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Ideal Gas Law

Ideal Gas Law. PV = nRT. re-arrange. n. = P. RT. V. n =. mol gas. = mass gas (g). molar mass (g/mol). mass of sample. = P. x molar mass. V. RT. P. = density. x molar mass. density = . mass. V. RT. A colorless liquid is isolated as a product in a reaction.

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Ideal Gas Law

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

  2. 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 x 373.15 0.213 L 0.08206 P x molar mass density = RT molar mass = 84.4 g/mol

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

  4. 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

  5. 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

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

  7. 3RT/M u = average velocity root mean square velocity urms urms = = molar mass (kg) M R = 8.314 J/K mol KE = ½ mu2 m = mass urms = 1926 m/s (2.01 g/mol) = H2 urms = 145 m/s = UF6 (352 g/mol) Dalton’s Law Ptotal= P1+ P2+ P3+ …

  8. 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

  9. 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

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

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

  12. acetylene (C2H2) produced in reaction CaC2 (s) + 2H2O (l)  C2H2 (g) + Ca(OH)2 (aq) PT = 738 torr gas collected over water 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 = PT Xi 0.0202 mol x 26.04 g/mol = 0.529 g

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