by Steven S. Zumdahl & Donald J. DeCoste University of Illinois

1. Introductory Chemistry: A Foundation, 6th Ed. Introductory Chemistry, 6th Ed. Basic Chemistry, 6th Ed. by Steven S. Zumdahl & Donald J. DeCoste University of Illinois

2. Chapter 13Gases

3. Properties of Gases • Expand to completely fill their container • Take the shape of their container • Low density • Much less than solid or liquid state • Compressible • Mixtures of gases are always homogeneous • Fluid

4. Gas Pressure • Pressure = total force applied to a certain area • Larger force = larger pressure • Smaller area = larger pressure • Gas pressure caused by gas molecules colliding with container or surface • More forceful or more frequent collisions mean higher gas pressure

5. Air Pressure • Constantly present when air present • Decreases with altitude • Less air = less pressure • Varies with weather conditions

6. Air Pressure (cont.) • Measured using a barometer • Column of mercury supported by air pressure • Longer mercury column supported = higher pressure • Force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury

7. Measuring Pressure of a Trapped Gas

8. Measuring Pressure of a Trapped Gas(cont.)

9. Units of Gas Pressure • Atmosphere (atm) • Height of a column of mercury (mm Hg, in Hg) • Torr • Pascal (Pa) • Pounds per square inch (psi, lbs/in2) • 1.000 atm = 760.0 mm Hg = 29.92 in Hg = 760.0 torr = 101,325 Pa = 101.325 kPa = 14.69 psi

10. Self check p 390 • On a summer day in Colorado, the atmospheric pressure is 525 mm Hg. What is this air pressure in atmospheres? • P418- • Q7. Convert the following into atmospheres- • 109.2 kPa, 781 torr, 781 mm Hg, 15.2 psi • Q9. Convert the following into mm Hg • 822 torr, 121.4 kPa, 1.14 atm, 9.75psi

11. Boyle’s Law • Pressure is inversely proportional to volume • Constant T and amount of gas • As P increases, V decreases by the same factor. • P x V = constant • P1 x V1 = P2 x V2

12. Boyle’s Law (cont.)

13. Boyle’s Law (cont.)

14. Example: What is the new volume if a 1.5 L sample of Freon-12 at 56 torr is compressed to 150 torr?

15. Example (cont.) • Choose the correct gas law: Since we are looking at the relationship between pressure and volume we use Boyle’s Law. P1 x V1 = P2 x V2 • Solve equation for the unknown variable:

16. Example (cont.) • Plug in the known values and calculate the unknown: P1 = 56 torr P2 = 150 torr V1 = 1.5 L V2 = ? L

17. Self check p 394 • A sample of neon to be used in a sign has a volume of 1.51 L at a pressure of 635 torr. Calculate the volume of a gas after it is pumped into the glass tubes of the signs where it shows a pressure of 785 torr. • P 418 q 17. Calculate new volume of the gas • V=249 mL @764 mmHg; 654mmHg, V=?L • V=1.04 L @1.21 atm; 0.671atm, V=?L • V=142 mL @20.9atm; 760mmHg, V=?

18. Absolute Zero • Theoretical temperature at which a gas would have zero volume and no pressure • Calculated by extrapolation • 0 K = -273.15 °C = -459 °F • Kelvin T = Celsius T + 273.15 • Never attainable (though we’ve gotten really close) • All gas law problems use Kelvin temperature scale.

19. Charles’ Law • Volume is directly proportional to temperature • Constant P and amount of gas • V = constant x T (T must be measured in Kelvin) • V1 = V2 T1 T2

20. Charles’ Law (cont.)

21. Charles’ Law (cont.)

22. Self check p 398 • A child blows a bubble that contains air at 8°C and has a volume of 23 cm3 a atm. As the bubble rises, it encounters a pocket of cold air (temp 18 ° C). If there is no change in pressure, will the bubble get larger or smaller as the air inside cools to 18 ° C? Calculate the new volume of the gas. • P 419 q31

23. Avogadro’s Law • Volume directly proportional to the number of gas molecules • V = constant x n (moles) • Constant P and T • More gas molecules = larger volume

24. Avogadro’s Law (cont.) • Count number of gas molecules by moles • One mole of any ideal gas occupies 22.414 L at standard conditions = molar volume • Equal volumes of gases contain equal numbers of molecules. • It doesn’t matter what the gas is!

25. Ideal Gas Law • By combining the proportionality constants from the gas laws we can write ageneral equation. • R is called the gas constant. • The value of R depends on the units of P and V. • Generally use R = 0.08206 when P in atm and V in L PV =nRT

26. Ideal Gas Law (cont.) • Use the ideal gas law when you have gas at one set of conditions • Most gases obey this law when pressure is low (at or below 1 atm) and temperature is high (above 0°C).

