Ideal Gas Law PV = nRT re-arrange n V = P RT n = molar mass (g/mol) mol gas= mass gas (g) mass of sample V x molar mass = P RT = density mass V density = P x molar mass RT

density = x molar mass RT P A colorless liquid is isolated as a product in a reaction. It might be cyclohexane, C 6 H 12. volume of flask = 213 mL T = o C P = 754 torr mass of flask = g g L = atm x molar mass x molar mass = 84.4 g/mol mass of flask + gas = g

Dalton’s Law of Partial Pressures P total = P dry air + P water vapor P total = P 1 + P 2 +P 3 + … In a mix of two gases, A and B P A = V nAnA RTP B = V nBnB RT partial pressures P T = V nAnA RT V nBnB + P T = RT (n A + n B ) V PAPA PTPT = n A n A + n B = X A mol fraction P i = XiXi PTPT

Kinetic Molecular Theory of Gases 1. Gases consist of a large number of molecules. V molecules Ideal gases have mass, but no volume << V container 2. Gas molecules are in constant, random motion. collisions with wall = Pressure 3. Attractive and repulsive forces negligible. 4. Energy transferred during collisions. 5. Average KE is proportional to temperature (K) all gases have same average KE at same T average KE does not change, at fixed T

Kinetic Molecular Theory of Gases 5. Average KE is proportional to temperature (K) all gases have same average KE at same T average KE same for all particles at T distribution of molecular velocity, u most probable u increases with T

Boyle’s Law V  1/P Charles’ Law V  T Avogadro’s Law V  n Dalton’s Law P total = P 1 + P 2 + P 3 + …

Dalton’s Law P total = P 1 + P 2 + P 3 + … = UF 6 = H 2 (2.01 g/mol) (352 g/mol) KE = ½ mu 2 m = mass u = average velocity root mean square velocity u rms u rms =  3RT/ M M = molar mass (kg) R = J/K mol u rms = 145 m/s 1926 m/s

Graham’s Law of Effusion escape of gases through a small hole rate 1 = rate 2  M 2 / M 1 diffusion mixing of gases mean free path 1 atm6 x m space 3 x m

Real Gases n RT 1. Gases consist of a large number of molecules. V molecules Ideal gases have mass, but no volume << V container need to correct V for V gas = PV

3. Attractive and repulsive forces negligible. Real Gases n = PV RT need to correct V for V gas need to correct P for interactions P + n 2 a V2V2 V - nb= nRT

P + n 2 a V2V2 V - nb= nRT van der Waals Equation a related to Intermolecular Forces molecular complexity b related to molecular volume a, b experimental

P i = XiXi PTPT acetylene (C 2 H 2 ) produced in reaction CaC 2 (s) + 2H 2 O (l)  C 2 H 2 (g) + Ca(OH) 2 (aq) gas collected over water P T = 738 torr V = 523 mL T = 23 o C How many grams of C 2 H 2 P water at 23 o C = 21 torr P T = P water + P acetylene 738 =21 +P acetylene P acetylene =717 torr=.943 atm n acetylene =.943 x L x 296 = molx g/mol= g