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Gases

Gases. Chapter 10. Characteristics of Gases. The particles in gases are far apart, therefore they are very compressible . Gases expand to fill the volume of their container (V cont. = V gas ) Their motion is constant, random, and very fast.

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Gases

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  1. Gases Chapter 10

  2. Characteristics of Gases • The particles in gases are far apart, therefore they are very compressible. • Gases expand to fill the volume of their container (V cont. = V gas) • Their motion is constant, random, and very fast. • Average Kinetic NRG of gas is determined by Temperature

  3. The volume and mass of gas particles is negligable. • For gas particles, the energy remains constant within a system. • During collisions between gas particles, the collision is perfectly ellastic. • When gas particles collide with the walls of their container, they exert a pressure.

  4. Pressure • Gases exert a pressure on the walls of their container. • Pressure is defined as force per unit area: F P = A SI unit: 1 N/m2 = 1 Pascal (Pa)

  5. Atmospheric Pressure • The result of ALL the gas molecules of the atmosphere from sea level to the top of the exosphere. • Gravity pulls all of them down toward the center of the earth. • A Large Force! • 1 m2 column air = 10,000 kg at sea level • Air pressure changes slightly from day to day, but changes dramatically with altitude.

  6. Where is there higher pressure: up in the mountains or down at the beach? • Why? • What does that mean for us?

  7. A Barometer measures atmospheric pressure Vacuum The pressure of the atmosphere at sea level at 25oC will hold a column of mercury 760 mm. 1 atm = 760 mm Hg 1 atm = 760 torr 1 atm = 101.3 kPa 1 atm = 29.9 inches Hg “Standard Atmospheric Pressure” 760 mm Hg 1 atm Pressure

  8. A Manometermeasures the pressure of gas in a container • Column of mercury measures pressure. • h is how much lower the pressure is than outside. • SUBTRACT h from the room pressure. h Gas

  9. Manometer • h is how much higher the gas pressure is than the atmosphere. • ADD the difference in the height to the room pressure h Gas

  10. Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals = 101.325 kPa • Use dimensional analysis to convert 1. What is 724 mm Hg in kPa? 2. in torr? 3. in atm? 96.5 kPa 724 torr 0.952 atm

  11. The Gas Laws • Boyle’s Law: • Pressure and volume are inversely related at constant temperature. • PV= k As one goes up, the other goes down. • P1V1 = P2 V2 Graphically. . .

  12. Boyle’s Law P V (at constant T)

  13. Slope = k P 1/V (at constant T)

  14. Charles’ Law • Volume of a gas varies directly with the absolute temperature at constant pressure. V = kT (if T is in Kelvin) V1 V2 T1 T2 Graphically . . . =

  15. V (L) -273.15ºC T (ºC)

  16. Gay- Lussac Law • At constant volume, pressure and absolute temperature are directly related. • P = k T P1 P2 T1 T2 Graphically . . . =

  17. Slope = k P Temperature K

  18. Avogadro's Law • At constant temperature and pressure, the volume of gas is directly related to the number of moles. V = k n (n is the number of moles) V1 V2 n1 n2 =

  19. Combined Gas Law • If the moles of gas remains constant, use this formula and cancel out the other things that don’t change. • P1 V1 = P2 V2 T1 T2

  20. Examples • A spray can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC? • What volume of gas could the can release at 22ºC and 743 torr?

  21. Ideal Gas Law • PV = nRT • V = 22.41 L at 1 atm, 0ºC, n = 1 mole, what is R? • R is the ideal gas constant. • R = 0.08306 L atm/ mol K • How do you get R for different units of P? • Tells you about a gas NOW. • The other laws tell you about a gas when it changes.

  22. Ideal Gas Law • An equation of state. (a state function) • Independent of how you end up where you are at. Does not depend on the path. • Given 3 you can determine the fourth. • An Empirical Equation - based on experimental evidence.

  23. Ideal Gas Law • A hypothetical substance - the ideal gas • Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. • Use the laws anyway, unless told to do otherwise. • They give good estimates.

  24. Examples • A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? • Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr? • A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr?

  25. Gas Stoichiometry • D = m/V • Let M stand for molar mass • M = m/n • n= PV/RT • M = m PV/RT • M = mRT = m RT = DRT PV V P P • May be easier to convert to moles, then use stoich.

  26. Examples • What is the density of ammonia at 23ºC and 735 torr? • A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains .80 g of the gaseous compound. What is the empirical formula?

