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Gases

Gases. 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

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Gases

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  1. Gases

  2. 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

  3. 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.

  4. 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

  5. Is caused by the collisions of molecules with the walls of a container is equal to force/unit area SI units = Newton/meter2 = Pascal (Pa) 1 atmosphere = 101,325 Pa 1 atmosphere = 1 atm = 760 mm Hg = 760 torr Pressure

  6. 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

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

  8. P = 1 atmosphere, 760 torr T = 0°C, 273 Kelvin The molar volume of an ideal gas is 22.42 liters at STP Standard Temperature and Pressure“STP”

  9. Converting Celsius to Kelvin Gas law problems involving temperature require that the temperature be in KELVIN! Kelvin = C + 273 °C = Kelvin - 273

  10. Are You Ready For Some Practice Time? Please complete handout 2-2 Practice Problems #1-10 & 13-2 Practice Problems (on back) #1-8 only!!! Units of Pressure 1 atm = 760mm Hg 760 torr 101,325 Pa 29.2 in Hg 14.7 lb/in2

  11. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

  12. Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant. Diving Spaceman

  13. Volume vs Pressure

  14. Volume vs 1/Pressure Slope = K PV = K

  15. Charles’s Law • The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant)

  16. Volume vs Temperature Absolute Zero

  17. Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant.

  18. Pressure vs Temperature

  19. 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

  20. Volume vs Moles

  21. Suppose we have a 12.2 L sample containing 0.50 mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25oC. If all the O2 were converted to ozone (O3) at the same temperature and pressure, what would be the volume of the ozone? What is the balanced equation? 3O2 (g) 2O3 (g) How many moles of O3 were produced? 0.33 mol O3

  22. Suppose we have a 12.2 L sample containing 0.50 mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25oC. If all the O2 were convertedto ozone (O3) at the same temperature and pressure, what would be the volume of the ozone? Rearrange to give: Avogadro’s law: V=an V a = V V n = n n So…..what is our volume of ozone?

  23. 8.1 L HAPPY? OR SAD?

  24. Ready for a challenge? Each gas is at STP. Make a table on your whiteboard with 4 columns (one for each gas) and fill in the following rows: Volume, Pressure, Temperature, Mass of gas and # of atoms/molecules Good Luck

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

  26. Standard Molar Volume Equal volumes of all gases at the same temperature and pressure contain the same number of molecules. - Amedeo Avogadro

  27. Gas Density … so at STP…

  28. 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 Kelvin

  29. 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) 3 moles H2 + 1 mole N2  2 moles NH3 3 liters H2 + 1 liter N2  2 liters NH3

  30. 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

  31. 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 = L O2 13.7

  32. 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? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 = “n” mol O2 0.612 mol O2 122.55 g KClO3 2 mol KClO3 = 16.7 L

  33. Kinetic Energy of Gas Particles At the same conditions of temperature, all gases have the same average kinetic energy. K.E. = 1/2 mv2

  34. 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 = L O2 13.7

  35. 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? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 = “n” mol O2 0.612 mol O2 122.55 g KClO3 2 mol KClO3 = 16.7 L

  36. Magnesium metal reacts with hydrochloric acid to produce hydrogen gas. Calculate the volume of hydrogen produced at 28oC and 665 mm Hg from 0.840 mol Mg and excess HCl.

  37. Ammonium sulfate is produced by reacting ammonia with sulfuric acid. What volume of ammonia at 15oC and 1.15 atm is required to produce 75.0 g of ammonium sulfate?

  38. 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.

  39. Try This! Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent “the bends.” For a particular dive, 46 L He at 25oC and 1.0 atm and 12 L O2 at 25oC and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25oC. Calculate the number of moles of each gas Good Luck! Wanna hint?

  40. And the answer is……….. nHe = 1.9 mol nO2 = 0.49 mol PHe = 9.3 atm PO2 = 2.4 atm PT = 11.7 atm Mole Fraction: The ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. n1 n1 Χ = = nTOTAL n1 + n2 + n3 +…… And…..the mole fraction of each component in a mixture of ideal gases is directly related to its partial pressure! n1 P1 Χ1 = = χ1 So….. P1 = X PTOTAL nTOTAL PTOTAL

  41. Try This! An aqueous solution of hydrochloric acid contains 36% HCl by mass. Calculate the mole fraction of HCl in the solution. Moles of HCl = 0.99 mol HCl Moles of H2O = 3.6 mol H2O 0.99 = 0.22 ΧHCl = 4.6

  42. And……Another! A mixture of helium (8.00 g) and argon (40.0 g) in a Container at 300 K has a total gas pressure of 0.906 atmosphere. What is the partial pressure of Helium in the mixture? Mol He = 2.00 mol He Mol Ar = 1.00 mol Ar 2.00 mol ΧHe = = 0.667 3.00 mol PHe = χHePtotal = (0.667) (0.906 atm) = 0.604 atm

  43. Collecting Gas Over Water Vapor pressure of water = the pressure exerted by the water vapor on the liquid phase with which it is in equilibrium.

  44. A sample of solid potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction: 2KClO3 (s) 2KCl (s) + 3O2 (g) The oxygen produced was collected by displacement of water At 22oC at a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of the water at 22oC is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed. Wanna hint? FIRST………..find the partial pressure of O2

  45. PTOTAL = PO2 + PH2O 754 torr = PO2 + 21 torr PO2 = 754 torr – 21 torr = 733 torr. Now…………use the ideal gas law to find the number of moles of O2 2.59 x 10-2 mol of O2 Now………calculate the mass of KClO3 in the sample. 2.12 g KClO3

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

  47. Diffusion Diffusion: describes the mixing of gases. Therateof diffusion is the rate of gas mixing.

  48. Effusion: describes the passage of gas through a tiny orifice into an evacuated chamber. Effusion

  49. Graham’s LawRates of Effusion and Diffusion Effusion: Diffusion:

  50. Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6), a gas used in the enrichment process to produce fuel for nuclear reactors. 13.2 =

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