As an expert in thermodynamics, I can provide you with an in-depth analysis of whether a positive entropy change is favorable. The concept of entropy is central to understanding the spontaneity of a process. Entropy, denoted as 'S', is a measure of the randomness or disorder in a system. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible.

Now, let's delve into the question at hand: Is a positive entropy change favorable?

### Favorability and Spontaneity

The favorability of a process is often linked to its spontaneity. A spontaneous process is one that occurs without the need for external intervention. The spontaneity of a reaction is determined by the Gibbs free energy change (\(\Delta G\)), which is defined as:

\[
\Delta G = \Delta H - T\Delta S
\]

where:
- \(\Delta H\) is the change in enthalpy (heat content),
- \(T\) is the temperature in Kelvin,
- \(\Delta S\) is the change in entropy.

A process is spontaneous if \(\Delta G < 0\), at a given temperature.

### Positive Entropy and Spontaneity

A positive entropy change (\(\Delta S > 0\)) indicates an increase in disorder. This is generally favorable for spontaneity because it aligns with the second law of thermodynamics, which favors processes that increase the overall entropy of the universe.

### Effect of Temperature

The effect of temperature on spontaneity is crucial. At low temperatures, enthalpy (\(\Delta H\)) often plays a more significant role in determining spontaneity. If \(\Delta H < 0\) and \(\Delta S < 0\), the reaction may still be spontaneous because the negative \(\Delta H\) can overcome the positive \(T\Delta S\) term, especially at low temperatures.

However, as the temperature increases, the \(T\Delta S\) term becomes more significant. If \(\Delta S < 0\) (unfavorable entropy change), the reaction becomes less spontaneous with increasing temperature because the positive \(T\Delta S\) term (which is actually subtracting a negative number, equivalent to adding) will make \(\Delta G\) less negative or even positive, thus reducing the spontaneity.

### Conclusion

In summary, a positive entropy change is generally favorable for spontaneity because it contributes to an increase in the randomness of the universe, which is a driving force for spontaneous processes. However, the overall spontaneity of a process is determined by the interplay between enthalpy, entropy, and temperature. A positive entropy change is more favorable at higher temperatures, where the entropy term has a more pronounced effect on the Gibbs free energy.

It's important to note that the spontaneity of a reaction does not guarantee that it will occur quickly; it merely indicates the direction in which the reaction will proceed if it does occur.

Now, let's proceed with the requested steps:

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If a reaction is favorable for enthalpy ( H < 0 ), but unfavorable for entropy ( S < 0 ), then the reaction becomes LESS SPONTANEOUS as temperature increases. ... If entropy is unfavorable, the S is negative. Subtracting a negative number is the same as adding the respective positive number.read more >>