Core High-Yield Fact Ledger
- Matter exists in four physical states: solid, liquid, gas, and plasma; plasma constitutes over 99% of the visible cosmos.
- Over 99.9% of a gas sample is empty intermolecular space, accounting for high mechanical compressibility.
- Standard atmospheric pressure equals 101,325 Pa, 760 mm Hg, 760 torr, 76 cm Hg, 1.01325 bar, and 14.7 psi.
- SI unit of pressure is the Pascal ($\text{Pa} = \text{N/m}^2$).
- Kinetic Molecular Theory assumes ideal gas particles have negligible volume and zero intermolecular attractions or repulsions.
- Gas collisions are completely elastic, conserving total kinetic energy.
- Average translational kinetic energy of gas molecules depends strictly upon absolute Kelvin temperature: $\overline{\text{KE}} = \frac{3RT}{2N_A} \propto T$.
- Clausius kinetic pressure equation: $PV = \frac{1}{3} m N \overline{c^2}$.
- Root-mean-square speed formula: $c_{\text{rms}} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3P}{d}}$.
- Speed ratio: $c_{\text{rms}} : c_{\text{avg}} : c_{\text{mp}} = \sqrt{3} : \sqrt{\frac{8}{\pi}} : \sqrt{2} \approx 1.224 : 1.128 : 1.000$.
- Boyle's Law: $P_1 V_1 = P_2 V_2$ at constant temperature; $P$ vs $V$ isotherm is a rectangular hyperbola shifting outward at higher temperatures.
- Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ at constant pressure; volume extrapolates to zero at absolute zero ($-273.15^\circ\text{C} = 0\text{ K}$).
- Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$; one mole of any ideal gas at STP occupies 22.414 dm^3 and contains $6.022 \times 10^{23}$ particles.
- Ideal Gas Equation: $PV = nRT$; combined gas law: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$.
- Gas density: $d = \frac{PM}{RT}$; molar mass: $M = \frac{mRT}{PV}$.
- Universal gas constant $R$ values: 0.0821 atm dm^3 / mol K, 8.314 J / mol K, 62.4 dm^3 torr / mol K, 1.987 cal / mol K.
- Real gases deviate from ideal behavior at high pressure and low temperature due to finite molecular volume and intermolecular attractions.
- Compressibility factor: $Z = \frac{PV}{nRT}$; $Z = 1$ for ideal gases; $Z < 1$ indicates attractive forces dominate; $Z > 1$ indicates excluded volume dominates.
- Van der Waals Equation: $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$.
- Constant $a$ accounts for intermolecular attraction; constant $b$ accounts for excluded volume ($b = 4 V_m$, four times actual molecular volume).