# Relation between size of ion and hydration energy [closed]

Suppose I take 1 tablespoon of an ionic crystal and put it in excess water. We know that shall the hydration energy of the crystal be more than the lattice energy, the crystal will separate in ions and water molecules will surround each ion, making it soluble. I wonder if the relation is direct or inverse in: i) Anion's size and hydration energy ii)Anion's size and lattice energy iii) Cation's size and lattice energy iv) Cation's size and hydration energy

I think the Cation's size is directly proportional to the hydration energy, since the bigger the atom, more easily shall it form the bond with the water molecules. The Anion's size should be inversely proportional to the hydration energy as the bigger the atom, more difficult would it be to form a strong bond between the water molecules. Similar reason goes for the other two.

PS: I'm new in chemistry so please try to explain a little.

We can look at solubility as a competition between lattice energy and hydration.

$$\Delta H_\text{solution} = \Delta H_\text{hydration} + \Delta H_\text{lattice}$$

If the enthalpy of solution is exothermic or slightly endothermic, the compound will be soluble (we are ignoring entropy here).

If we take a simplified view of both lattice energy and enthalpy of hydration, we can see that they are both generally proportional to both the size of the ions as well as the charges, that is:

$$E \propto\frac{|q_1q_2|}{r}$$

Where $$q_1$$ and $$q_2$$ are the charges on the species in question and $$r$$ is the inter-nuclear distance. So, ions with higher charges are more attracted to each other AND form strong ion-dipole interactions with water. At the same time, larger ions experience weaker attractions to each other AND form weaker ion-dipole interactions with water.

It is important to remember that this simplified analysis does not take lattice structure and crystal packing into account at all.

The differences in solubility between different ionic compounds follows two general trends.

1. Mismatch in Ion Size In general, when there is a difference in the size of the ions in a compound, the compound is more soluble. This probably arises from poorer packing in the solid state. For example at room temperature, $$\ce{MgSO4}$$ has a solubility of 1.16 g/100mL while $$\ce{BaSO4}$$ has a solubility of $$2.45*10^{-4}$$ g/100mL$$^{}$$. The barium ($$159$$ pm) and sulfate ($$242$$ pm) ions are much closer in size than magnesium ($$86$$ pm) and sulfate$$^{}$$.

2. Covalent Character In general, the more covalent character present in an ionic compound, the lower it's solubility. We can estimate covalent character by looking at the difference in electronegativities of the ions in the compound. The larger the difference in electronegativities, the less covalent character in the compound.

For example, $$\ce{AgF}$$ has

$$\Delta \mathrm{EN} = (4.0 - 1.93) = 2.07$$

Solubility = $$\dfrac{180}{100} \mathrm{~g~mL^{-1}}$$

While $$\ce{AgCl}$$ has

$$\Delta \mathrm{EN}= (3.5 - 1.93) = 1.57$$

Solubility = $$\dfrac{0.193}{100}\mathrm{~g~mL^{-1}}$$

In summary, the solubility of ionic compounds is greater when there is a significant size difference between the ions and when there is a greater difference in their electronegativities.

Footnotes

 Tro et al, Chemistry, A Molecular Approach, 2nd Canadian Edition

For the lattice energy, both cation and anion radii release more potential energy, when they are smaller.

It is similar as if a satellite goes to the lower orbit, or an electron in an atom goes to the quantum state with lower energy.

For multiatom anions, it is more complicated due their structure and charge distribution.

For hydration energy and cations of the similar kind, like alkali metals, smaller the radius, bigger hydration energy, as there is stronger electrostatic fields. It has e.g. direct impact on ion mobility and conductivity.

For different kinds of captions, the electrophilic affinity of cations plays role as well.

Hydration of anions does not have as big effect as for cations. The anions are often rather big, charge of anions is often delocalized and hydration via water H atoms is less effective.