What values of delta S will give a spontaneous reaction if the reaction is endothermic? An endothermic reaction has a positive value for delta H. If delta S is negative and the product of T x delta S is large enough, then delta G will be negative and the reaction will proceed spontaneously. An endothermic reaction has a negative value for delta H. If delta S is positive and if T x delta S is large enough, then the reaction will be spontaneous. An endothermic reaction has a positive value for delta H. If delta S is positive, then the reaction may be spontaneous if -T x delta S is larger in a negative direction than delta H is in a positive direction.
The Correct Answer and Explanation is:
To determine the conditions under which a reaction is spontaneous, we use the Gibbs free energy equation:ΔG=ΔH−TΔS\Delta G = \Delta H – T\Delta SΔG=ΔH−TΔS
Where:
- ΔG\Delta GΔG is the Gibbs free energy change.
- ΔH\Delta HΔH is the enthalpy change (heat absorbed or released).
- TTT is the temperature in Kelvin.
- ΔS\Delta SΔS is the entropy change.
For a reaction to be spontaneous, ΔG\Delta GΔG must be negative (ΔG<0\Delta G < 0ΔG<0).
Case 1: Endothermic Reaction (Positive ΔH\Delta HΔH)
In an endothermic reaction, ΔH\Delta HΔH is positive, meaning the system absorbs heat from the surroundings. This alone doesn’t guarantee spontaneity, as ΔG\Delta GΔG will tend to be positive unless TΔST \Delta STΔS can sufficiently counteract the positive ΔH\Delta HΔH.
Case 2: Negative ΔS\Delta SΔS (Decreasing Disorder)
If ΔS\Delta SΔS is negative, the reaction leads to a decrease in disorder. In this case, the term −TΔS-T \Delta S−TΔS becomes positive. For spontaneity, TΔST \Delta STΔS must be large enough in magnitude to make ΔG\Delta GΔG negative, meaning:ΔH−TΔS<0\Delta H – T \Delta S < 0ΔH−TΔS<0
This can happen when TΔST \Delta STΔS is sufficiently large (at higher temperatures), but it is generally less likely because ΔS\Delta SΔS is negative.
Case 3: Positive ΔS\Delta SΔS (Increasing Disorder)
If ΔS\Delta SΔS is positive, the system becomes more disordered during the reaction. In this case, the term −TΔS-T \Delta S−TΔS will be negative, and for spontaneity, the reaction will be more likely to occur if:ΔH−TΔS<0\Delta H – T \Delta S < 0ΔH−TΔS<0
In this case, a positive ΔS\Delta SΔS can drive spontaneity, especially at higher temperatures, where the product TΔST \Delta STΔS becomes large enough to overcome the positive ΔH\Delta HΔH.
Thus, for an endothermic reaction, the reaction will be spontaneous if:
- At high temperatures and if ΔS\Delta SΔS is positive, the product TΔST \Delta STΔS will likely outweigh the positive ΔH\Delta HΔH, resulting in a negative ΔG\Delta GΔG.
Conclusion
For an endothermic reaction to be spontaneous:
- ΔS\Delta SΔS must be positive and the temperature must be high enough for the TΔST \Delta STΔS term to be large enough to overcome the positive ΔH\Delta HΔH.
