[Schrödinger]

I read in a book that if there are two ions to be compared on the basis of their sizes, then the one which is more hydrated will be smaller than the other in the hydrated form.

i.e, the more hydrated ion will be smaller than a less hydrated one.

For instance, the size of gaseous ions of Li and Na vary as :


But the size of the hydrated ions varies as :



I mean it's like illogical to me...If the size of the gaseous ion is large, so will be its hydrated form, as water molecules simply surround the ion, thereby making it bigger...
I tried to comprehend this, but wasn't able to...

Please help

[MrTeo]

I mean it's like illogical to me...If the size of the gaseous ion is large, so will be its hydrated form, as water molecules simply surround the ion, thereby making it bigger...

This fact is caused by the high (in modulus) hydratation enthalpy of Litium (-519 kJ/mol) compared to the other Alkali Metals (Na -406 kJ/mol, K -322 kJ/mol, Rb -300 kJ/mol, Cs -264 kJ/mol), that's why the Litium cation creates more and more stable bonds with water molecules causing its hydratated from to be larger than the other ones. This fact becomes clear also if you consider that in the crystallization of Litium salts in watery solutions quite often the resulting crystal is hydratated (e.g. Li(H₂0)₃⁺ClO₄^-). This happens sometimes also with Sodium salts but there are no known salts with K⁺, Rb⁺ or Cs⁺ hydratated ions.

[Schrödinger]

This fact is caused by the high (in modulus) hydratation enthalpy of Litium (-519 kJ/mol) compared to the other Alkali Metals (Na -406 kJ/mol, K -322 kJ/mol, Rb -300 kJ/mol, Cs -264 kJ/mol), that's why the Litium cation creates more and more stable bonds with water molecules causing its hydratated from to be larger than the other ones.

What you are saying is that Li has more number of water molecules associated with it (around it) in the hydrated form, that's OK.

Yet, if you consider ions larger than Li like :

or
or
or
,

These ions are already large. So, putting some water molecules (even if less in number) around these ions will only increase the size to a greater extent right?

How does having many water molecules around Li and having lesser number of water molecules around , say K, change the sizes of the respective ions.

I mean like there are already spheres and you are just adding stuff on the spheres. The radii of the spheres must increase by a certain amount.

The initially larger one will end up getting a larger radius finally. Although the radius of the smaller one has also increased, how can it become larger than the other finally?


To put it mathematically:

 Let us say the radius of     is  .

 Let us say the radius of   is  .

 Obviously, .

Now,
 Let us say we add radius   to  (during hydration).

 Let us say we add radius to . (during hydration).


 Well, according to the facts, .
  But how?? Why is this

 I know what I have written is confusing, but that is the state of confusion I am in.

 Pl. help me out.

[MrTeo]

Don't worry... I understand your confusion but consider also that the topic we've been discussing (litium ion hydratation) has been the object of many researches which have confirmed the theoretical approach to this problem with experimental data. I tried looking for some papers on the net and though there are many of them I didn't found any free ones so all you get without paying is a quite useless preview of the files...

Anyway first of all I don't think you should consider because if you compare the radius of Na⁺ (102 pm) and Li⁺ (76 pm) it's quite clear that the difference is not so great and if you take a look at the water molecule dimensions you see that it's easily filled. Moreover there are two things to keep in mind: first of all we're working with an atom with only 2 electrons, thus the shielding actions of the attractive force to the nucleus usually caused by the electron cloud doesn't matter while in the sodium, with 8 electrons on the outermost level this shielding effect is more effective; then you have to think that as the litium ion is very small and has a quite strong attraction force not only a row of molecules can form bonds but there are more of them surrounding the atom, according to some papers even 8 water molecules can link to the cation.

Here is an image of the molecule of water with its dimensions... 1Å=100pm An obviously feel free to ask any other information... I'll try to help you as I can

[Schrödinger]

then you have to think that as the litium ion is very small and has a quite strong attraction force not only a row of molecules can form bonds but there are more of them surrounding the atom, according to some papers even 8 water molecules can link to the cation.

So, does that mean if you have more water molecules around the atom, its size will increase by a greater amount than that of an atom hydrated to a lesser extent?
If yes, why?

[zxt]

Oops! I made a mistake that message was duplicated here and I deleted it and wrote this since I cannot remove the post.Please check the message below.

[zxt]

Since it has been proved by scientist, so it's yes I think. Considering the number of water molecules around Li⁺ ion, the final hydrated size of Li⁺ may surpass that of the other elements in groupⅠ_A because of Lithium's strong electrical attraction. But this conclusion may not fit to elements in other groups.

[Schrödinger]

Well, according to the facts, i guess this holds for other group elements as well. What i read was not some element in particular, the author had generalized it.

[zxt]

Well, according to the facts, i guess this holds for other group elements as well. What i read was not some element in particular, the author had generalized it.

The conclusion is based on electrostatic force effect obviously I think. 

[Schrödinger]

Well, that's probably one way to put it , but i am still not convinced.
Please help

[zxt]

Well, that's probably one way to put it , but i am still not convinced.
Please help

There is a way to explain it. As to Lithium, when it lose it's second(the furthest) orbit's electron, there lefts only 2 electrons on it's innermost orbit while for the rests in Group Ⅰ_A there are 8 electrons on their orbit closest to the outermost which block the attraction to water molecules more greatly than Lithium does. And if you get the data of Group Ⅰ_A elements' atom size and that of H₂O with the number they are hydrated by, you can calculate it just by addition even though this method is not precise and totally correct.

[Schrödinger]

And if you get the data of Group Ⅰ_A elements' atom size and that of H₂O with the number they are hydrated by, you can calculate it just by addition even though this method is not precise and totally correct.

That's the exact problem, how can you just add up the radii of all the water molecules around the ion?

I mean, like if 8 molecules of water are present on Li, then the size increases by 8 times the radius of one water molecule, and if 4 water molecules are present on Na, then 4 times radius of water is the increase. This may give you the required answer, but how is it right??? It's not like the water molecules are accumulated one on the other...They are all symmetrically arranged on a sphere.

[MrTeo]

That's the exact problem, how can you just add up the radii of all the water molecules around the ion?

You can't 

You have to think that all these considerations on the hydratation of the Lithium molecule are only integrated by theoretical approach and maybe confirmed: the nature is the model for our research and our models can only become step by step closer to its real behaviour but can't fully describe it...

If they ask you why this happens you can quote all the facts I told you but you can't just sum up (as you correctly pointed out) the radii to get the final radius... it's useless and obviously not real. Moreover if you consider that also a hydratated ion is a dynamic system, our radius is only an average measure, got from spectroscopic and microscopic analysis and our struggle to accord it to mathematical models can't be fulfilled if we don't accept a significant grade of approximation...

Let me show you just one simple example about how theory adapts to experimental observation: as you certainly know the hydrogen bond, while stronger than other intermolecular bonds, has an average energy of 30 kJ/mol. Well, in the HF^2- ion there's an hydrogen bond with an energy of 230 kJ/mol...
Seems incredible but the observations told us so and it's a problem of scientist to make the model accord with reality (in this case, using the MO theory they hypotesized a triple nucleus orbital like the one of diborane)...

Hope it's all clear now... the base of all is the experimental effectiveness: here we try to easily understand it with abstract images and approximate concepts, so that we can justify this unusual behaviour of the ion 

[Schrödinger]

You're probably right. Theory must adapt itself to experimental observation. We mustn't be using very strict logic everywhere... it doesn't help.

Thanks a lot MrTeo