Question

Sulphates of Be and \(\mathrm{Mg}\) are readily soluble in water but sulphates of \(\mathrm{Ca}, \mathrm{Sr}\) and \(\mathrm{Ba}\) are insoluble. This is due to the fact (a) the greater hydration enthalpies of \(\mathrm{Be}^{2+}\) and \(\mathrm{Mg}^{2+}\) overcome the lattice enthalpy (b) high lattice enthalpy of \(\mathrm{Be}^{2+}\) and \(\mathrm{Mg}^{2+}\) makes them soluble in water (c) solubility decreases from \(\mathrm{BeSO}_{4}\) to \(\mathrm{BaSO}_{4}\) due to increase in ionic size (d) \(\mathrm{BeSO}_{4}\) and \(\mathrm{MgSO}_{4}\) are ionic in nature while other sulphates are covalent.

Short answer

The correct answer is (a) the greater hydration enthalpies of \(\mathrm{Be}^{2+}\) and \(\mathrm{Mg}^{2+}\) overcome the lattice enthalpy, making their sulphates readily soluble in water.

Step-by-step solution

Understanding the Solubility Concept

Solubility of a compound in water is affected by two main factors: lattice enthalpy (the energy required to separate the ions in a crystal lattice) and hydration enthalpy (the energy released when ions are hydrated by water molecules). If the hydration enthalpy is greater than or compensates for the lattice enthalpy, then the compound will be soluble.

Analyzing the Given Sulphates

As we move down the group from beryllium to barium in the periodic table, the ionic size increases, which generally decreases lattice enthalpy at a slower rate than the decrease in hydration enthalpy. Therefore, since Be and Mg have smaller ions, they will have higher hydration enthalpies that can overcome their lattice enthalpies, making their sulphates more soluble.

Comparing the Options

Among the options, (a) is correct because the greater hydration enthalpies of \(\mathrm{Be}^{2+}\) and \(\mathrm{Mg}^{2+}\) overcome the lattice enthalpy, leading to their sulphates being soluble in water. Options (b), (c), and (d) do not accurately describe the solubility trends in comparison to the effect of hydration and lattice enthalpies.

Key concepts

Hydration Enthalpy

When discussing solubility, hydration enthalpy is a pivotal concept. It refers to the amount of energy released when water molecules attach to ions, effectively 'hydrating' them. Imagine throwing a sponge into water and it instantly soaks up and swells – ions do a similar thing by absorbing water molecules.

In terms of chemistry, smaller ions with higher charges attract water molecules more strongly, releasing more energy – and thus have higher hydration enthalpies. This is particularly important for metal cations like \( \mathrm{Be}^{2+} \) and \( \mathrm{Mg}^{2+} \), which, due to their smaller size compared to others in the same group, have high hydration enthalpies.

Understanding this concept helps explain why certain salts are more soluble in water. A high hydration enthalpy can counteract the lattice enthalpy (the energy that holds the salt’s crystal structure together), which makes it easier for the salt to dissolve in water.

Lattice Enthalpy

On the flip side of hydration enthalpy, we have lattice enthalpy. Lattice enthalpy is the energy needed to break apart the ions in a crystal lattice when a compound is dissolved in water. It's like the energy you need to rip apart Velcro strips – the stronger they adhere, the more energy you need.

For our sulphates, \( \mathrm{BeSO}_{4} \) and \( \mathrm{MgSO}_{4} \), they have high lattice enthalpies due to the strong ionic bonds within their crystal structures. However, these bonds are not unbreakable. If the hydration energy provided by water molecules is sufficient, it will overcome this lattice enthalpy, akin to having a stronger person tearing apart those Velcro strips.

The whole solubility game is about the balance between the lattice enthalpy and hydration enthalpy; if it takes less energy to separate the ions than the energy released by water molecules surrounding them, then you’ll see the salt dissolve.

Sulphate Solubility Trend

Now let's put it all together and talk about the solubility trend of sulphates in water. Generally, as we move from \( \mathrm{BeSO}_{4} \) to \( \mathrm{BaSO}_{4} \) down group 2 of the periodic table, the ionic size increases. Larger ions have a lower charge density and thus, lower lattice enthalpy, because their charge is spread out over a larger volume. Think of it like trying to attach a postage stamp to a huge box – it won't stick as effectively as it would to a smaller, more concentrated area.

However, this trend does not continue smoothly. The hydration enthalpy decreases more quickly than the lattice enthalpy as we move down the group. So, when we reach calcium, strontium, and barium sulphates, their much larger ions result in such reduced hydration enthalpy that it cannot compensate for their lattice enthalpy. Therefore, these sulphates are less soluble in water compared to those of beryllium and magnesium.

This explains why \( \mathrm{BeSO}_{4} \) and \( \mathrm{MgSO}_{4} \) are quite soluble in water – their high hydration enthalpy can counterbalance their lattice enthalpy. It also sheds light on why the trend of solubility decreases as you go down the group from beryllium to barium.