1 / 91

Chapter 5 The Gaseous State

Chapter 5 The Gaseous State. Contents and Concepts. Gas Laws We will investigate the quantitative relationships that describe the behavior of gases. Gas Pressure and Its Measurement Empirical Gas Laws The Ideal Gas Law Stoichiometry Problems Involving Gas Volumes

dmonica
Download Presentation

Chapter 5 The Gaseous State

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 5The Gaseous State

  2. Contents and Concepts Gas Laws We will investigate the quantitative relationships that describe the behavior of gases. • Gas Pressure and Its Measurement • Empirical Gas Laws • The Ideal Gas Law • Stoichiometry Problems Involving Gas Volumes • Gas Mixtures; Law of Partial Pressures

  3. Kinetic-Molecular Theory This section will develop a model of gases as molecules in constant random motion. • Kinetic Theory of Gases • Molecular Speeds; Diffusion and Effusion • Real Gases

  4. Learning Objectives • Gas Pressure and Its Measurement • a. Define pressure and its units. • b. Convert units of pressure. • Empirical Gas Laws • a. Express Boyle’s law in words and as an equation. • b. Use Boyle’s law. • c. Express Charles’s law in words and as an equation.

  5. d. Use Charles’s law. • e. Express the combined gas law as an equation. • f. State Avogadro’s law. • g. Define standard temperature and pressure (STP). • 3. The Ideal Gas Law • a. State what makes a gas an ideal gas. • b. Learn the ideal gas law equation. • c. Derive the empirical gas laws from the ideal gas law.

  6. d. Use the ideal gas law. • e. Calculate gas density. • f. Determine the molecular mass of a vapor. • g. Use an equation to calculate gas density. • 4. Stoichiometry Problems Involving Gas Volumes • a. Solving stoichiometry problems involving gas volumes.

  7. 5. Gas Mixtures; Law of Partial Pressures • a. Learn the equation for Dalton’s law of partial pressures. • b. Define the mole fraction of a gas. • c. Calculate the partial pressure and the mole fraction of a gas in a mixture. • d. Describe how gases are collected over water and how to determine the vapor pressure of water. • e. Calculate the amount of gas collected over water.

  8. 6.Kinetic Theory of An Ideal Gas • a. List the five postulates of the kinetic theory. • b. Provide a qualitative description of the gas laws based on the kinetic theory.

  9. 7. Molecular Speeds; Diffusion and Effusion • a. Describe how the root-mean square (rms) molecular speed of gas molecules varies with temperature. • b. Describe the molecular-speed distribution of gas molecules of different temperatures. • c. Calculate the rms speed of a molecule. • d. Define effusion and diffusion. • e. Describe how individual gas molecules move while undergoing diffusion. • f. Calculate the ratio of effusion rates of gases.

  10. 8. Real Gases • a. Explain how and why a real gas is different from an ideal gas. • b. Use the van der Waals equation.

  11. Gases differ from liquids and solids: They are compressible. Pressure, volume, temperature, and amount are related.

  12. Pressure, P • The force exerted per unit area. • It can be given by two equations: • The SI unit for pressure is the pascal, Pa.

  13. Other Units atmosphere, atm mmHg torr bar

  14. A barometer is a device for measuring the pressure of the atmosphere. • A manometer is a device for measuring the pressure of a gas or liquid in a vessel.

  15. The water column would be higher because its density is less by a factor equal to the density of mercury to the density of water.

  16. Empirical Gas Laws • All gases behave quite simply with respect to temperature, pressure, volume, and molar amount. By holding two of these physical properties constant, it becomes possible to show a simple relationship between the other two properties. • The studies leading to the empirical gas laws occurred from the mid-17th century to the mid-19th century.

  17. Boyle’s Law • The volume of a sample of gas at constant temperature varies inversely with the applied pressure. • The mathematical relationship: • In equation form:

  18. Figure B shows the plot of (1/V) versus P for 1.000 g O2 at 0°C. This plot is linear, illustrating the inverse relationship. Figure A shows the plot of V versus P for 1.000 g O2 at 0°C. This plot is nonlinear.

  19. At one atmosphere the volume of the gas is 100 mL. When pressure is doubled, the volume is halved to 50 mL. When pressure is tripled, the volume decreases to one-third, 33 mL.

  20. When a 1.00-g sample of O2 gas at 0°C is placed in a container at a pressure of 0.50 atm, it occupies a volume of 1.40 L. When the pressure on the O2 is doubled to 1.0 atm, the volume is reduced to 0.70 L, half the original volume.

  21. A volume of oxygen gas occupies 38.7 mL at 751 mmHg and 21°C. What is the volume if the pressure changes to 359 mmHg while the temperature remains constant? Vi = 38.7 mL Pi = 751 mmHg Ti = 21°C Vf= ? Pf = 359 mmHg Tf= 21°C

  22. Vi = 38.7 mL Pi = 751 mmHg Ti = 21°C Vf= ? Pf = 359 mmHg Tf= 21°C = 81.0 mL (3 significant figures)

  23. A graph of V versus T is linear. Note that all lines cross zero volume at the same temperature, -273.15°C.

  24. The temperature -273.15°C is called absolute zero. It is the temperature at which the volume of a gas is hypothetically zero. • This is the basis of the absolute temperature scale, the Kelvin scale (K).

