If a rx has delta S positive and delta H negative, the rx is
A. non-spontaneous at all temp
B. spontaneous at all temp
C. spontaneous only at high temp
D. spontaneous only at low temp
The correct answer and explanation is:
Correct Answer: B. spontaneous at all temp
To determine the spontaneity of a chemical reaction, we use the Gibbs free energy change (ΔG), which is given by the equation:
ΔG = ΔH – TΔS
Where:
- ΔG is the change in Gibbs free energy
- ΔH is the change in enthalpy
- T is the temperature in Kelvin
- ΔS is the change in entropy
A reaction is spontaneous when ΔG is negative. Now, consider the signs given in the question:
- ΔH is negative (this means the reaction is exothermic)
- ΔS is positive (this means the reaction leads to an increase in disorder)
Plugging these values into the Gibbs free energy equation:
ΔG = (negative number) – T × (positive number)
Since T is always a positive value in Kelvin, the term TΔS will also be positive. Subtracting a positive value from a negative ΔH makes ΔG even more negative. In other words, both terms (ΔH and –TΔS) contribute to making ΔG negative.
This means that regardless of the temperature, the reaction will always have a negative ΔG. Therefore, it will be spontaneous at all temperatures.
This type of situation represents the most favorable thermodynamic condition for a reaction to occur. A negative ΔH indicates that the reaction releases energy, while a positive ΔS suggests that the disorder of the system increases. Both of these are characteristics that favor spontaneity.
In summary, when a reaction has a negative ΔH and a positive ΔS, it will always result in a negative ΔG. This ensures that the reaction is spontaneous no matter the temperature. Therefore, the correct choice is B. spontaneous at all temp.