## hw: 9.89

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Yinhan_Liu_1D
Posts: 51
Joined: Sat Sep 24, 2016 3:00 am

### hw: 9.89

I didn't quite understand why the definition of S=0 (H+) determines that the aqueous ions has a negative entropy.

Could anyone kindly explain it?

Chem_Mod
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### Re: hw: 9.89

Hello Yinhan,

I already answered a similar question here and will just link you the post. If you are still confused,please write what still does not make sense.

So there are two important ideas behind this.

The first is that because S is measured relative to the $S(H^{^{+}}(aq))$, all values are relative to that. Because all the values are measured relative to that value, whenever you measure the entropy to it, it can actually decreases the surrounding and become more ordered.

Second, When you dissolve solids into liquids, they create solvent shells around them.These solvent shells can create more order combinations around themselves with the water, causing a increase in order for the water. So yes, the solid dissolved became less ordered, but the water became more ordered. So much more ordered, that the disorder created by dissolving the solid into its ions is not enough to have a positive entropy value.

Thus the increase in order for the water overall decreases the entropy, resulting in negative entropy values.

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