States of Matter: Gases and Liquids - Gas Laws

Measurable properties of gases include Pressure ($P$), Volume ($V$), Temperature ($T$ in Kelvin), and Amount ($n$ in moles). Temperature must always be converted using $T(K) = t(^{\circ}C) + 273.15$.

Boyle's Law: For a fixed mass of gas at constant temperature, volume is inversely proportional to pressure ($V \propto \frac{1}{P}$), meaning $PV = \text{constant}$.

Charles's Law: For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature ($V \propto T$).

Gay-Lussac's Law: For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature ($P \propto T$).

Avogadro's Law: Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules ($V \propto n$).

Ideal Gas Equation: Combining Boyle's, Charles's, and Avogadro's laws gives $PV = nRT$, where $R$ is the Universal Gas Constant ($0.0821 \text{ L atm K}^{-1}\text{mol}^{-1}$ or $8.314 \text{ J K}^{-1}\text{mol}^{-1}$).

Dalton's Law of Partial Pressures: The total pressure of a mixture of non-reacting gases is the sum of the partial pressures of the individual gases: $P_{\text{total}} = P_1 + P_2 + P_3 + \dots$.

Graham's Law of Diffusion/Effusion: The rate of diffusion ($r$) of a gas is inversely proportional to the square root of its molar mass ($M$) or density ($d$): $r \propto \frac{1}{\sqrt{M}}$.

Kinetic Molecular Theory (KMT): Postulates that gas particles are in constant random motion, have negligible volume compared to the container, and undergo perfectly elastic collisions.

Real Gases and Deviation: Real gases deviate from ideal behavior at high pressure and low temperature. The van der Waals equation accounts for intermolecular forces ($a$) and molecular volume ($b$): $(P + \frac{an^2}{V^2})(V - nb) = nRT$.