Chapter 5 Gases

1. Chemistry: A Molecular Approach, 1st Ed.Nivaldo Tro Chapter 5Gases Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2008, Prentice Hall

2. Mixtures of Gases • when gases are mixed together, their molecules behave independent of each other • therefore, in certain applications, the mixture can be thought of as one gas Tro, Chemistry: A Molecular Approach

3. Partial Pressure • the pressure of a single gas in a mixture of gases is called its partial pressure • we can calculate the partial pressure of a gas if • the sum of the partial pressures of all the gases in the mixture equals the total pressure • Dalton’s Law of Partial Pressures • because the gases behave independently Tro, Chemistry: A Molecular Approach

4. Composition of Dry Air Tro, Chemistry: A Molecular Approach

5. The partial pressure of each gas in a mixture can be calculated using the ideal gas law Tro, Chemistry: A Molecular Approach

6. Example • PHe=341 mmHg, PNe=112 mmHg, Ptot = 662 mmHg, V = 1.00 L, T=298 K Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

7. Mole Fraction the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction, c for gases, = volume % / 100% the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure Tro, Chemistry: A Molecular Approach

8. Deep Sea Divers & Partial Pressure • its also possible to have too much O2, a condition called oxygen toxicity • PO2 > 1.4 atm • oxygen toxicity can lead to muscle spasms, tunnel vision, and convulsions • its also possible to have too much N2, a condition called nitrogen narcosis • also known as Rapture of the Deep • when diving deep, the pressure of the air divers breathe increases – so the partial pressure of the oxygen increases • at a depth of 55 m the partial pressure of O2 is 1.4 atm • divers that go below 50 m use a mixture of He and O2 called heliox that contains a lower percentage of O2 than air Tro, Chemistry: A Molecular Approach

9. Mountain Climbing & Partial Pressure • our bodies are adapted to breathe O2 at a partial pressure of 0.21 atm • Sherpa, people native to the Himalaya mountains, are adapted to the much lower partial pressure of oxygen in their air • partial pressures of O2 lower than 0.1 atm will lead to hypoxia • unconsciousness or death • climbers of Mt Everest carry O2 in cylinders to prevent hypoxia • on top of Mt Everest, Pair = 0.311 atm, so PO2 = 0.065 atm Tro, Chemistry: A Molecular Approach

10. Partial Pressure & Diving Tro, Chemistry: A Molecular Approach

11. Example • Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K • A diver breathes a heliox mixture with an oxygen mole fraction of 0.050. What must the total pressure be for the partial pressure of oxygen to be 0.21 atm?

12. Collecting Gases • gases are often collected by having them displace water from a container • the problem is that since water evaporates, there is also water vapor in the collected gas • the partial pressure of the water vapor, called the vapor pressure, depends only on the temperature • if you collect a gas sample with a total pressure of 758.2 mmHg* at 25°C, the partial pressure of the water vapor will be 23.78 mmHg – so the partial pressure of the dry gas will be 734.4 mmHg • Table 5.4* Tro, Chemistry: A Molecular Approach

13. Vapor Pressure of Water Tro, Chemistry: A Molecular Approach

14. Collecting Gas by Water Displacement Tro, Chemistry: A Molecular Approach

15. Examples • 1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2. • 0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.

16. Reactions Involving Gases • the principles of reaction stoichiometry from Chapter 4 can be combined with the gas laws for reactions involving gases • in reactions of gases, the amount of a gas is often given as a volume • the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio • when gases are at STP, use 1 mol = 22.4 L P, V, T of Gas A mole A mole B P, V, T of Gas B Tro, Chemistry: A Molecular Approach

17. Examples • How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP?O2(g) + 2 H2(g) → 2 H2O(g) • What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO?2 HgO(s)  2 Hg(l) + O2(g)

18. 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 Tro, Chemistry: A Molecular Approach

19. Kinetic Molecular Theory • the particles of the gas (either atoms or molecules) are constantly moving • the attraction between particles is negligible • when the moving particles hit another particle or the container, they do not stick; but they bounce off and continue moving in another direction • like billiard balls Tro, Chemistry: A Molecular Approach

20. Kinetic Molecular Theory • there is a lot of empty space between the particles • compared to the size of the particles • the average kinetic energy of the particles is directly proportional to the Kelvin temperature • as you raise the temperature of the gas, the average speed of the particles increases Tro, Chemistry: A Molecular Approach

