Q.Phenol in water partially associates to give dimer molecule. 0.94 g $C_6H_5OH$ dissolved in 50 g water freezes at $-0.21°C$. Calculate van't Hoff factor (molal freezing point of water is $1.86°C$) of the solution. OR $H_2SO_4$ used in lead storage cell is 38% by weight and its density is 1.30 gcm$^{-3}$. Calculate the molality of the $H_2SO_4$ solution.

Solubility Rules: Why They Work (Not Just What They Say)

Solubility rules are not arbitrary — they emerge from thermodynamics and electrostatic interactions between ions in water. Let's break down the why behind the key patterns.

1. The Core Idea: "Like Dissolves Like" at the Ionic Level

Water dissolves ionic compounds because it is polar. The $\delta^+$ hydrogen ends attract anions, and the $\delta^-$ oxygen end attracts cations.

• Driving force: The lattice energy (energy holding the solid together) vs. the hydration energy (energy released when ions are surrounded by water).
• Net energy change:

If $\Delta H_{\text{solution}}$ is negative (exothermic) or small positive, the compound tends to dissolve.

2. Why Some Salts Are Always Soluble (Group 1 & NH₄⁺)

Rule: All salts of $\ce{Na+}$, $\ce{K+}$, $\ce{NH4+}$ are soluble.

Why?

• These cations are large and have low charge density (charge/size ratio is small).
• Their lattice energies are relatively low because the ions are far apart in the crystal.
• Their hydration energies are high enough to overcome the lattice energy.

Key formula: For a cation like $\ce{K+}$, the hydration energy is roughly:

$\Delta H_{\text{hyd}} \propto \frac{q^2}{r}$

where $q$ is charge and $r$ is ionic radius.

Since $q=1$ and $r$ is large, $\Delta H_{\text{hyd}}$ is moderate — but lattice energy is even smaller.

Result: The net $\Delta H_{\text{solution}}$ is negative → spontaneous dissolution.

3. Why Nitrates, Acetates, and Chlorates Are Always Soluble

Rule: All nitrates ($\ce{NO3-}$), acetates ($\ce{CH3COO-}$), and chlorates ($\ce{ClO3-}$) are soluble.

Why?

• These anions are large and polyatomic — their charge is spread over many atoms.
• This delocalization of charge means they have low charge density.
• They form weak ionic bonds with cations (low lattice energy).
• Water can easily hydrate them because the negative charge is not concentrated.

Key insight: The lattice energy for $\ce{NaNO3}$ is much smaller than for $\ce{NaCl}$ because $\ce{NO3-}$ is larger and more polarizable.

4. The "Exceptions" — Why Some Salts Are Insoluble

4.1. Carbonates, Phosphates, Sulfides (Except with Group 1 & NH₄⁺)

Rule: Most carbonates ($\ce{CO3^{2-}}$), phosphates ($\ce{PO4^{3-}}$), and sulfides ($\ce{S^{2-}}$) are insoluble.

Why?

• These anions have high charge ($-2$ or $-3$) and are small (especially $\ce{S^{2-}}$).
• This gives them very high charge density.
• They form extremely strong ionic bonds with cations (very high lattice energy).
• The hydration energy, though large, is not enough to overcome the lattice energy.

Example: For $\ce{CaCO3}$:

$\text{Lattice energy} \approx -2800 \text{ kJ/mol}$

$\text{Hydration energy} \approx -2400 \text{ kJ/mol}$

Net $\Delta H_{\text{solution}} \approx +400 \text{ kJ/mol}$ → insoluble

4.2. Silver, Lead, Mercury Halides

Rule: $\ce{AgCl}$, $\ce{PbCl2}$, $\ce{Hg2Cl2}$ are insoluble (most other chlorides are soluble).

Why?

• $\ce{Ag+}$, $\ce{Pb^{2+}}$, $\ce{Hg2^{2+}}$ are soft (polarizable) cations.
• They form covalent character in their bonds with halides (especially $\ce{Cl-}$, $\ce{Br-}$, $\ce{I-}$).
• This covalent contribution increases the effective lattice energy beyond what simple ionic models predict.
• Water cannot break these partially covalent bonds.

Key formula: The polarizing power of a cation is:

$\phi = \frac{q}{r}$ …