Chapter 10 Gases

1. Chapter 10Gases

2. 10.1 Characteristics of Gases • Gases are a state of matter that, unlike liquids and solids, • Expand to fill their containers. • Are highly compressible. • Have extremely low densities. • Form homogeneous mixtures with each other regardless of their identities or relative proportions. • The characteristic properties of gases arise because individual gas particles (molecules or atoms) are, relatively speaking, very far apart from each other. • Gases can be individual atoms (such as noble gases), diatomic molecules, or individual molecules

3. 10.2 Pressure

4. Units of Pressure: 1 atm = 760 mm Hg = 760 torr = 1.01325 x 105 P = 101.325 kPa • The SI unit of pressure is the pascal (Pa) • mm Hg or torr • These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury. • Atmosphere (atm) • 1.00 atm = 760 torr

5. Manometer A device used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

6. Standard Pressure • Normal atmospheric pressure at sea level. • It is equal to • 1.00 atm • 760 torr (760 mm Hg) • 101.325 kPa

7. 10.3 The Gas Laws • Boyle’s Law: Pressure-volume relationship • The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

8. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k As P and V are inversely proportional -- A plot of V versus P results in a curve. http://www.itstactical.com/wp-content/uploads/2010/03/Boyles_Law_animated.gif

9. V T = k i.e., Charles’s Law: Temperature-Volume relationship • The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. A plot of V versus T will be a straight line. http://www.sgibson.k12.in.us/gshs_new/kd_chemistry/Charles_law.gif

10. Avogadro’s Law: Quantity-Volume relationship • The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. • Mathematically, this means V = kn • Law of Combining Volumes (1808): at a given temperature and pressure, the volumes of gases that react with each other are in the ratio of whole numbers.

11. Combining these, we get nT P V 10.4 Ideal-Gas Equation • So far we’ve seen that V 1/P (Boyle’s law) VT (Charles’s law) Vn (Avogadro’s law)

12. The proportionality constant is known as R, the ideal-gas constant:

13. nRT P nT P V V= The relationship then becomes or PV = nRT

14. The ideal-gas equation can be used to derive relationships between any two gas variables.

15. n V P RT = 10.5 Applications of the Idel Gas Equation • Gas Densities • If we divide both sides of the ideal-gas equation by V and by RT, we get

16. m V P RT = • We know that moles  molecular mass = mass n  = m • So multiplying both sides by the molecular mass ( ) gives

17. m V P RT d = = • Mass  volume = density • So, • Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

18. P RT dRT P d =  = • Molar Mass • We can manipulate the density equation to enable us to find the molecular mass of a gas: Becomes

19. 10.6 Dalton’s Law of Partial Pressures • The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. • In other words, Ptotal = P1 + P2 + P3 + …

20. To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure. • See App B for water vapor pressure at various temperatures. Ptotal = Pgas + PH2O • When one collects a gas over water, there is water vapor mixed in with the gas.

21. 10.7 Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

22. Main Tenets of Kinetic-Molecular Theory • Gases consist of large numbers of molecules that are in continuous, random motion. • The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. • Attractive and repulsive forces between gas molecules are negligible. • Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

23. The average kinetic energy of the molecules is proportional to the absolute temperature.

24. 10.8 Effusion and Diffusion http://chem.libretexts.org/@api/deki/files/8708/SLOWEDEFFUSION.gif?size=bestfit&width=360&height=267&revision=1

25. Diffusion: • The spread of one substance throughout a space or throughout a second substance. • The ratio of rates of diffusion of two gases is approximated by Graham’s law. • Speeds of molecules at room temp are very high. For example, the speed of N2 at room temp is 525 m/s, or about 1150 mi/hr. • Because of molecular collisions, the direction of motion of a gas molecule is constantly changing. (Fig 10.22) • The average distance traveled by by a molecule between collisions is called the mean free path of the molecule. • The mean free path varies with the pressure. • The mean free path for air molecules at sea level is about 60 nm (6 x 10-8 m). At 100 km, the mean free path is about 10 cm.

27. 10.9 Real Gases: Deviations from Ideal Behavior • In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

28. The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.

29. The corrected ideal-gas equation is known as the van der Waals equation. • Corrections must be made for the finite volume occupied by the gas molecules and for attractive forces between the gas molecules. See [10.26] • The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.

30. (P + ) (V−nb) = nRT n2a V2 The van der Waals Equation

31. Van der Waals Constants for gas Molecules