Representations from particles to formulas

The Three Scales of Chemistry

Chemistry operates simultaneously at three connected levels:

Moving fluidly across this representation triangle separates genuine understanding from mere formula plugging.

Ionic equilibrium governs sparingly soluble salts $A_b B_a$:

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

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

Ionic strength is calculated as:

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

At high ionic strength, activities deviate from concentrations, requiring activity coefficients $\gamma_i$ where $a_i = \gamma_i [C_i]$.

Titrations & Pitfalls

Titration curves reveal reaction properties through specific features:

Common-ion effect: $K_{sp}$ is fixed at a given temperature, but adding a common ion shifts the equilibrium and reduces solubility.

Common pitfall: Molecular formulas record composition, not identity. Isomers like ethanol and dimethyl ether share $C_2H_6O$ but differ completely in properties.