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Gases, Gas Laws

Gases, Gas Laws. The Ideal Gas Law : Variables- V = volume (liters, cm 3 , m 3 ), n = amount in moles, T = temperature (K), P = pressure (atmospheres, mm Hg). The Ideal Gas Law. PV = nRT R = ideal gas law constant (see text) Often R = 0.0821 L*atm/mol*K. The Ideal Gas Law.

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Gases, Gas Laws

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  1. Gases, Gas Laws • The Ideal Gas Law: • Variables- V = volume (liters, cm3, m3), n = amount in moles, T = temperature (K), P = pressure (atmospheres, mm Hg).

  2. The Ideal Gas Law • PV = nRT • R = ideal gas law constant (see text) • Often R = 0.0821 L*atm/mol*K

  3. The Ideal Gas Law • Initial and Final State Problems: • [P1V1 = n1RT1] / [P2V2 = n2RT2] • (initial conditions/final conditions)

  4. The Ideal Gas Law • A cylinder contains a gas at a pressure of 255 lb/in2. If the valve is opened and 75% of the gas escapes, what is the final pressure? P2 = 64 lb/in2

  5. The Ideal Gas Law • Calculation of P, V, n or T. • What is the pressure exerted by 15.0 mol of O2 in a 50.0 L tank at 25o C?

  6. The Ideal Gas Law What is the pressure exerted by 15.0 mol of O2 in a 50.0 L tank at 25o C? 7.34 atm

  7. The Ideal Gas Law • Calculation of density or molar mass. • PV = mRT/M; m/V = d = PM/RT • Note: M = g/mol

  8. The Ideal Gas Law • What is the density of O2 at 27o C, 735 mm Hg?

  9. The Ideal Gas Law • A flask weighs 52.693 g empty and 53.117 g when filled with acetone vapor at 100o C and 752 mm Hg. Taking the volume of the flask to be 226.2 mL, calculate the molar mass of acetone?

  10. The Ideal Gas Law • Volume of gases involved in reactions: • Zn(s) + 2 H+(aq) --> Zn2+(aq) + H2(g) • What is the mass of zinc required to form 16.0L of H2(g) at 20oC, 735 mm Hg?

  11. Dalton’s Law • Gas mixtures: Ptot = P1+P2+…Pn. Where P1 is the partial pressure of gas 1, etc. • Most often used in collection of gases over water.

  12. Dalton’s Law • Pgas = Ptot - PH2O, where PH2O is the vapor pressure of water.

  13. Dalton’s Law • P1 = X1 * Ptot, where Xis the mole fraction of the gas in the mixture.

  14. Dalton’s Law • What is the partial pressure of oxygen in air (X = 0.2095) when the barometric pressure = 734 mm Hg?

  15. Kinetic Theory • Etrans = 1/2 mu2 = C * T, where m = mass of molecule, u = average speed, T = temperature in K, and C is a constant which has the same value for all gases.

  16. Kinetic Theory • Graham’s law: relates m to u for two different gases at the same T. • m2u22 = m1u12

  17. Kinetic Theory • (rate2)/(rate1) = (M1/M2)1/2 = (time1)/(time2).

  18. Kinetic Theory • A certain gas takes 2.42 times as long to effuse as O2 at the same T and P. What is the molar mass of the unknown gas?

  19. Kinetic Theory • u = (3RT/M)1/2 where R = 8.31 x 103 (g*m2)/(s2*mol*K)

  20. Kinetic Theory • What is the average velocity of H2 molecules at 0oC?

  21. Real Gases • Deviate at least slightly from ideal gases due to two factors: 1. Gas molecule attract each other. 2. Gas molecules occupy a finite volume.

  22. Real Gases • At high pressures and low temperatures (P+an2/V2)(V-bn) = nRT, where a and b are proportionality constants. • Why is this true?

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