1. GASES Pressure Gas Laws (Boyle, Charles, Avogadro) Stoichiometry Gas Mixtures (Dalton) Kinetic Molecular Theory of Gases Effusion and Diffusion Real Gases

2. 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 –pascal = N/m 2 = kg/(m s 2 ) 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 that present mathematical relationships between properites of gases (P, V, T, n) based on expt observations rather than derived from a theory of gases. Boyle’s Law relates V vs P: V α 1/P or PV = k at constant n and T (Fig 5.5, 5.6). Charles’ Law relates V vs T (K): V α T or V/T = b at constant n and P (Fig 5.8, 5.9). Avogadro’s Law relates V vs n: V α n or V/n = a at constant P and T.

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

6. Figure 5.9 Plots of V versus T as Before, Except Here the Kelvin Scale is Used for Temperature 1

7. GAS LAWS (2) IDEAL GAS LAW (IGL)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 unknown –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.

8. OTHER R = Universal Gas Constant = 0.0821 (L- atm)/(mol-K) = 8.3145 J/(mol-K) –Note units of P – atm, V – L, T – K, n = 3mol STP 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)

9. STOICHIOMETRY of GAS PHASE REACTIONS Use gas laws in stoichiometric problems Law of Combining Volumes (Gay-Lussac) Use the gas laws to find molar mass: –Use V, P, T and IGL to find n = #mol; then apply stoich unit from Ch. 3. –Use n and m to find molar mass, M = m/n –Use P, T and density of gas, d, to find M because M = dRT/PEqn 5.1

10. MIXTURES of IDEAL GASES DALTON’S LAW –Law of Partial Pressures –P TOTAL = P = ∑ P i at constant T and V –P i = n i RT/V = partial pressure of a gas –x i = mole fraction = n i /n TOTAL = P i /P TOTAL

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

12. MIXTURES of IDEAL GASES COLLECTING GASES OVER WATER –P TOTAL = P = P g + P w

13. Fig 5.13 The Production of O 2 by Thermal Decomposition of KCIO 3

14. KINETIC MOLECULAR THEORY OF GASES (1) GAS MOLECULES are FAR APART FROM EACH OTHER and THEIR VOLUMES ARE NEGLIGIBLE. THEY MOVE CONSTANTLY, RAPIDLY and RAMDONLY IN ALL DIRECTIONS AND AT VARIOUS SPEEDS. THERE ARE NO INTERMOLECULAR FORCES EXCEPT FOR COLLISIONS.

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

16. 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.

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

18. Figure 5.21 A Plot of the Relative Number of N 2 Molecules that Have a Given Velocity at 3 Temperatures

19. Figure 5.23 Relative Molecular Speed Distribution of H 2 and UF 6

20. 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 u rms α (1/ √ M) α (1/T) –or Effusion time α M α (1/T)

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

22. REAL GASES IDEAL: PV= nRT van der Waals Eqn of State –P eff V eff = P’V’ = (P obs + n 2 a/V 2 ) (V obs - 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

23. KMT OF GASES (1-revisited) GAS MOLECULES are FAR APART FROM EACH OTHER and THEIR VOLUMES ARE NOT NEGLIGIBLE. (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)

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

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