Free energy, G=H-TS, is a state function that includes whether a reaction is spontaneous or non-spontaneous. If you think of TS as the part of the system's energy that is disordered already, then (H-TS) is the part of the system's energy that is still ordered and therefore free to cause spontaneous change by becoming disordered.
Also, `DeltaG=DeltaH-TDeltaS`
To see what this equation for free energy change has to do with spontaneity let us return to relationship.
`DeltaS_("total")=DeltaS_("sys")+DeltaS_("surr") = DeltaS + DeltaS_("surr")`
(It is generally understood that symbols without subscript refer to the system not the surroundings.)
`DeltaS_("surr")=-(DeltaH)/T`, where `DeltaH` is the heat gained by then system at constant pressure.
`DeltaS_("total") = DeltaS -(DeltaH)/T`
`rArr TDeltaH_("total")=DeltaH-TDeltaS`
`rArr -TDeltaS_("total") =DeltaH-TDeltaS`
i.e. `DeltaG=-TDeltaS_("total")`
From second law of thermodynamics, a reaction is spontaneous if `DeltaS_("total")` is positive, non-spontanous if `DeltaS_("total")` is negative and at equilibrium if `DeltaS_("total")` is zero.
Since, `-TDeltaS=DeltaG` and since `DeltaG` and `DeltaS` have opposite signs, we can restate the thermodynamic criterion for the spontaneity of a reaction carried out at constant temperature and pressure.
If `DeltaG lt 0`, the reaction is spontaneous.
If `DeltaG gt 0`, the reaction is non-spontanous.
If `DeltaG=0`, the reaction is at equilibrium.
In the equation, `DeltaG=DeltaH-TDeltaS`, temperature is a weighting factor that determine the relative importance of enthalpy contribution to `DeltaG`.
Read the above paragraph carefully and answer the following questions based on above comprehension:
If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then

Options

A. `DeltaG` is -ve and `DeltaS` is +ve
B. `DeltaH` and `DeltaS` both are +ve
C. `DeltaH` and `DeltaS` both are `-ve`
D. `DeltaH` is positive and `DeltaS` is negative.

Explanation

To solve the question regarding the spontaneity of an endothermic reaction at different temperatures, we will analyze the relationship between ΔG (Gibbs free energy), ΔH (enthalpy change), and ΔS (entropy change) using the provided equations and concepts.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The reaction in question is endothermic, which means it absorbs heat. Therefore, ΔH > 0 (positive).

2. **Spontaneity at Different Temperatures**:
- At the freezing point of water (0°C or 273 K), the reaction is non-spontaneous. This implies that ΔG > 0.
- At the boiling point of water (100°C or 373 K), the reaction becomes feasible (spontaneous), which means ΔG < 0.

3. **Using the Gibbs Free Energy Equation**:
- The Gibbs free energy equation is given by:
\[ \Delta G = \Delta H - T \Delta S \]
- Since ΔH is positive (endothermic), we can rewrite the equation as:
\[ \Delta G = \text{positive value} - T \Delta S \]

4. **Analyzing at Freezing Point (0°C)**:
- At 273 K, since ΔG > 0 (non-spontaneous), we can deduce:
\[ \Delta H - (273 \, \text{K}) \Delta S > 0 \]
- Rearranging gives:
\[ \Delta H > (273 \, \text{K}) \Delta S \]
- This indicates that the positive enthalpy change is greater than the product of temperature and entropy change, leading to a positive ΔG.

5. **Analyzing at Boiling Point (100°C)**:
- At 373 K, the reaction becomes spontaneous, so ΔG < 0:
\[ \Delta H - (373 \, \text{K}) \Delta S < 0 \]
- Rearranging gives:
\[ \Delta H < (373 \, \text{K}) \Delta S \]
- This suggests that at this higher temperature, the entropy change must be sufficiently large (positive) to outweigh the positive enthalpy change, resulting in a negative ΔG.

6. **Conclusion on ΔS**:
- Since ΔH is positive and the reaction is non-spontaneous at lower temperatures but becomes spontaneous at higher temperatures, we conclude that ΔS must be positive. This is because a positive ΔS contributes to making ΔG negative at higher temperatures.

### Final Answer:
- **ΔH is positive** (since the reaction is endothermic).
- **ΔS is positive** (since the reaction becomes spontaneous at higher temperatures).