Gases: Properties and Behaviour

1. Gases: Properties and Behaviour Gas Laws Partial Pressures Kinetic Theory and Ideal Gases Real Gases Diffusion and Effusion

2. Features of gases • Gases are always miscible • Gases are compressible • Gases exert pressure • Gases are mostly nothing: less than 0.1 % of the volume is occupied by molecules (contrast 70 % for solids and liquids) • The ideal gas law assumes molecules occupy zero percent

3. Molecular interactions • The strength of the interactions between molecules determines the state • Strong attractions make for high melting point ionic solids • Weaker interactions between molecules occur in liquids

4. Molecular interactions in gases are negligible • Gases are mostly empty space: molecules occupy <0.1 % volume • 1,000 times less dense than solids and liquids • Emptiness allows complete mixing

5. The Ideal gas • The ideal gas is defined as follows • Interactions between molecules are nonexistent • Volume occupied by molecules is zero

6. Collisions • There are two types of collision • Between the molecules and the container • Between molecules • In the ideal gas these collisions are perfectly elastic (no energy loss) Collisions between billiard balls mirrors the collisions between the molecules of an ideal gas

7. Origins of pressure • Pressure is force per unit area F/A • Force is mass x acceleration F = ma • Molecules colliding with the walls of the container exchange momentum

8. Origins of pressure • Pressure if force per unit area F/A • Force is mass x acceleration F = ma • Molecules colliding with the walls of the container exchange momentum

9. Units of pressure • The S.I. unit of pressure is the pascal (Pa) • 1 Pa = 1 N/m2, where N is the S.I. unit of force • 1 N = 1 kgm/s2 • The weight of the air exerts pressure – atmospheric pressure • This pressure is about 100,000 Pa

10. Older is better • 101 kPa is an inconvenient way of measuring pressure • Traditional units are still used in preference to the SI system • Atmospheres, cm (or mm) of Hg and torr are the most common

11. How do I measure the atmosphere? Let me count the ways

12. Standard temperature and pressure (STP) • Standard conditions allow direct comparison of properties of different substances • Standard temperature is 273 K (0ºC) • Standard pressure is 760 mm Hg • At STP, 1 mole of any ideal gas occupies 22.414 L

13. The barometer of pressure • The weight of the air supports an equal weight of mercury (or other liquid) • Mercury being dense, the column is only 76 cm compared to the height of the atmosphere • 76 cm (760 mm) Hg = 1 atm

14. Manometers measure pressure in a container • (a) If the pressure inside the bulb is less than atmospheric, the atmosphere pushes down more. • (b) If the pressure inside the bulb is above atmospheric, the column is pushed towards the open end.

15. Measuring pressure with a ruler • The pressure in the container is given by atmospheric pressure plus (minus) the difference in levels for pressures greater (lower) than atmospheric

16. Gas Laws • Physical properties of gases were among the first experiments performed in the “modern” scientific era, beginning in the 17th century • All gases exhibit similar physical properties even if their chemical properties differ widely • Properties can be summarized in a few simple laws • Variables are pressure, volume, temperature and quantity. Keep one (or two) constant and vary the others

17. The four variables • Pressure (P) • Volume (V) • Temperature (T in Kelvin) • Number of molecules (n in moles)

18. Variables and constants • In the elementary gas laws two of the four variables are kept constant • Each law describes how one variable reacts to changes in another variable • All the simple laws can be integrated into one combined gas law

19. Boyle’s law • The first experimental gas law • Pressure increases, volume decreases (T, n constant)

20. Mathematical form • The volume of a fixed amount of an ideal gas varies inversely with pressure at constant temperature • PV = constant • P α 1/V

21. Charles’ Law • Pressure and amount constant • As temperature increases, the volume increases

22. Mathematical form • The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressure V α T V/T = constant • NOTE: Temperature must be in Kelvin (ºC + 273) • At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero

23. Avogadro’s Law • Pressure and temperature constant • Increase the amount, the volume increases • Summary of gas laws

24. Mathematical form • The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressure • V α T • V/T = constant • NOTE: Temperature must be in Kelvin (ºC + 273) • At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero

25. Mathematical form • The volume of an ideal gas varies directly with its molar amount at constant T and P • V α n • V/n = constant • The same volume of any gas contains the same number of moles at constant T,P • The standard molar volume at 273 K and 1 atm is 22.414 L

26. Comparison with reality • The standard molar volume of 22.41 L can be compared with the experimental values of common real gases • Agreement shows that these ideal gas laws can be widely applied for real gases

27. Putting them together: the ideal gas law • P1V1/T1 = P2V2/T2 • PV = nRT • R is the gas constant = 0.0821 L-atm/mol-K • Note the units of R. This constant also appears in thermodynamic calculations, but with different units and numerical value (8.315 k/K-mol). Use the one appropriate to the calculation • Units of pressure – atm • Units of temperature – K • Units of volume – L • Standard temperature and pressure: T = 0 ºC and P = 1 atm

28. The combined gas law • Allows us to calculate change in one variable for changes in the three other variables

29. Applications • A system under an initial set of conditions represented by a changes to a new set of conditions b • If we know three of the conditions, the fourth can be obtained

30. The “simple” laws are derived from the combined law • For any change of conditions where a variable does not change its value, a = b • Example: if T and n are unchanged, • Boyle’s law is regenerated:

31. Getting some exercise • An exercise ball is at a pressure of 1000 mm Hg and has a volume of 60 L • When sat on, the volume is only 40 L. What is the new pressure? • Check: P increases as V decreases

32. Stoichiometry and gas reactions • Solids: mass and molar mass • Solutions: volume and molarity • Gases: volume and ideal gas law • Calculate volume of gas produced (product) or consumed (reactant) in a reaction at given conditions of P and T • Also can calculate molar mass or density of a gas using ideal gas law

33. Mixtures of gases: partial pressures • Dalton’s law states that, in a mixture of gases, each gas behaves independently of the others and exerts the same pressure that it would by itself • The total pressure exerted is the sum of the individual (partial) pressures of the components of the mixture • P = P1 + P2 + P3 +…

34. Mole fraction • The pressure exerted by component i = • Pi = ni(RT/V) • Where ni is the number of moles of i • The total pressure is then: • P(total) = (n1 + n2 + n3 + …)RT/V • The mole fraction is the ratio of the moles of component I to the total number of moles ntotal

35. Mole fraction and the ideal gas law • But n = PV/RT

36. Mole fractions and partial pressures • The partial pressure exerted by any gas is equal to the mole fraction x the total pressure • What is the partial pressure of each component if the total pressure is 600 mm Hg?

37. Visual summary of the gas laws