Unit 7: Topic 14 - Free Energy of Dissolution

Question 1

What three main processes go in dissolution?

Answer 1

1. The solute (commonly water), breaks it’s intermolecular bonds with each other and expands
2. The solvent (perhaps an ionic salt), breaks it’s intermolecular bonds with each other and expands
3. Solute and solvent rearrange and form strong interactions

Question 2

How does the free energy change (ΔG°) for dissolution of a substance tell us about solubility of a compound?

Answer 2

As always, ΔG° tells us about the spontaneity of a reaction.

If ΔG° of dissolution is greatly negative, then the reaction is very spontaneous and Ksp will be&raquo_space; 1. (compound is very soluble)

If ΔG° of dissolution is very positive, then the reaction is not spontaneous at all and Ksp will be &laquo_space;1. (compound is very insoluble)

If ΔG° of dissolution is zero, then Ksp = 1 (compound is somewhat soluble)

Question 3

What “equation” can we use to find ΔG°? Can we find ΔG°? What are the underlying principles behind the sign of ΔG°?

Answer 3

ΔG° of dissolution is defined as (ΔG° of solute expanding) + (ΔG° of solvent expanding) + (ΔG° of solute/solvent rearrangement)

Since ΔG° = ΔH - TΔS°, we would need to know the total ΔH and total ΔS° to find the ΔG° of dissolution.

In practice, you wouldn’t actually calculate this.

Let’s consider why NaCL dissolves in water but not Fe(OH)₃.
Note : ΔG° of solvent expanding isn’t important for our purposes so we will ignore it
Note : It’s hard to quantify ΔS° so we can also ignore it for now

In general, the dissolutions of salts have positive entropy because water will surround the ions and decrease “disorder”

Let’s look at NaCI first :
As mentioned before, we need to consider ΔG° of solute expanding. Both Na⁺ and CI⁻ are relatively large and only singly charged so the ionic bond strength isn’t too strong. Therefore, ΔH will be positive but not too positive.

The energy released from the formation of intermolecular bonds between Na⁺, CI⁻, and water is large enough to overcome the positive ΔH of solute expansion so total ΔH will be negative. ΔS° for this dissolution is positive (side note : most salts have positive ΔS but larger molecules that can form many hydrogen bonds like glucose have negative ΔS) so ΔG° is always negative for the dissolution of NaCL. We also know that salt does in fact dissolve in water so this makes sense.

Looking at Fe(OH)₃ :
To break this ionic bond will require a lot of energy due to Coulomb’s law. This is because Fe³⁺ is small (bond length is therefore short) and very highly charged. Therefore, ΔH for this process will be positive and extremely large. In essence, it basically overshadows all the other variables.

The energy released from the formation of intermolecular bonds between Fe³⁺, OH⁻, and water isn’t enough to overcome this ΔH so the ΔG° of dissolution for Fe(OH)₃ will be&raquo_space;0 and Fe(OH)₃ is insoluble in water.

We didn’t even consider total ΔS° because at room temperature, TΔS° has negligible effect compared to the overwhelming total ΔH.

For Fe(OH)₃, the main idea is that the ionic bonds between Fe³⁺ and OH⁻ are a lot stronger than the bonds between Fe³⁺, OH-, and water.
For NaCI, the ionic bonds between Na⁺ and CI- are weaker than the bonds between Na⁺,CI-, and water.

Question 4

The overall ΔH for the dissolution of NH₄NO₃ (ammonium nitrate) is positive. However, ammonium nitrate is used in cold packs and it can actually dissolve in water. Why is this surprising?

Answer 4

Let’s take a look at ΔG° = ΔH - TΔS°

For ammonium nitrate to dissolve, ΔG° must be negative. If we know that ΔH is positive, then TΔS° must be even more positive than ΔH (keep in mind TΔS° is being subtracted).

Temperature (Kelvins) is always positive so ΔS° is positive here (entropy is increasing)

The surprising part is that TΔS° can outweigh ΔH. This means that the dissolution of ammonium nitrate increases entropy enough for the dissolution to be favorable even when ΔH is significantly negative.

Note : When you puncture the pouch of the cold pack, ammonium nitrate dissolves in water. The dissolution takes in heat from the surrounding (because ΔH is positive) which makes the pack cold.