  27. The molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere. • 5.9 g/L

  28. 2NaN3(s) 2Na (s) + 3 N2(g) • The safety air bags in automobiles are inflated by nitrogen gas (see the equation above). If an air bag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0oC, how many grams of NaN3 must be decomposed? • 72 g NaN3

  29. Gases and Stoichiometry • Reactions happen in moles • At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies 22.42 L. • If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.

  30. Examples • Mercury can be achieved by the following reaction above. What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP? • At 400.ºC and 740 torr?

  31. Examples • Using the following reaction • calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm. • If 27 L of gas are produced at 26ºC and 745 torr when 2.6 L of HCl are added what is the concentration of HCl?

  32. Examples • Consider the following reaction What volume of NO at 1.0 atm and 1000ºC can be produced from 10.0 L of NH3 and excess O2 at the same temperature and pressure? • What volume of O2 measured at STP will be consumed when 10.0 kg NH3 is reacted?

  33. The Same reaction • What mass of H2O will be produced from 65.0 L of O2 and 75.0 L of NH3 both measured at STP? • What volume Of NO would be produced? • What mass of NO is produced from 500. L of NH3 at 250.0ºC and 3.00 atm?

  34. Dalton’s Law of Partial Pressures • The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. • The total pressure is the sum of the partial pressures. • PTotal = P1 + P2 + P3 + P4 + P5 ... • For each P = nRT/V

  35. Dalton's Law • PTotal = n1RT + n2RT + n3RT +... V V V • In the same container R, T and V are the same. • PTotal = (n1+ n2 + n3+...)RT V • PTotal = (nTotal)RT V

  36. The mole fraction • Ratio of moles of the substance to the total moles. • symbol is Greek letter chi c • c1 = n1 = P1 nTotal PTotal

  37. Examples • The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? • What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm? 0.787 4.13 atm

  38. Examples • When these valves are opened, what is each partial pressure and the total pressure? 4.00 L CH4 1.50 L N2 3.50 L O2 0.752 atm 2.70 atm 4.58 atm

  39. When valve is opened, the gases mix and fill the total volume of all vessels: 4.0 L + 1.5 L + 3.5 L = 9.0 L • Since the #moles and temp. is constant, this is a simple Boyle’s Law problem: 4.0 L PCH4 = 2.7 atm = 1.2 atm 9.0 L So, the total pressure of all the gases is 1.2 + 0.76 + 0.29 = 2.25 atm 1.5 L PN2 = 4.58 atm = 0.76 atm 9.0 L 3.5 L PO2 = .752 atm = 0.29 atm 9.0 L

  40. Kinetic Molecular Theory (KMT) • Theory tells why the things happen. • Explains why ideal gases behave the way they do. • Assumptions that simplify the theory, but don’t work in real gases.

  41. Kinetic Molecular Theory… • The particles are so small we can ignore their volume. • The particles are in constant motion and their collisions cause pressure. • The particles do not exert forces on each either (attractive or repulsive) • The average Kinetic NRG is proportional to the Kelvin temperature (KE = 1/2 mv2 )

  42. What it tells us • (KE)avg = 3/2 RT • This the meaning of temperature. • Molecules move about at a random average KE. • It is not a true average, but the root-mean-square speed (RMS speed). • RMS is the square root of the average squared speeds. It is close to the average.

  43. Combine these two equations • (KE)avg = NA(1/2 mu 2 ) • (KE)avg = 3/2 RT

  44. Combine these two equations • (KE)avg = NA(1/2 mu 2 ) • (KE)avg = 3/2 RT Where M is the molar mass in kg/mole, and R has the units 8.3145 J/Kmol. • The velocity will be in m/s

  45. Range of velocities • The average distance a molecule travels before colliding with another is called the mean free path and is small (near 10-7) • Temperature is an average. There are molecules of many speeds in the average. • Shown on a graph called a velocity distribution

  46. 273 K number of particles Molecular Velocity

  47. 273 K 1273 K number of particles Molecular Velocity

  48. 273 K 1273 K number of particles 2273 K Molecular Velocity

  49. Velocity • Average increases as temperature increases. • Spread increases as temperature increases.

  50. Molecular Effusion and Diffusion • Effusion: Movement of gas through a small opening into an evacuated container (vacuum) • The effusion rate measures how fast this happens. • Graham’s Law -the rate of effusion is inversely proportional to the square root of the mass of its particles.

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