21. Gas Properties Explained – Indefinite Shape and Indefinite Volume Because the gas molecules have enough kinetic energy to overcome attractions, they keep moving around and spreading out until they fill the container. As a result, gases take the shape and the volume of the container they are in. Tro, Chemistry: A Molecular Approach

22. Gas Properties Explained - Compressibility Because there is a lot of unoccupied space in the structure of a gas, the gas molecules can be squeezed closer together Tro, Chemistry: A Molecular Approach

23. Gas Properties Explained – Low Density Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density Tro, Chemistry: A Molecular Approach

24. Density & Pressure • result of the constant movement of the gas molecules and their collisions with the surfaces around them • when more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure • also higher density Tro, Chemistry: A Molecular Approach

25. Gas Laws Explained – Dalton’s Law of Partial Pressures • Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures • kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact • therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy • since the average kinetic energy is the same, the total pressure of the collisions is the same Tro, Chemistry: A Molecular Approach

26. Dalton’s Law & Pressure • since the gas molecules are not sticking together, each gas molecule contributes its own force to the total force on the side Tro, Chemistry: A Molecular Approach

27. Calculating Gas Pressure Tro, Chemistry: A Molecular Approach

28. Kinetic Energy and Molecular Velocities • average kinetic energy of the gas molecules depends on the average mass and velocity • KE = ½mv2 • gases in the same container have the same temperature, the same average kinetic energy • if they have different masses, the only way for them to have the same kinetic energy is to have different average velocities • lighter particles will have a faster average velocity than more massive particles Tro, Chemistry: A Molecular Approach

29. Molecular Speed vs. Molar Mass • in order to have the same average kinetic energy, heavier molecules must have a slower average speed Tro, Chemistry: A Molecular Approach

30. Temperature vs. Molecular Speed • as the absolute temperature increases, the average velocity increases • the distribution function “spreads out,” resulting in more molecules with faster speeds Tro, Chemistry: A Molecular Approach

31. Mean Free Path • molecules in a gas travel in straight lines until they collide with another molecule or the container • the average distance a molecule travels between collisions is called the mean free path • mean free path decreases as the pressure increases Tro, Chemistry: A Molecular Approach

32. Diffusion and Effusion • the process of a collection of molecules spreading out from high concentration to low concentration is called diffusion • the process by which a collection of molecules escapes through a small hole into a vacuum is calledeffusion • both the rates of diffusion and effusion of a gas are related to its rms average velocity • for gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of the molar mass Tro, Chemistry: A Molecular Approach

33. Effusion Tro, Chemistry: A Molecular Approach

34. Graham’s Law of Effusion • for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation: Tro, Chemistry: A Molecular Approach

35. Ideal vs. Real Gases • Real gases often do not behave like ideal gases at high pressure or low temperature • Ideal gas laws assume • no attractions between gas molecules • gas molecules do not take up space • based on the kinetic-molecular theory • at low temperatures and high pressures these assumptions are not valid

36. The Effect of Molecular Volume • at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume • the molecular volume makes the real volume larger than the ideal gas law would predict • van der Waals modified the ideal gas equation to account for the molecular volume • b is called a van der Waals constant and is different for every gas because their molecules are different sizes Tro, Chemistry: A Molecular Approach

37. Real Gas Behavior • because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures Tro, Chemistry: A Molecular Approach

38. The Effect of Intermolecular Attractions • at low temperature, the attractions between the molecules is significant • the intermolecular attractions makes the real pressure less than the ideal gas law would predict • van der Waals modified the ideal gas equation to account for the intermolecular attractions • a is called a van der Waals constant and is different for every gas because their molecules are different sizes Tro, Chemistry: A Molecular Approach

39. Real Gas Behavior • because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures Tro, Chemistry: A Molecular Approach

40. Van der Waals’ Equation • combining the equations to account for molecular volume and intermolecular attractions we get the following equation • used for real gases • a and b are called van der Waal constants and are different for each gas Tro, Chemistry: A Molecular Approach

41. Real Gases • a plot of PV/RT vs. P for 1 mole of a gas shows the difference between real and ideal gases • it reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideality for “low” pressures – meaning the most important factor is the intermolecular attractions • it reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideality for “high” pressures – meaning the most important factor is the molecular volume Tro, Chemistry: A Molecular Approach

42. PV/RT Plots Tro, Chemistry: A Molecular Approach