27. Ideal Gas Law (cont.)

28. Combined Gas Law

30. Self check p 405 • A sample of argon gas with a volume of 11 L at a temp of 13C, and a pressure of 0.747 atm is heated to 56°C and a pressure of 1.18 atm. Calculate the final volume. • Avogadro’s law- p 420 q 41. If 0.105 mol of helium gas occupies a vol of 2.35 L at a certain temp and pressure, what volume would 0.337 mol of helium occupy under the same conditions? • Q43- If 3.25 mol of Ar gas occupies a vol of 100L at a particular temp and pressure, what vol does 14.15 mol of Ar occupy under the same conditions?

31. Self check p 403, 404 • A weather balloon contains 1.1X105 mol of He and has a vol of 2.7 X 106 L at 1 atm pressure. Calculate the temp of the helium in the balloon in kelvins and in °C. • Ra can pose a hazard to humans by seeping into houses, and there is a concern about this problem in many areas. A 1.5 mol sample of this gas has a vol of 21 L at 33°C. What is the pressure of this gas? • A sample of methane gas has a vol of 3.8L at 5 °C and is heated to 86C at constant pressure. Calculate its new volume.

32. Dalton’s Law • The total pressure of a mixture of gases equals the sum of the pressures each gas would exert independently. • Partial pressure: the pressure a gas in a mixture would exert if it were alonein the container • Ptotal = Pgas A + Pgas B + …

33. Dalton’s Law (cont.) • Particularly useful for determining the pressure a dry gas would have after it is collected over water • Pair = Pwet gas = Pdry gas + Pwater vapor • Pwater vapor depends on the temperature, look up in table

34. Partial Pressures The partial pressure of each gas in a mixture can be calculated using the Ideal Gas Law:

35. Self check p 409, 410 • A 2 L flask contains a mixture of nitrogen gas and oxygen gas at 25°C. The total pressure of the gaseous mixture is 0.91 atm, and the mixture is known to contain 0.050 mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present. • Consider a sample of hydrogen gas collected over water at 25C where the vapor pressure of water is 24 torr. The volume occupied by the gaseous mixture is 0.5 L and the total pressure is 0.95 atm. Calculate the partial pressure of H2 and the number of moles of H2 present.

36. Kinetic-Molecular Theory • The properties of solids, liquids, and gases can be explained based on the speed of the molecules and the attractive forces between molecules. • In solids, the molecules have no translational freedom. They are held in place by strong attractive forces. • May only vibrate

37. Kinetic-Molecular Theory (cont.) • In liquids, the molecules have some translational freedom, but not enough to escape their attraction to neighboring molecules. • They can slide past one another and rotate, as well as vibrate.

38. Kinetic-Molecular Theory (cont.) • In gases, the molecules have “complete” freedom from each other. They have enough energy to overcome “all” attractive forces. • Kinetic energy depends only on the temperature.

39. Describing a Gas • Gases are composed of tiny particles. • The particles are small compared to the average space between them. • Assume the molecules do not have volume • Ideal gas law assumes volume of molecules=zero!

40. Describing a Gas (cont.) • Molecules constantly and rapidly move in a straight line until they bump into each other or the wall. • Average kinetic energy proportional to the temperature • Results in gas pressure • Assume that the gas molecules attraction for each other is negligible. • Ideal gas law assumes this attraction=zero!

41. Visual

42. The Meaning of Temperature • Temperature is a measure of the average kinetic energy of the molecules in a sample. • Not all molecules have same kinetic energy • Kinetic energy is directly proportional to the Kelvin temperature. • Average speed of molecules increases as the temperature increases

43. Gas Properties Explained • Gases have indefinite shape and volume because the freedom of the molecules allows them to move and fill the container they’re in. • Gases are compressible and have low density because of the large spaces between the molecules.

44. Pressure and Temperature • As the temperature of a gas increases, the average speed of the molecules increases. • The molecules hit the sides of the container with more force (on average) and more frequently, resulting in an increase in pressure.

45. Pressure and Temperature (cont.)

46. Volume and Temperature • In a rigid container, raising the temperature increases the pressure. • For a cylinder with a piston, the pressure outside and inside stays the same.

47. Volume and Temperature (cont.)

48. Gas Stoichiometry • Use the general algorithms discussed previously to convert masses or solution amounts to moles. • Use gas laws to convert amounts of gas to moles.

49. Self check p 415 • Calculate the volume of hydrogen produced at 1.5 atm and 19C by the reaction of 26.5 g of zinc with excess HCl according to the balanced equation • Zn (s)+ 2HCl (aq)--> ZnCl2(aq)+H2(g) • Ammonia is commonly used as a fertilizer to provide a source of nitrogen for plants. A sample of NH3 (g) occupies a volume of 5L at 25°C and 15atm. What volume will this sample occupy at STP? • Book Assignment- p 420 q 49, 51, 55, 57, 67, 73, 85, 87, 89, 95. Turn in on April 5th. Late work will result in lowered credit.