1. 1 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Section 5 Gases

2. 2 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Gas Laws In the first part of this chapter we will examine the quantitative relationships, or empirical laws, governing gases. First, however, we need to understand the concept of pressure.

3. 3 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Pressure Pressure - force exerted per unit area of surface by molecules in motion. – – 1 atmosphere (atm) = 14.7 psi – 1 atmosphere = 760 mm Hg = 760 Torr – 1 atmosphere = 101,325 Pascals – 1 Pascal = 1 kg/m. s 2 –1 atm = 0.101325 MPa = 1.01325 bar P = Force/unit area

4. 4 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A mercury barometer.

5. 5 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Pressure Conversions The pressure of gas in a flask is 797.7 mmHg. What is the pressure in atm? HW 37

6. 6 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Empirical Gas Laws Boyle’s Law: The volume of a sample of gas at a constant temperature varies inversely with the applied pressure. V  1/P [constant moles (n) and T] or

7. 7 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume? HW 38

8. 8 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Empirical Gas Laws Charles’s Law: The volume occupied by any sample of gas at constant pressure is directly proportional to its absolute temperature. V  T abs (constant moles and P) or

9. 9 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider A sample of methane gas that has a volume of 3.8 L at 5.0°C is heated to 86.0°C at constant pressure. Calculate its new volume. HW 39

10. 10 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Empirical Gas Laws Gay-Lussac’s Law: The pressure exerted by a gas at constant volume is directly proportional to its absolute temperature. P  T abs (constant moles and V) or

11. 11 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider An aerosol can has a pressure of 1.4 atm at 25°C. What pressure would it attain at 1200°C, assuming the volume remained constant? HW 40

12. 12 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Empirical Gas Laws Combined Gas Law: In the event that all three parameters, P, V, and T, are changing, their combined relationship is defined as follows (at constant n):

13. 13 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider A sample of carbon dioxide gas occupies 4.5 L at 30°C and 650 mm Hg. What volume would it occupy at 800 mm Hg and 200°C? HW 41

14. 14 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The volume of one mole of gas is called the molar gas volume, V m. Volumes of gases are often compared at standard temperature and pressure (STP), chosen to be 0 o C (273 K) and 1 atm pressure. The Empirical Gas Laws Avogadro’s Law: Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules. at constant T & P

15. 15 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. –At STP, the molar volume, V m, that is, the volume occupied by one mole of any gas, is 22.4 L/mol at STP, 1 mol of any gas = 22.4 L The Empirical Gas Laws Avogadro’s Law HW 42

16. 16 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Ideal Gas Law From the empirical gas laws, we See that volume varies in proportion to pressure, absolute temperature, and moles.

17. 17 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Ideal Gas Law This implies that there must exist a proportionality constant governing these relationships. where “R” is the proportionality constant referred to as the ideal gas constant (independent of gas).

18. 18 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Ideal Gas Law At STP, only missing “R”: 1 mol, 22.4 L, 273 K, 1 atm

19. 19 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The Ideal Gas Law Thus, the ideal gas equation, is usually expressed in the following form: P is pressure (in atm) V is volume (in liters) n is number of atoms (in moles) R is universal gas constant - 0.0821 L. atm/K. mol T is temperature (in Kelvin)

20. 20 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider An experiment calls for 3.50 moles of chlorine gas, Cl 2. What volume would this be if the gas volume is measured at 34°C and 2.45 atm? HW 43

21. 21 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Molecular Weight Determination In section 3 we showed the relationship between moles and mass. or

22. 22 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Molecular Weight Determination If we substitute this in the ideal gas equation, we obtain If we solve this equation for the molecular mass, we obtain

23. 23 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider A 9.25 gram sample of an unknown gas occupied a volume of 5.75 L at 25°C and a pressure of 1.08 atm. Calculate its molecular mass. Which of the following gases is most likely to be the unknown gas - N 2, O 2, or HCl?

