Q.What is isotonic solution? Why do gases always tend to be less soluble in liquids as the temperature is raised? OR What is solubility? What are the factors affecting the solubility of solid in a liquid?

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:

$\phi = \frac{q}{r}$ …