Representations from particles to formulas

Chemistry operates at multiple scales simultaneously. Connecting the particulate (atoms, ions) to the symbolic (formulas, equations) and the macroscopic (mass, volume, colour) is a core skill.

Ionic equilibrium

For a sparingly soluble salt $A_b B_a$:

K_{sp} = [A^{m+}]^{b}\,[B^{n-}]^{a}

If the ion product $Q > K_{sp}$, a precipitate forms.

Ionic strength

$$I = \frac{1}{2}\sum c_i\,z_i^{2}$$

At high ionic strength, activities $a_i = \gamma_i [C_i]$ deviate from concentrations, and we must use activity coefficients $\gamma_i$.

Titration curves revisited

• The curve's shape depends on whether the acid/base is strong or weak.
• Buffer regions resist pH change; they appear before the equivalence point.
• The inflection point of the curve marks the equivalence.

Representation triangle

$$\text{Particulate} \;\longleftrightarrow\; \text{Symbolic} \;\longleftrightarrow\; \text{Macroscopic}$$

Being able to move fluidly between these three levels is what separates formula plugging from genuine chemical understanding.

Key insight: $K_{sp}$ is an equilibrium constant — it is fixed at a given temperature. Adding a common ion shifts the equilibrium and reduces solubility (common-ion effect).

Common pitfall: Same formula, different substance: isomers like ethanol and dimethyl ether share C₂H₆O but differ completely in properties. A molecular formula records composition, not identity.