Extent of solubility - Entropy: how far?

Extent of solubility

·         Calculation of enthalpy of solution:

The enthalpy of solution is calculated according to that equation:

ΔH _solution =  -ΔH _lattice + ΔH_hyd (X⁺) + ΔH_hyd (Y^-)

However, extra care must be taken with ionic compounds of formula MX₂. The hydration enthalpy of the anion must be multiplied by two, because there’re two anions in the compound:
M²⁺ and 2X^-.

·         Extent of solubility of solid

Solubility of a solid is determined by the total entropy change ΔS° _(total). For a solid to dissolve ΔS° _(total) must be +ve. Its value depends on both the ΔS° _(system) and ΔH _solution.

 ΔS° _(total) = ΔS° _(system) + ΔS° _{(surroundings)} = ΔS° _(system)  + (-ΔH _solution/T)

-          Entropy of the surroundings ΔS° _{(surroundings)}

 For endothermic reactions ΔS° _{(surroundings)} is negative. Therefore, for the ionic solid to be soluble ΔS° _(system) must be positive and must outweigh the negative ΔS° _{(surroundings)}. Insoluble solids have a negative ΔS° _(total). That means that the ΔS° _(system) has a smaller positive value than the value of ΔS° _{(surroundings)} or is negative.

  The same concept applies to exothermic dissolving of solids.

-          Entropy change of the system

The entropy of the system is made up of the entropy change of the solute and the entropy change of the solvent.

ΔS° _(system) = ΔS° _(solute) + ΔS° _(solvent)

Entropy of the solute ΔS° _(solute) is ALWAYS positive and increases when the solute’s dissolved, as the particles go from the state of being arranged in a regular pattern to being distributed randomly in solution.

However, the entropy of the solvent ΔS° _(solvent) could be either +ve or –ve.

It is positive when the solvent mixes with the solute particles, i.e. more disorder

It is negative when the water molecules surround the ions of the anhydrous ionic compound, i.e. water molecules become more ordered.

The δ^- oxygen atoms in the water bond with the positive ions causing the δ⁺ hydrogen atoms of the same molecule to be more positive hence they bind a second sphere of water molecules.  

The extent to which this (hydration) happens depends on the charge density of the cation. The greater the charge density of the cation, the more ordered the water molecules are.

Cations with large charge density have a greater positive charge and smaller ionic radius.

For instance, lithium ion Li⁺ decreases the entropy of the solvent water (more ordered) to a greater extent than the other group 1 ions; this is because Li⁺ has the smallest ionic radius of all group 1 ions. That means Li⁺ has the greatest charge density of all group 1 ions.

 Ammonium ion NH₄⁺ has smaller charge density than Li⁺ because the positive charge of NH₄⁺ is spread over the whole ion (which has a much larger ionic radius). Therefore, the entropy of the solvent water is not affected as much (less ordered).

Therefore we assume that dissolving group 1 compounds and ammonium compounds causes only a small change in the entropy of water, so ΔS° _(system) is always positive.

Group 2 cations have greater positive charge. Their ionic radius is much less than of the group 1 ions in the same period. So they have a greater charge density, causing a larger decrease in the entropy of the water. Therefore, we assume that dissolving group 2 compounds results in negative ΔS° _(system).