor (\( \Delta H \)):
If \( \Delta H \) is negative (\(<0 \), Exothermic), the reaction releases energy, which generally favors spontaneity. The first term in the equation is negative.
2. Entropy Factor (\( \Delta S \)):
If \( \Delta S \) is positive (\(>0 \), increasing randomness), then the term \( -T\Delta S \) becomes negative because \( T \) is positive.
Combining them:
\[ \Delta G = (\text{Negative}) - (\text{Positive}) \times (\text{Positive}) \]
\[ \Delta G = (\text{Negative}) + (\text{Negative}) = \text{Always Negative} \]
Under these conditions (\( \Delta H<0 \) and \( \Delta S>0 \)), \( \Delta G \) will be negative regardless of how large or small \( T \) is.
In other scenarios:
- If both are positive: Spontaneous only at high temperatures.
- If both are negative: Spontaneous only at low temperatures.
- If \( \Delta H \) is positive and \( \Delta S \) is negative: Never spontaneous.
Step 4: Final Answer:
For a reaction to be spontaneous at all temperatures, the signs must be \( \Delta H = \) negative and \( \Delta S = \) positive.