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Chapter 10:

Chapter 10:. Gases. Overview. Pressure Barometer & Atmospheric Pressure Standard Conditions Gas Laws Boyle’s Law Charles’ Law Avogadro’s Law Ideal Gas Law. Gas Laws under Two Conditions Gas Densities Darlton’s Law of Partial Pressure Kinetic Molecular Theory

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Chapter 10:

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  1. Chapter 10: Gases

  2. Overview • Pressure • Barometer & Atmospheric Pressure • Standard Conditions • Gas Laws • Boyle’s Law • Charles’ Law • Avogadro’s Law • Ideal Gas Law

  3. Gas Laws under Two Conditions • Gas Densities • Darlton’s Law of Partial Pressure • Kinetic Molecular Theory • Molecular Effusion/Diffusion • Graham’s Law • Deviation from Ideality

  4. Characteristics • Solids • have own shape and volume • particles close together with strong interaction • Liquids • have own volume but assume shape of container • particles farther apart but have moderate interaction • Gases • assume shape and volume of container • particles far apart with little/no interaction • highly compressible

  5. Pressure • P = F/A • Force in Newtons • Area in m2 • Barometer • P in N/m2 = Pascal unit • 1 x 105 N/m2 = 1 x 105 Pa or 100 kPa • Standard Pressure • 1 atm = 760 mm Hg = 1.01325 x 105 Pa = 101.325 kPa (or torr)

  6. force of the atmosphere force of the column h when atmospheric force equals the force of the column the atmospheric pressure is measured as “h”

  7. Gas Laws • Boyle’s Law • P µ 1/V constant T, n • volume increases as pressure decreases • Charles’ Law • V µ T constant P, n • volume increases as temperature increases • Avogadro’s Law • V µ n constant P, T • volume increases as moles of gas (n) increases

  8. Ideal Gas Law • combines all gas laws PV = nRT • R = 0.0821 L-atm mol-K • any volumes must be in liters • any temperatures must be in kelvin • any pressures must be in atmospheres • STP or SC -- standard temperature/pressure • P = 1 atm (same as 760 mm Hg) • T = 273 K (same as 0° C)

  9. Problem 10.3: A flashbulb contains 2.4 x 10 -4 mol of O2 gas at 1.9 atm and 19°C . What is the volulme? • PV = nRT or V = nRT P • V = 2.4x10 -4 mol x 0.0821 L-atm x 292 K mol-K 1.9 atm V = 3.0 x 10 -3 L or 3.0 mL or 3.0 cm3

  10. Gas Laws Under Two Conditions • P1V1 = P2V2 T1 T2 • Problem 10.4: Pressure in a tank is kept at 2.20 atm. When the temp. is -15°C the volume is 28,500 ft3. What is the volume is the temp. is 31°C • P1 = P2 = 2.20 atm T1 = 258 K T2 = 304 K V1 = 28,500 ft3 • V2 = P1 V1 T2 P2 T1 • V2 = 28,500 ft3 x 304 K = 258 K 33,600 ft3

  11. Gas Densities • n = P from PV = nRT V RT • n = moles x g/mol = g = d = PMMV L L RT • d = PMM RT (atm)g mol L atm ( K)mol K

  12. Dalton’s Law of Partial Pressures • total pressure of a mixture = sum of each partial pressure • PT = P1 + P2 + P3 . . . . • each partial pressure = the pressure each gas would have if it were alone • P1 = n1RT P2 = n2RT P3 = n3RT V1 V2 V3 • PT = n1RT+ n2RT + n3RT = (n1 + n2 + n3) RT V1 V2 V3 V volumes are the same

  13. P1 = n1 therefore P1 = n1 PTPT nT nTn1 = X1 mole fractionnTP1 = X1 PT

  14. Kinetic Molecular Theory • Gases consist of particles in constant, random motion • Volume of gas particles is negligible • Attractive and repulsive forces are negligible • Average kinetic energy is proportional to temperature • Collisions are elastic

  15. molecular speed • u = root mean square speed or speed of molecule with average kinetic energy • R is the gas constant (8.314 J/mol-K), T is temp. in K & MM is molar mass • What is the rms speed of an He atom at 25°C? • u = (3 x 8.314 kg-m2/s2-mol-K x 298 K)1/2 ( 4.00 x 10 -3 kg/mol ) • u = 1.36 x 103 m/s

  16. Effusion/Diffusion • small molecules will effuse/diffuse faster than large molecules • effusiondiffusion

  17. Graham’s Law • where r is rate of speed & MM is the molar mass • Problem 10.14: Calculate the ratio of the effusion rates of N2 and O2. rN2 = 1.07 rO2

  18. Deviation from Ideality • Occurs at very high pressure or very low temperature • Correction due to volume • ideal law assumes molecules have no volume • for molecules which are far apart, this is a good assumption • must correct for the volume of the molecules themselves

  19. Correction due to attraction of molecules • ideal law assumes the molecules have no attraction to each other • for molecules which are far apart, this is a good assumption • must correct for actual attraction of molecules correction for molecular volume correction for molecular attraction

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