Chemistry · Ch 6 — Gaseous State

Summary

The state of a gas is fully described by four variables -- pressure (P), volume (V), temperature (T) and number of moles (n) -- and their pairwise relationships are the individual gas laws: Boyle's law ( $PV=\text{constant}$ , at constant n and T; $P_1V_1=P_2V_2$ ), Charles's law ( $V/T=\text{constant}$ , at constant P and n; $V_1/T_1=V_2/T_2$ ), Gay-Lussac's law ( $P/T=\text{constant}$ , at constant V and n; $P_1/T_1=P_2/T_2$ ), Avogadro's hypothesis ( $V/n=\text{constant}$ , at constant T and P; $V_1/n_1=V_2/n_2$ ), and the combined gas law ( $PV/T=\text{constant}$ , at constant n; $P_1V_1/T_1=P_2V_2/T_2$ ).
Dalton's law of partial pressures: $P_{Total}=p_1+p_2+p_3+\dots$ (at constant T and V).
Graham's law of diffusion: rate $\propto 1/\sqrt{M}$ (at constant T and P); $r_1/r_2=\sqrt{M_2/M_1}$ .
Gases that obey $PV=nRT$ under every condition are called ideal gases -- but no real gas actually does. Real gases tend toward ideal behaviour at high temperature and low pressure. Van der Waals corrected the ideal gas equation for real gases by adding a pressure-correction term (for intermolecular attraction) and a volume-correction term (for the molecules' own size): $\left(P+\dfrac{an^2}{V^2}\right)(V-nb)=nRT$ . …