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Gases

Gases. Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of the equivalent liquid or solid Gases are compressible Gases effuse and diffuse. The Nature of Gases. Ideal Gases. Ideal gases are imaginary gases that perfectly

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Gases

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  1. Gases

  2. Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of the equivalent liquid or solid Gases are compressible Gases effuse and diffuse The Nature of Gases

  3. Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. • Gases consist of tiny particles that are • far apart relative to their size. • Collisions between gas particles and between • particles and the walls of the container are • elastic collisions • No kinetic energy is lost in elastic • collisions

  4. Ideal Gases (continued) • Gas particles are in constant, rapid motion. • They therefore possess kinetic energy, the • energy of motion • There are no forces of attraction • between gas particles • The average kinetic energy of gas • particles depends on temperature, not • on the identity of the particle.

  5. Pressure Pressure is the force created by the collisions of molecules with the walls of a container

  6. 1 standard atmosphere (atm) 101.3 kPa (kilopascals) 14.7 lbs/in2 760 mm Hg (millimeters of mercury) 760 torr Standard Pressure

  7. Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century. The device was called a “barometer” • Baro = weight • Meter = measure

  8. An Early Barometer The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

  9. The Kelvin Scale

  10. Either of these: • 273 Kelvin (273 K) • 0 C Standard Temperature and Pressure“STP” • And any one of these: • 1 atm • 101.3 kPa • 14.7 lbs/in2 (psi) • 760 mm Hg • 760 torr

  11. Gas Laws Robert Boyle Jacques Charles Amadeo Avogadro Joseph Louis Gay-Lussac

  12. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

  13. Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant.

  14. The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant) Charles’s Law Temperature MUST be in KELVINS!

  15. Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. Temperature MUST be in KELVINS!

  16. For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas Avogadro’s Law

  17. PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant = 0.08206 L atm/ mol·K T = temperature in Kelvins Ideal Gas Law Holds closely at P < 1 atm

  18. Real Gases At high pressure (smaller volume) and low temperature (attractive forces become important) you must adjust for non-ideal gas behavior using van der Waal’s equation. ­ ­ corrected pressure corrected volume Pideal Videal

  19. Gas Density … so at STP…

  20. Density and the Ideal Gas Law Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically: M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins

  21. Gas Stoichiometry #1 If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios. 3 H2(g) + N2(g)  2NH3(g) 3moles H2 +1mole N2 2moles NH3 3liters H2 + 1liter N2 2liters NH3

  22. Gas Stoichiometry #2 How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g)  2NH3(g) 12 L H2 2 L NH3 = L NH3 8.0 3 L H2

  23. Gas Stoichiometry #3 How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 22.4 L O2 122.55 g KClO3 2 mol KClO3 1 mol O2 = 13.7 L O2

  24. Gas Stoichiometry #4 How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2KClO3(s)  2KCl(s) + 3O2(g) 50.0 g KClO3 1 mol KClO3 3mol O2 0.612 = mol O2 122.55 g KClO3 2mol KClO3 = 16.7 L

  25. For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . Dalton’s Law of Partial Pressures This is particularly useful in calculating the pressure of gases collected over water.

  26. Dalton’s Law of Partial Pressures

  27. Kinetic Molecular Theory ki⋅net⋅ic Origin: 1850–55; < Gk kīnētikós moving, equiv. to kīnē- (verbid s. of kīneîn to move) + -tikos Source: Websters Dictionary

  28. Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of the equivalent liquid or solid Gases are compressible Gases effuse and diffuse The Nature of Gases

  29. Particles of matter are ALWAYS in motion Volume of individual particles is  zero. Collisions of particles with container walls cause the pressure exerted by gas. Particles exert no forces on each other. Average kinetic energy is proportional to Kelvin temperature of a gas. Kinetic Molecular Theory

  30. Kinetic Energy of Gas Particles At the same conditions of temperature, all gases have the same average kinetic energy. m = mass v = velocity  At the same temperature, small molecules move FASTER than large molecules

  31. The Meaning of Temperature • Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

  32. Diffusion • Diffusion describes the mixing of gases. The rate of diffusion is the rate of gas mixing. • Diffusion is the result of random movement of gas molecules • The rate of diffusion increases with temperature • Small molecules diffuse faster than large molecules

  33. Effusion: describes the passage of gas into an evacuated chamber. Effusion

  34. Graham’s Law of Effusion M1 = Molar Mass of gas 1 M2 = Molar Mass of gas 2

  35. Root Mean Square Velocity (μrms) Indicates the speed of particles in a gas M is measured in kg mol-1 R = 8.314 J mol-1 K-1 Note, as M , μ Effusion 1J = 1kgm2s-2

  36. Alternative Graham’s Law

  37. Example, An unknown diatomic gas effuses at a rate only 0.355 times that of oxygen at the same temperature. What is the identity of the unknown gas? Effusion

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