Chapter 5: Gases

1. Chapter 5: Gases Pressure KMT Gas Laws Effusion and Diffusion Stoichiometry Real Gases Gas Mixtures

2. Properties of a Gas • State of Matter • Compressible since molecules are far apart. • Takes the shape and volume of container. • Forms homogeneous mixtures with other gases. • Pressure is a gas property which tells us about the amount of gas present.

3. PRESSURE • Pressure = Force/Area • Devices to measure pressure: manometer and barometer • Pressure Units (see p 181) • pascal = N/m2 = kg/(m s2) SI derived unit • 1 mm Hg = 1 torr • 1 std atm = 1 atm = 760 torr = 760 mm Hg = 1.01325E+05 Pa = @100kPa

4. GAS LAWS • These are empirical laws (based on expts rather than derived from theory) that define mathematical relationships between any two gas properties (P, V, T, n). • For example: If T and n are held constant, what happens to V if you increase P? • V will decreases: Boyle’s Law relates V vs P: V α 1/P or PV = k at constant n and T (Fig 5.5, 5.6).

5. Figure 5.15 Increased Pressure due to Decreased Volume

6. Figure 5.5 a&b Plotting Boyle's Data (Table 5.1)

7. GAS LAWS (2) • If P and n are held constant, what happens to V if you increase T? • V will increase: Charles’ Law relates V vs T (K): V α T or V/T = b at constant n and P (Fig 5.8, 5.9). • If P and T are held constant, what happens to V if n increases? • V will increase: Avogadro’s Law relates V vs n: V α n or V/n = a at constant P and T.

8. Figure 5.17 The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure

9. Figure 5.9 Plots of V versus T (Charles’ Law)

10. Figure 5.18 Increased Volume due to Increased Moles of Gas at Constant Temperature and Pressure

11. IDEAL GAS LAW PV = nRT • Combine Boyle, Charles and Avogadro’s Laws • Equation of state for ideal gas; hypothetical state • Note universality of equation; I.e. identity of the gas is not needed. • Limiting law (in the limit of high T and low P~1 atm); this means that as T increases and P decreases, real gases start to behave ideally.

12. IDEAL GAS LAW • R = Universal Gas Constant = PV/nT • 0.0821 (L-atm)/(mol-K) = 8.3145 J/(mol-K) • Note units of P = atm, V = L, T = K, n = #mol • STP = Standard Temperature and Pressure means 1 atm AND 273.15 K • Molar volume of a gas = Volume of one mole of gas at STP = 22.42 L (see T5.2)

13. OTHER • Use P, T and d to find molar mass (M) of gas. • Start with IGL: PV = nRT divide by VRT to get • n/V = P/RT then multiply by M to get • n (M)/V = d = MP/RT or M = dRT/P • Eqn 5.1

14. Problems • 19, 21, 34, 36, 42, 56, 62

15. STOICHIOMETRY of GAS PHASE REACTIONS • Use IGL to find # mol gas in stoichiometric problems • Law of Combining Volumes (Gay-Lussac) • Problems: 54, 58

16. MIXTURES of IDEAL GASES • DALTON’S LAW • Law of Partial Pressures • PTOTAL = P = ∑ Pi at constant T and V • Pi = niRT/V = partial pressure of a gas • xi = mole fraction = ni/nTOTAL = Pi/PTOTAL

17. Fig 5.12 The Partial Pressure of each Gas in a Gas Mixture in a Container Depends on n = #mol of that Gas

18. MIXTURES of IDEAL GASES • COLLECTING GASES OVER WATER • PTOTAL = P = Pg + Pw

19. Fig 5.13 The Production of O2 by Thermal Decomposition of KCIO3

20. Problems • 67, 72, 76

21. KINETIC MOLECULAR THEORY OF GASES (1) • Gas molecules are far apart form each other and their volumes are • They move constantly, rapidly and randomly in all directions and at various speeds. • There are no intermolecular forces between gas molecules except when they collide. Collisions are elastic.

22. Figure 5.19 Collisions with Walls and other Particles Cause Changes in Movement

23. Figure 5.20 A Plot of the Relative Number of O2 Molecules that Have a Given Velocity at STP

24. KINETIC MOLECULAR THEORY (2) • MEASURED PRESSURE OF A GAS IS DUE TO COLLISIONS WITH WALL. • COLLISIONS ARE ELASTIC. • THE AVERAGE KINETIC ENERGY OF A MOLECULE IS PROPORTIONAL TO T (K). • EXPLAINS MACROSCOPIC PROPERTIES LIKE P, T, V, v AND EMPIRICAL GAS LAWS.

25. KINETIC MOLECULAR THEORY (QUANT.) • Average kinetic energy = [(3/2) RT] α T • KE depends on T only • i.e. KE does not depend on identity of gas (M) • Root mean square velocity • urms = √(3RT/M) where R = 8.314 J/(K-mol) • As T increases, urms [dec, stays the same, inc] • As M increases, urms [dec, stays the same, inc]

26. Figure 5.21 A Plot of the Relative Number of N2 Molecules that Have a Given Velocity at 3 Temperatures

27. Figure 5.23 Relative Molecular Speed Distribution of H2 and UF6

28. EFFUSION AND DIFFUSION • Diffusion: Mixing of gases • Diffusion rate is a measure of gas mixing rate • Diffusion distance traveled α (1/√M) • Effusion • Passage of gas through orifice into a vacuum • Graham’s Law describes • Effusion rate α urms α(1/√M) α (1/T) • or Effusion time αM α (1/T)

29. Figure 5.22 The Effusion of a Gas Into an Evacuated Chamber

30. Problems • 78, 80, 82, 88

31. REAL GASES • IDEAL: PV= nRT • van der Waals Eqn of State • PeffVeff = P’V’ = (Pobs + n2a/V2) (Vobs - nb) = nRT • 1st term corrects for non-zero attractive intermolecular forces • 2nd term corrects for non-zero molecular size • a and b values depend on the gas’s identity – loss of universality in gas law

32. KMT OF GASES (1-revisited) • GAS MOLECULES are FAR APART FROM EACH OTHER and THEIR VOLUMES ARE NOTNEGLIGIBLE. (b ≠ 0) • THEY MOVE CONSTANTLY, RAPIDLY and RAMDONLY IN ALL DIRECTIONS AND AT VARIOUS SPEEDS. • THERE ARE (NO) INTERMOLECULAR FORCES EXCEPT FOR COLLISIONS. (a ≠ 0)

33. Figure 5.25 Plots of PV/nRT versus P for Several Gases (200K)

34. Table 5.3 Values of the van der Waals Constants for Some Common Gases