Chem Exam 3 (Gas Laws and Thermo)

Boyle’s Law

$$\frac{P_1}{V_1}=\frac{P_2}{V_2}$$

Charles’ Law

$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$

Amonton’s Law

$$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$

Avogadro’s Law

$$\frac{V_1}{n_1}=\frac{V_2}{n_2}$$

Combined Gas Law

$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$

Ideal Gas Law

$$PV=nRT$$

Dalton’s Law of Partial Pressures

$$P_{total}=P_1+P_2+..\ldots$$

Mole Fraction

$$X_{A}=\frac{n_{A}}{n_{total}}$$

Partial Pressure from Mole Fraction

$$P_{A}=X_{A}\cdot P_{total}$$

Gas Collected Over Water

$$P_{dry_{}gas}=P_{total}-P_{H_2O}$$

Gas density

$\rho=\frac{MP}{RT}$ M = molar mass

Graham’s Law of Effusion

$$\frac{rate_{A}}{rate_{B}}=\sqrt{\frac{M_{B}}{M_{A}}}$$

Root-Mean-Square Speed

$$v_{rms}=\sqrt{\frac{3RT}{M}}$$

M in kg/mol; R in Jmol^-1K^-1

Average kinetic energy (per mole)

$$KE_{avg}=\frac32RT$$

Compressibility factor

$$Z=\frac{PV}{nRT}$$

Z = 1: Ideal gas behavior

Z < 1: Attractive forces dominate

Z > 1 Repulsive/excluded volume effects dominate

van der Waals equation

$$\left(P+\frac{an^2}{V^2}\right)\left(V-nb\right)=nRT$$