[XGen]

Which statements are true?

1.S° values for all elements in their standard states are positive.
2.S° values for all aqueous ions are positive.
3.∆S°  values for all spontaneous reactions are positive.

a. 1 only
b. 1 and 2 only
c. 2 and 3 only
d. 1, 2 and 3

I can easily conclude that statement 3 is incorrect (a reaction that is highly exothermic will still be spontaneous provided the temperature is low enough).

However, I am unsure about the first two statements. I initially thought that statement 2 was true, because when a solid is placed in a solvent at least a small portion of it is soluble, however small. After finding out I was wrong on the answer key, I realized that the statement was not change in entropy, but rather entropy.

I am rather lost now.

Can anyone offer any insight?

[Olympiad_Tutor]

what is the standard state for an ion?

[XGen]

I am not sure what you mean... like in an aqueous solution?

[Olympiad_Tutor]

I am not sure what you mean... like in an aqueous solution?

The way I understand it, the standard state is the natural state for the substance.  The natural state for an ion would be the ion in the air (vacuum?), not in water.

I may have started to explain not in the most correct way but the correct idea is there.

[juanrga]

Which statements are true?

1.S° values for all elements in their standard states are positive.
2.S° values for all aqueous ions are positive.
3.∆S°  values for all spontaneous reactions are positive.

a. 1 only
b. 1 and 2 only
c. 2 and 3 only
d. 1, 2 and 3

I can easily conclude that statement 3 is incorrect (a reaction that is highly exothermic will still be spontaneous provided the temperature is low enough).

However, I am unsure about the first two statements. I initially thought that statement 2 was true, because when a solid is placed in a solvent at least a small portion of it is soluble, however small. After finding out I was wrong on the answer key, I realized that the statement was not change in entropy, but rather entropy.

I am rather lost now.

Can anyone offer any insight?

Entropy, standard or not, is always positive.

For the latter use :delta: Gº = :delta: Hº - T :delta: Sº and the spontaneity condition.

[XGen]

I am not sure what you mean... like in an aqueous solution?

The way I understand it, the standard state is the natural state for the substance.  The natural state for an ion would be the ion in the air (vacuum?), not in water.

I may have started to explain not in the most correct way but the correct idea is there.

Oh, do you mean like all things tend to go to a position of greater entropy, and since it is closer to its natural state, it has positive entropy?

Thank you juanrga, do you have any reasoning behind entropy being always positive? Or is it just a commonly accepted fact?

[Olympiad_Tutor]

Entropy for a pure substance in the standard state is positive by convention. That's the starting point to solve the problem. Since a pure ion is just the substance +/- e^-s we can safely assume that S^o for a naked ion is also positive.

Now if we place the ion in water what happens?

[juanrga]

Thank you juanrga, do you have any reasoning behind entropy being always positive? Or is it just a commonly accepted fact?

I would correct my post and say that is positive or zero. Entropy
$$S = k_B \mathrm{ln} (W)$$
cannot be negative because ##W \geq 1 ##.

[Olympiad_Tutor]

Entropy of a substance can't be negative.  But entropy of a reaction can be.  Placing an ion in water is a reaction/process.

[XGen]

Ah okay. Thanks everyone for their contributions!

[Sophia7X]

"S° values for all aqueous ions are positive."

Funny how I asked my teacher the same question last Friday (1999 national exam right?). He showed me a chart of entropy values and a few aq. ons such as OH^- and S^-2 actually had negative entropy.

He said a perfect crystal has 0 entropy. So what does negative entropy mean?

It really doesn't mean anything. A solution is significantly different from a solid/liquid/gas.

There are some aqueous ions with negative entropy values because aqueous H⁺'s assigned standard entropy value is 0. Since this is a relative scale, some aq. ions have negative entropy relative to H⁺.

Ions in solution surround themselves with water so they are causing order on their surroundings.

[juanrga]

"S° values for all aqueous ions are positive."

Funny how I asked my teacher the same question last Friday (1999 national exam right?). He showed me a chart of entropy values and a few aq. ons such as OH^- and S^-2 actually had negative entropy.

He said a perfect crystal has 0 entropy. So what does negative entropy mean?

It really doesn't mean anything. A solution is significantly different from a solid/liquid/gas.

There are some aqueous ions with negative entropy values because aqueous H⁺'s assigned standard entropy value is 0. Since this is a relative scale, some aq. ions have negative entropy relative to H⁺.

Ions in solution surround themselves with water so they are causing order on their surroundings.

A perfect crystal has an absolute entropy equal to zero.

The others are conventional or relative entropies and are related to a given reference entropy. Denote the absolute entropy of H⁺ by S(H⁺). If you use this absolute entropy as reference, the relative entropy of any X will be

S^H+(X) = S(X) - S(H⁺)

where the superindex H⁺ emphasizes that we are using this ion as reference.

The relative values S^H+(X) will be positive, negative, or zero in function of the value of the absolute entropy of X.

Evidently, the above formula implies S^H+(H⁺) = 0, because this is the reference; i.e., the zero of the scale.

You can build a table with lots of values of S^H+(X) for many Xs. If you take the lowest negative value in that table as new reference, then you can built a new table with all the relative entropies positives, but now related to that new reference.