Solutions, Gases & Electrolysis

Solutions

Molarity is $M = n/V$ with $V$ in litres; molality is moles per kilogram of solvent. Dilution keeps the moles fixed, so $M_1V_1 = M_2V_2$. In solution stoichiometry, $n = MV$ gives moles to carry across the balanced equation. Colligative properties ($\Delta T_b = K_b m i$, $\Delta T_f = K_f m i$, $\Pi = iMRT$) depend on particle count, not identity. Net ionic equations drop the spectator ions, and a precipitate forms when $Q > K_{sp}$.

Gases and Electrolysis

$PV = nRT$ with $R = 0.0821$ L·atm/mol·K and $T$ in kelvin. Partial pressures add to the total (Dalton), and the lighter gas effuses faster, $\text{rate}_A/\text{rate}_B = \sqrt{M_B/M_A}$ (Graham). Real gases deviate most at high pressure and low temperature. In electrolysis, mol $e^- = It/F$; divide by the electrons each ion gains to get moles of product.

Key Takeaways

• Convert mL to L before using $n = MV$, and °C to K before any gas law.
• Multiply by the van 't Hoff factor $i$: NaCl gives 2 particles, $\text{CaCl}_2$ gives 3.
• Subtract water's vapor pressure for a gas collected over water.