24. 24 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Density Determination If we look again at our derivation of the molecular mass equation, we can solve for m/V, which represents density.

25. 25 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider Calculate the density of ozone gas, O 3 (M m = 48.0g/mol), at 50°C and 1.75 atm of pressure. HW 44

26. 26 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Stoichiometry Problems Involving Gas Volumes Suppose you heat 0.0100 mol of potassium chlorate, KClO 3, in a test tube. How many liters of oxygen can you produce at 298 K and 1.02 atm?

27. 27 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Stoichiometry Problems Involving Gas Volumes Many air bags are inflated with N 2 gas by the following rxn: 6NaN 3 (s) + Fe 2 O 3 (s)  3 Na 2 O (s) + 2Fe (s) + 9N 2 (g) How many grams of NaN 3 would be needed to provide 75.0 L of N 2 gas at 25 o C and 748 mmHg? HW 45

28. 28 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Partial Pressures of Gas Mixtures Dalton’s Law of Partial Pressures: the sum of all the pressures of all the different gases in a mixture equals the total pressure of the mixture.

29. 29 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Partial Pressures of Gas Mixtures The composition of a gas mixture is often described in terms of its mole fraction. –The mole fraction of a component gas is the fraction of moles of that component in the total moles of gas mixture.

30. 30 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Partial Pressures of Gas Mixtures The partial pressure of a component gas, “A”, is then defined as –Applying this concept to the ideal gas equation, we find that each gas can be treated independently.

31. 31 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider A 10.0 L flask contains 1.031 g O 2 and 0.572 g CO 2 gases at 18 o C. What are the partial pressures of O 2 and CO 2 ? What is the total pressure? What is the mole fraction of O 2 in the mixture? HW 46

32. 32 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Collecting Gases “Over Water” A useful application of partial pressures arises when you collect gases over water. –As gas bubbles through the water, the gas becomes saturated with water vapor. –The partial pressure of the water in this “mixture” depends only on the temperature (vapor pressure of water).

33. 33 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider Suppose a 156 mL sample of H 2 gas was collected over water at 19 o C and 769 mm Hg. What is the mass of H 2 collected?

34. 34 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. HW 47 & 48

35. 35 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Kinetic-Molecular Theory of gases A simple model based on the actions of individual atoms Volume of particles can be neglected but volume of container cannot. Particles are in constant motion; move in straight lines in all directions and at various speeds (smaller mass, faster it moves). No inherent attractive or repulsive forces When molecules collide, the collisions are elastic (total KE remains constant). The average kinetic energy of a collection of particles is proportional to the temperature (K) – higher T, greater KE

36. 36 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Molecular Speeds; Diffusion and Effusion The root-mean-square (rms) molecular speed, u – m/s, is a type of average molecular speed, equal to the speed of a molecule having the average molecular kinetic energy. It is given by the following formula:

37. 37 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Molecular Speeds; Diffusion and Effusion Diffusion is the transfer of a gas through space or another gas over time. Effusion is the transfer of a gas through a membrane or orifice. –The equation for the rms velocity of gases shows the following relationship between rate of effusion and molecular mass (inversely proportional). Graham’s Law:

38. 38 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. The rate of effusion of molecules from a container depends on three factors: 1.) cross-sectional area of the hole (the larger it is; the more likely molecules are to escape) 2.) the number of molecules per unit volume (conc of gas). 3.) the average molecular speed (affected by temp and molar mass) Therefore, temp, conc., molar mass, and size of hole affects rate of effusion.

39. 39 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. Molecular Speeds; Diffusion and Effusion According to Graham’s law, the rate of effusion or diffusion is inversely proportional to the square root of its molecular mass. (for same container at constant T & P). Following relationship allows for comparison of gases:

40. 40 Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline. A Problem to Consider How much faster would H 2 gas effuse through an opening than methane, CH 4 ? So hydrogen effuses 2.8 times faster than CH 4 HW 49