0906 Can we predict the solubilities of ionic salts?

Energy used vs. energy recovered .........

(but don't forget entropy)
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​We are able to make reasonable predictions about the solubility (or miscibilty) of molecular liquids in each other, and this has been discussed in Module 0902 Miscibility of liquids.
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Can we make similar predictions about the probability that an ionic salt is soluble (or not) in water?

​In Module 0905 Dissolution of ionic salts in water, a model was proposed that the process of dissolving involves a competition for ions on the surface of a crystal in water between:

1. forces of attraction to oppositely charged ions in the bulk of the crystal (resisting dissolution), and
2. forces of attraction to the oppositely charged ends of water molecules (favouring dissolution).

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If a salt is soluble in water, we can conclude that Type 2 forces dominate Type 1 forces.
If a salt is insoluble in water, we can conclude that Type 1 forces dominate Type 2 forces.

The two questions posed in this module are:

• What are the factors that govern which type of force dominates?
• Can we predict from the formula of a salt the probability that it is soluble (or insoluble) in water?

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First of all we need to recognise that in every situation, there is a “driving force” to increase entropy – in simple terms, that means for objects (like ions) to disperse among each other.

We have encountered this “driving force” of entropy before in Module 0902 Miscibility of liquids.

Objects would always intermingle (for examples ions would disperse among water molecules) if there were no forces of attraction resisting that from happening.
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But there are forces of attraction in the system that we are considering (an ionic crystal in water): (i) between the ions of opposite charge in the crystal, and (ii) between any ions on the surface of the crystal and the polar water molecules which can rotate to point their negative end toward positively charged ions (and their positive end toward negative ions).

Forces of attraction affect the energy (as distinct from the entropy) of a system:

• To separate two objects of opposite charge requires energy input.
• If those two objects are allowed to come together again, energy is recovered.
  

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We can compare the energy inputs and gains when sodium chloride (NaCl) is dissolved in water, with those when magnesium chloride (MgCl2) dissolves in water.

The key factor is that a sodium ion has a +1 charge, and a magnesium ion has a +2 charge.

And the key relationship that describes the force of attraction between oppositely charged ions is 
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where q1 and q2 are the charges on the ions, and d is the distance between them.
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The dissolution of a salt can be theoretically considered as two steps (although obviously it doesn’t happen in this way):
1.     Separation of the ions from each other into a vacuum: for example:

2.     Aquation (or hydration) of the isolated ions: for example:

The energy required for Step 1 is called the lattice energy of a salt. Consistent with the equation (1), the lattice ergy for magnesium chloride is much greater than that for sodium chloride:
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This data is representative of the generalisation that the higher are the charges on the ions in salt, the higher is the lattice energy.

And so a reasonable conclusion is that the forces of attractions between ions in a magnesium chloride crystal resist dissolution more than do those forces in a sodium chloride.
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But this cannot, on its own, allow us to predict relative solubilities.

Water is not a passive receiver of ions into its midst: it is an active participant in the dissolving process by aquating the ions.

Again, we could predict that the energy “recovered” during aquation is larger for magnesium ions (compared with sodium ions). This is borne out by comparison of energies of hydration of these ions:
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So, magnesium ions “use up” more energy of lattice separation (than sodium ions), but also they “recover” more energy in the process of hydration/aquation. Is the lattice energy of MgCl2 so large that dissolution does not happen?

We cannot answer this question from the data at this level of explanation.

But the experimental observation that magnesium chloride is very soluble in water allows us to conclude that, again, water molecules “win” the competition.
 
It seems that the energy “recovered” by aquation is enough to overcome the resistance to dissolution due to the expenditure of the lattice energy – especially since hydration energy does not have to be greater than the lattice energy to allow the natural tendency to mix due to entropy to be expressed.
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So what to do?

The more that we are familiar with the solubilities of substances through experience, the better we can function in chemistry.
 
There are lists of generalisations that can be made about relative solubilities of ionic solids.
 
Despite common practice, it does not make sense to call these “solubility rules”: They are not rules. the word “rule” implies that the observed solubility of sodium nitrate is due to a “rule” that all nitrates are soluble. Rubbish! Sodium nitrate does not dissolve to conform with the “rule”. It does what it does.

And we have reference lists to remind us what it does.
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Post script 1

In this module, we have focused on the charges on the ions, and ignored the influence of their sizes. The smaller are ions, the shorter can be the distance between them and, consistent with equation (1), the stronger the force between them.

In general, the higher the charge on a positive ion, the smaller it is. Indeed the diameter of +2 magnesium ions (158 pm) is smaller than that of +1 sodium ions.(196 pm).

So based on size, we would again expect that magnesium ions are more strongly attracted to oppositely charged ions in the lattice, but also more strongly held by water molecules when aquated.

On these grounds, we are also unable to predict the net outcome (Who "wins" the competition?) and whether a salt is soluble or not.
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Post script 2

I have referred in this module to lattice energy and energy of hydration (or aquation). We will see elsewhere that the correct terms are  lattice enthalpy and enthalpy of hydration.
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SELF CHECK
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Q 1.  Are the following statements correct or incorrect?

1. The separation of ions in a crystal from each other (the energy of which is the lattice enthalpy) is an exothermic process.
2. Aquation of postive ions is an exothermic process.
3. Aquation of negative ions is an exothermic process.
4. If the lattice energy of an ionic salt is larger than the energy of hydration of both ions, we can presume that the salt is insoluble.

Q 2.  The lattice energy of calcium phosphate, Ca3(PO4)2, is very large (10 600 kJ per mol).

1. Explain why this is so.
2. Does this mean that we can presume that calcium phosphate is insoluble in water?

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Answers
Q 1.

1. Incorrect
2. Correct
3. Correct
4. Incorrect. No we cannot presume this: For the salt to be insoluble, the effect of the lattice energy must overcome the effects of both the energy of hydration and the entropy (both of which "encourage" dissolving).

Q 2.

1. ​The ions have high electrostatic charges: calcium ions have +2 charge, and phosphate ions have +3 charge.
2. No, because the factors which contribute to the high lattice energy of the solid (ie, high charges on the ions) also contribute to high energy of hydration - maybe cancelling out the resistance to dissolution due to the high lattice energy.

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