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

A colorless liquid is isolated as a product in a reaction. It might be cyclohexane, C6H12. volume of flask = 213 mL mass of flask = 77.834 g T = 100.0oC P = 754 torr mass of flask + gas = 78.416 g 0.582 g = 0.992 atm x molar mass 0.213 L 0.08206 x 373.15 density = P x molar mass RT molar mass = 84.4 g/mol

Dalton’s Law of Partial Pressures Ptotal = Pdry air + Pwater vapor Ptotal = P1 + P2 + P3+ … partial pressures In a mix of two gases, A and B PA = nA RT PB = nB RT PT = V nA RT + V nB RT V V PT = RT (nA + nB) PA = nA = XA mol fraction V nA + nB PT Pi = Xi PT

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

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

Boyle’s Law V 1/P Charles’ Law V T Avogadro’s Law V  n Dalton’s Law Ptotal= P1+ P2+ P3+ …

 root mean square velocity urms urms = 3RT/M M = molar mass (kg) R = 8.314 J/K mol KE = ½ mu2 m = mass u = average velocity (2.01 g/mol) urms = 1926 m/s = H2 urms = = UF6 (352 g/mol) 145 m/s Dalton’s Law Ptotal= P1+ P2+ P3+ …

 Graham’s Law of Effusion escape of gases through a small hole rate1 =  M2 / M1 rate2 diffusion mixing of gases mean free path 1 atm 6 x 10-9 m space 3 x 1010 m

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

Real Gases n = PV RT need to correct V for Vgas need to correct P for interactions P + n2a V - nb = nRT V2 3. Attractive and repulsive forces negligible.

van der Waals Equation P + n2a V - nb = nRT V2 a, b experimental a related to Intermolecular Forces molecular complexity b related to molecular volume

acetylene (C2H2) produced in reaction CaC2 (s) + 2H2O (l)  C2H2 (g) + Ca(OH)2 (aq) gas collected over water PT = 738 torr V = 523 mL How many grams of C2H2 T = 23oC Pwater at 23oC = 21 torr PT = Pwater + Pacetylene 738 = 21 + Pacetylene Pacetylene = 717 torr = .943 atm nacetylene = .943 x 0.523 L = 0.0202 0.0821 x 296 Pi = Xi PT 0.0202 mol x 26.04 g/mol = 0.529 g