1 / 61

Chapter 5

Chapter 5. The Gas Laws. Pressure. Force per unit area. Gas molecules fill container. Molecules move around and hit sides. Collisions are the force. Container has the area. Measured with a barometer. Barometer. Vacuum.

idola-knowles
Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 The Gas Laws

  2. Pressure • Force per unit area. • Gas molecules fill container. • Molecules move around and hit sides. • Collisions are the force. • Container has the area. • Measured with a barometer.

  3. Barometer Vacuum • The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg. • 1 atm = 760 mm Hg 760 mm Hg 1 atm Pressure

  4. Manometer • Column of mercury to measure pressure. • h is how much lower the pressure is than outside. h Gas

  5. Manometer • h is how much higher the gas pressure is than the atmosphere. h Gas

  6. Units of pressure • 1 atmosphere = 760 mm Hg • 1 mm Hg = 1 torr • 1 atm = 101,325 Pascals = 101.325 kPa • Can make conversion factors from these. • What is 724 mm Hg in kPa? • in torr? • in atm?

  7. 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

  8. V P (at constant T)

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

  10. 22.41 L atm O2 PV CO2 P (at constant T)

  11. Examples • 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? • 30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa?

  12. Charle’s 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

  13. He CH4 H2O V (L) H2 -273.15ºC T (ºC)

  14. Examples • What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant? • At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant pressure?

  15. Avogadro's Law • Avagadro’s • 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

  16. Example A 5.20 L sample at 18.0 C and 2.00 atm pressure contains 0.436 moles of gas. If we add an additional 1.27 moles of the gas at the same temperature and pressure, what will the total volume occupied by the gas be?

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

  18. 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

  19. Examples • A deodorant 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? • A sample of gas has a volume of 4.18 L at 29 C and 732 torr. What would its volume be at 24.8 C and 756 torr?

  20. Kinetic Molecular Theory • 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. • The particles are so small we can ignore their volume. • The particles are in constant motion and their collisions cause pressure.

  21. Kinetic Molecular Theory • The particles do not affect each other, neither attracting or repelling. • The average kinetic energy is proportional to the Kelvin temperature.

  22. 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 = 0.0821 L atm/ mol K • Tells you about a gas is NOW. • The other laws tell you about a gas when it changes.

  23. Ideal Gas Law • An equation of state. • 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.

  24. Ideal Gas Law • A hypothetical substance - the ideal gas • Think of it as a limit. • Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature.

  25. 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? • What volume will 1.18 moles of O2 occupy at STP?

  26. Let’s try this one! A sample containing 15.0 g of dry ice (CO2 (s)), is put into a balloon and allowed to sublime according to the equation: CO2 (s) → CO2(g) How big will the balloon be at 22.0°C and 1.04 atm?

  27. Gas Density and Molar Mass • 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

  28. Examples • A gas at 34.0 °C and 1.75 atm has a density of 3.40 g/L. Calculate the molar mass of the gas. • What is the density of ammonia at 23ºC and 735 torr?

  29. Gases and Stoichiometry • Reactions happen in moles • At Standard Temperature and Pressure (STP, 0ºC and 1 atm): 1 mole of any gas takes up 22.42 L of space. • 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 • 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 temperture 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 • 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 • A volume of 2.0L of He at 46 °C and 1.2 atm pressure was added to a vessel that contained 4.5L of N2 at STP. What is the total pressure and the partial pressure of each gas at STP after the He was added? • Calculate the # of moles of N2. • Calculate the mole fractions of N2 and He, using the mole data, then the pressure data.

  38. Examples • When these valves are opened, what is each partial pressure and the total pressure? (hint: what happens to the volume when the valves are opened) 4.00 L CH4 1.50 L N2 3.50 L O2 0.752 atm 2.70 atm 4.58 atm

  39. Vapor Pressure • Water evaporates! • When that water evaporates, the vapor has a pressure. • Gases are often collected over water so the vapor. pressure of water must be subtracted from the total pressure. • It must be given.

  40. Example • N2O can be produced by the following reaction • What volume of N2O collected over water at a total pressure of 94 kPa and 22ºC can be produced from 2.6 g of NH4NO3? ( the vapor pressure of water at 22ºC is 21 torr)

  41. What MKT tells us • Applying the laws of physics, the expression (KE) = ½ mu2 represents the average KE of a gas particle • Using this idea and applying it to the ideal gas law (see appendix 2 for derivation) we arrive at a very important relationship: (KE)avg = 3/2 RT • This the meaning of the Kelvin temperature of a gas.

  42. Root Mean Square Velocity u represents the average particle velocity. __ u 2 is the average particle velocity squared. The root mean square velocity is Öu 2 = urms

  43. 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

  44. Example • Calculate the root mean square velocity of Helium at 25ºC • What do we know? • T= 25 C + 273 = 298 K • R= 8.314 J/K mol • What information do we need? • What is the mass of a mole of He in Kg? • Now plug into the formula • Since the units of J are Kg m2/s2, the resulting units are appropriate for velocity!

  45. Calculate the root mean square velocity of Carbon dioxide at 25ºC. Calculate the root mean square velocity of chlorine at 25ºC.

  46. 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

  47. 273 K number of particles Molecular Velocity

  48. 273 K 1273 K number of particles Molecular Velocity

  49. 273 K 1273 K number of particles 1273 K Molecular Velocity

  50. Velocity • What happens as the temperature increases? • The average velocity increases as temperature increases. • The spread of velocities increases as temperature increases.

More Related