Solutions, solvents, solvability and statistics

[Storm89]

First of all I apologize for my lack of English skills in the world of chemistry. I've just started taking a very basic course in Chemistry and one week in an experiment got me wondering.

Na$_{2}$SO$_{4}$ (aq) + BaCL$_{2}$ (aq) $\rightarrow$ BaSO$_{4}$ (s) + 2NaCl (aq).

Now my teacher kept saying that there was literally no chance that the ions would just go back and form Na$_{2}$SO$_{4}$ (aq) and BaCL$_{2}$ (aq) again. I guess we're talking whether they're immiscible or miscible here. While I understand that the probability for this to happen would be extremely low, I'm struggling to grasp that it wouldn't be a possibility in say...the history of the universe. And I couldn't really get a clear answer from my teacher. So I thought, hell, I'll ask here!

 

[Borek]

1. Use [noparse] and [/noparse] tags to format formulas, so for example [noparse]BaCl₂[/noparse] is BaCl₂.

2. Miscibility and immiscibility are not related to the situation. They are used to describe behavior of liquids, not mixtures containing salts, solutions and solids.

3. You won't get any reasonable answer to your question. The way I see it explanation your teacher gave is misleading, so your question - based on misunderstanding - makes not much sense. BaSO₄ precipitated out of the solution because it "prefers" to be a solid, just like brick "prefers" to lie on the ground instead of floating in the air. There are thermodynamic reasons for that, but I guess for now you just have to accept that's the way these things behave.

Edit: there is a statistical component to that, but let's not go there, it will only confuse you at this stage.

 

[Storm89]

The misunderstandings might very well be from language barriers. I honestly don't know the English terms for any of these things as I'm Danish.

So to sum it up, what you are saying is that there is no chance that mixing (again, sorry, probably the wrong word) those two, BaCL₂ and Na₂SO₄, having then ions of Ba²⁺, Cl^-, SO₄^2- and Na²⁺ won't ever mix back to those we came from? Will they ALWAYS react to then give BaSO₄ and 2NaCl?

EDIT: Thanks for the subs/sups!

 

[Borek]

When you mix solutions containing Ba²⁺, Cl^-, Na⁺ and SO₄^2-, BaSO₄ will precipitate out, while Cl^- and Na⁺ will stay in the solution.

BaSO₄ will never dissolve back - it will be there as a solid.

While we often write NaCl as a product of the reaction, what is really happening is

Ba²⁺ + SO₄^2- -> BaSO₄(s)

and both Cl^- and Na⁺ simply stay unchanged in the solution (they are called spectators, and the equation as I wrote it is called a net ionic reaction equation).

 

[Storm89]

It wasn't so much that BaSO₄ was going to dissolve back. I understand that it won't. But is there really no chance that the ions once free as Ba²⁺, Cl^-, Na⁺ and SO₄^2- in the liquid will not form directly back to BaCL₂ and Na₂SO₄ without ever forming BaSO₄?

I hope that's made my question somewhat clearer. Not had chemistry since ground school, which is quite a while back. So, on probability, isn't there a chance of say once in 10¹⁰⁰ that they will never form the Barium Sulfate?

I do understand the reactions and so on, net ionic equations and spectators, though I think the more I talk about it or read about it, the more it gets stuck in my brain, mind you.

I'm not sure my question is even concerning chemistry, is it? More so on probabilities?

 

[Borek]

It wasn't so much that BaSO₄ was going to dissolve back. I understand that it won't. But is there really no chance that the ions once free as Ba²⁺, Cl^-, Na⁺ and SO₄^2- in the liquid will not form directly back to BaCL₂ and Na₂SO₄ without ever forming BaSO₄?

Now you have lost me.

You have these ions in the solution - how do you want them to form back BaCl₂ and Na₂SO₄? As solids? Won't happen without drying the solution out.

To some extent you can't even say what were the staring compounds. Think about it - it doesn't matter if you dissolve 1 mole of KCl and 1 mole of NaBr, or 1 mole of KBr and 1 mole of NaCl - final solution will be identical, it will contain 1 mole of each Na⁺, K⁺, Cl^- and Br^-. In the case of BaCl₂ and Na₂SO₄ situation is slightly different because of the precipitate that forms, but the general idea remains the same - you can't say if the mixture was prepared by combining solutions of Na₂SO₄ and BaCl₂, or by adding solid BaSO₄ to the solution of NaCl.

When you have a solution containing ions these ions don't form salts out of nowhere, unless either one of the salts is insoluble and precipitates out, or you dry the solution out (which is not much different from the first case - when you dry the solution out, at some moment it becomes saturated and salts start to precipitate, just some salts precipitate much earlier, while others hold much longer in the solution).

 

[Storm89]

Now you have lost me.

You have these ions in the solution - how do you want them to form back BaCl₂ and Na₂SO₄? As solids? Won't happen without drying the solution out.

