## Total entropy change determining spontaneity

$\Delta S = \frac{q_{rev}}{T}$

Angela 1K
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### Total entropy change determining spontaneity

I was working on homework problem 9.73, and it asks how $\Delta S$TOT could help assess spontaneity, and according to the solutions manual, the total change in entropy has to be positive.

Can someone explain why, both mathematically and logically, a positive change in entropy signifies spontaneity?

Thanks.

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### Re: Total entropy change determining spontaneity

I can help LOGICALLY (and sort of mathematically), think about a firecracker. The deltaS for a firecracker exploding is extremely positive when ignited because it leads to a tremendous amount more of disorder, where S represents entropy (disorder). However, think about the reverse process, an exploded firecracker will NEVER turn back into a new firecracker because the deltaS for the reverse rxn is EXTREMELY negative and logically, that just wouldn't make sense. We have never seen that, nor will we, in real life.

Jonathan Tangonan 1E
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### Re: Total entropy change determining spontaneity

If you look at the equation delta G= deltaH-TdeltaS, we can determine why we want entropy to be positive for a spontaneous reaction. For a reaction to be spontaneous we want delta G to be a negative value because a negative value indicates spontaneity. There's a table in the textbook Table 9.5 on page 349 which shows the factors that favor spontaneity when looking at this equation.

melissa carey 1f
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Joined: Fri Sep 29, 2017 7:06 am

### Re: Total entropy change determining spontaneity

Since total entropy of an isolated system must always increase (2nd law) - then ∆S_tot must always be positive. Order cannot come from disorder without an input on energy. For example, think about freezing ice. Liquid > solid is a decrease of energy, but you must put in MORE energy (electrical from the fridge) to cause this process to occur, creating a larger increase in S than the decrease that is happening to the water. ∆S is positive.