  25. Charles’s Law • The volume of a sample of gas at constant pressure is directly proportional to the absolute temperature (K). • The mathematical relationship: • In equation form:

  26. As the air inside warms, the balloon expands to its orginial size. A balloon was immersed in liquid nitrogen (black container) and is shown immediately after being removed. It shrank because air inside contracts in volume.

  27. A 1.0-g sample of O2 at a temperature of 100 K and a pressure of 1.0 atm occupies a volume of 0.26 L. When the absolute temperature of the sample is raised to 200 K, the volume of the O2 is doubled to 0.52 L.

  28. You prepared carbon dioxide by adding HCl(aq) to marble chips, CaCO3. According to your calculations, you should obtain 79.4 mL of CO2 at 0°C and 760 mmHg. How many milliliters of gas would you obtain at 27°C? Vi = 79.4 mL Pi= 760 mmHg Ti = 0°C = 273 K Vf = ? Pf = 760 mmHg Tf = 27°C = 300. K

  29. Vi= 79.4 mL Pi = 760 mmHg Ti = 0°C = 273 K Vf = ? Pf = 760 mmHg Tf = 27°C = 300. K = 87.3 mL (3 significant figures)

  30. Combined Gas Law • The volume of a sample of gas at constant pressure is inversely proportional to the pressure and directly proportional to the absolute temperature. • The mathematical relationship: • In equation form:

  31. Divers working from a North Sea drilling platform experience pressure of 5.0 × 101 atm at a depth of 5.0 × 102 m. If a balloon is inflated to a volume of 5.0 L (the volume of the lung) at that depth at a water temperature of 4°C, what would the volume of the balloon be on the surface (1.0 atm pressure) at a temperature of 11°C? Vi= 5.0 L Pi = 5.0 × 101 atm Ti = 4°C = 277 K Vf= ? Pf = 1.0 atm Tf = 11°C = 284 K

  32. Vi = 5.0 L Pi = 5.0 × 101 atm Ti = 4°C = 277 K Vf = ? Pf= 1.0 atm Tf = 11°C = 284 K = 2.6 x 102 L (2 significant figures)

  33. a. Decreasing the temperature at a constant pressure results in a decrease in volume. Subsequently increasing the volume at a constant temperature results in a decrease in pressure. • b. Increasing the temperature at a constant pressure results in an increase in volume. Subsequently decreasing the volume at a constant temperature results in an increase in pressure.

  34. Avogadro’s Law • Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.

  35. Standard Temperature and Pressure (STP) • The reference condition for gases, chosen by convention to be exactly 0°C and 1 atm pressure. • The molar volume, Vm, of a gas at STP is 22.4 L/mol. The volume of the yellow box is 22.4 L. To its left is a basketball.

  36. Ideal Gas Law The ideal gas law is given by the equation PV=nRT The molar gas constant, R, is the constant of proportionality that relates the molar volume of a gas to T/P.

  37. You put varying amounts of a gas into a given container at a given temperature. Use the ideal gas law to show that the amount (moles) of gas is proportional to the pressure at constant temperature and volume.

  38. A 50.0-L cylinder of nitrogen, N2, has a pressure of 17.1 atm at 23°C. What is the mass of nitrogen in the cylinder? V = 50.0 L P = 17.1 atm T= 23°C = 296 K mass = 986 g (3 significant figures)

  39. Gas Density and Molar Mass Using the ideal gas law, it is possible to calculate the moles in 1 L at a given temperature and pressure. The number of moles can then be converted to grams (per liter). To find molar mass, find the moles of gas, and then find the ratio of mass to moles. In equation form:

  40. What is the density of methane gas (natural gas), CH4, at 125°C and 3.50 atm? Mm= 16.04 g/mol P = 3.50 atm T= 125°C = 398 K

  41. A 500.0-mL flask containing a sample of octane (a component of gasoline) is placed in a boiling water bath in Denver, where the atmospheric pressure is 634 mmHg and water boils at 95.0°C. The mass of the vapor required to fill the flask is 1.57 g. What is the molar mass of octane? (Note: The empirical formula of octane is C4H9.) What is the molecular formula of octane?

  42. d = 1.57 g/0.5000 L = 3.140 g/L P = 634 mmHg = 0.8342 atm T= 95.0°C = 368 K

  43. Molar mass = 114 g/mol Empirical formula: C4H9 Empirical formula molar mass = 57 g/mol Molecular formula: C8H18

  44. Assume the flasks are closed. • a. All flasks contain the same number of atoms. • b. The gas with the highest molar mass, Xe, has the greatest density. • c. The flask at the highest temperature (the one containing He) has the highest pressure. • d. The number of atoms is unchanged.

  45. Stoichiometry and Gas Volumes • Use the ideal gas law to find moles from a given volume, pressure, and temperature, and vice versa.

  46. When a 2.0-L bottle of concentrated HCl was spilled, 1.2 kg of CaCO3 was required to neutralize the spill. What volume of CO2 was released by the neutralization at 735 mmHg and 20.°C?

  47. First, write the balanced chemical equation: CaCO3(s) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g) Second, calculate the moles of CO2 produced: Molar mass of CaCO3 = 100.09 g/mol Moles of CO2 produced = 11.99 mol

  48. n = 11.99 mol P = 735 mmHg = 0.967 atm T= 20°C = 293 K = 2.98 × 102 L (2 significant figures)

More Related