To some extent you can't even say what were the staring compounds. Think about it - it doesn't matter if you dissolve 1 mole of KCl and 1 mole of NaBr, or 1 mole of KBr and 1 mole of NaCl - final solution will be identical, it will contain 1 mole of each Na⁺, K⁺, Cl^- and Br^-. In the case of BaCl₂ and Na₂SO₄ situation is slightly different because of the precipitate that forms, but the general idea remains the same - you can't say if the mixture was prepared by combining solutions of Na₂SO₄ and BaCl₂, or by adding solid BaSO₄ to the solution of NaCl.

When you have a solution containing ions these ions don't form salts out of nowhere, unless either one of the salts is insoluble and precipitates out, or you dry the solution out (which is not much different from the first case - when you dry the solution out, at some moment it becomes saturated and salts start to precipitate, just some salts precipitate much earlier, while others hold much longer in the solution).

I might have lost myself before I even started!

Well, I wouldn't exactly know how they would form back as BaCl₂ and Na₂SO₄. Not as solids though. Perhaps just as liquids separated by the very improbable chance that one was on top and one on bottom or whatever it might be (say similar to the way some solutions of stay on top of water, or Galliano below the coffee - not comparing the two, by the way, just trying to express what I'm thinking here). I do agree that it wouldn't be likely, but I'm just wondering what makes the Barium ion say: "Oh, hey, I think I'll hook up with the sulfate!", instead of "hey, I felt pretty comfortable around the Chloride, I'll go back there".

Well, I guess that took my question somewhat elsewhere, and it might be I have missed something along the lines of reading my chemistry book, but regardless even if they form Barium Sulfate, which doesn't dissolve... well, on probability I'm just struggling even then to see them do that 100¹⁰⁰ out of 100¹⁰⁰ times.

I guess this is somewhat related: when Barium Sulfate and Natrium Chloride is formed out of Barium Chloride and Natrium Sulfate, does all of the Barium ions and Sulfate combine to Barium Sulfate or does some of the Barium ions combine with the chloride to once again form Barium Chloride?

EDIT: Sorry if I'm sort of going around in circles here. Struggling to grasp that this process could go flawless and perfect, if that makes sense. If we wanted to form BaSO₄, I'd expect some of the barium ions to hook up to the chloride again. But that may be wrong, of course - I'll gladly admit that, I'm just struggling with this perfection.

 

[Borek]

As explained earlier, ions in the solution don't belong to compounds - they float on their own, so classifying dissolved compounds as this or that doesn't make sense. All you can do it to list all ions and their concentrations. Alternatively, you can list salts used when preparing the solution - but this list will be never unique, for every solution it will be possible to give alternative list of salts that will produce exactly the same composition.

Not all barium and sulfates precipitate out - they will precipitate till their concentrations are described by the solubility product, that is till

$$K_{sp}=[Ba^{2+}][SO_4^{2-}]=10^{-10}$$

where 10^-10 is a characteristic value of barium sulfate that we have measured in the past. Every salt has its own value of K_sp.

Technically there are no "insoluble" salts, as every salt dissolves - but if they dissolve in very tiny amounts (like barium sulfate, or silver chloride) we call them "insoluble". No, there is no sharp border between what is considered soluble and what is considered insoluble.

 

[ajkoer]

Solubility is a statistical concept. That is why, upon addition of some HNO3, one can, with work, get some of the BaSO4 to dissolve.

 

[Borek]

Solubility is a statistical concept. That is why, upon addition of some HNO3, one can, with work, get some of the BaSO4 to dissolve.

Please elaborate. The way you worded your post it doesn't make sense to me.

 

[ajkoer]

Please elaborate. The way you worded your post it doesn't make sense to me.

A qualitative test for the presence of Barium uses the fact that BaCO3, a slightly soluble salt in water, becomes soluble in dilute acid solutions of HCl, HNO3 and even Acetic acid.

Per the current discussion topic, this is effected by the fact that even a largely insoluble salt must dissociate, to some extent, to interact with the acid to foster its dissolution.

[EDIT] Borek, I do confess some fondness for statistics as that is where I hold one of my advanced degrees.

 

[Borek]

A qualitative test for the presence of Barium uses the fact that BaCO3, a slightly soluble salt in water, becomes soluble in dilute acid solutions of HCl, HNO3 and even Acetic acid.

Per the current discussion topic, this is effected by the fact that even a largely insoluble salt must dissociate, to some extent, to interact with the acid to foster its dissolution.

What is statistical about it?

 

[ajkoer]

What is statistical about it?

Some definitions first: Solubility is the ratio of the maximum amount of solute to the volume of solvent in which this solute can dissolve.

Thus, the Ksp is, in my opinion, a statistically base estimate relating to (that is, function of) a sampling of the maximum amount of solute to the volume of solvent. To this expected maximum is a sampling (or error) distribution.

Thus, in my opinion, "Solubility is a statistical concept" based on actual sampling. But, let us assume, for the moment, their is no uncertainty in the mean estimate of maximum solubility in a solute. However, would not a kinetic model of molecular interaction with the solute result in some uncertainty as well? The so called sampling error distribution may be representative of this uncertainty factor.