2. The Gaseous State of Matter Preparation for College Chemistry Columbia University Department of Chemistry

3. Chapter Outline KMT Gas Laws Ideal Gas Equation Gas Stoichiometry Air Pollution

4. Preliminary Observations Molar mass of water: 18g /mole 6.02x10 23 molecules weigh 18g Density of water: 1g/cc 18 g liquid water occupies 18mL 18 g gaseous water occupies 22,400mL

5. Kinetic Molecular Theory of Gases KE = 1 2 mc = 2 p = m c p 2m 2 v=+10cm/s c=10cm/s Wall -x+x { v=-10cm/s c=10cm/s

6. Kinetic Molecular Theory of Gases

7. 0600100014001800200 0.4 0.6 0.8 1.0 1.2 1.4 Molecular Speed # Molecules O 2 at 1000°C O 2 at 25°C Distribution of Molecular Speeds

8. Graham’s Law of Effusion At the same T and P, the rates of Effusion of two gases are inversely proportional to their densities or molar masses.

9. Vacuum Gas Naturally occurring Uranium : U-235 / U238 = 1 / 140 2nd step: Effusion through thousands of membranes (cascades) 1st step: U + 6 F 235 UF 6 238 UF 6 (g) 3rd step: 235 UF 6 235 U Fully enriched weapons-grade Uranium

10. State Variables V = volume (liters, cm 3, m 3 ) T = temperature (in K) P = pressure (atmospheres, mmHg, kPa)

11. 101.325 mbar 29.9 in. Hg 14.7 lb/in 2 (PSI) 76 cmHg 760 mmHg 760 torr 1 atm Torricelli’s barometer At sea level

12. Atmospheric Pressure 150 km Hg height air

13. 01357 Pressure (atm) 9 1 2 3 4 5 6 Volume (L) 0 7 Boyle’s Law P x V = k At Constant T For an Ideal Gas P 1 x V 1 = P 2 x V 2 P1P1 V2V2 P2P2 V1V1 =

14. 1 2 3 4 5 6 Volume (L) 0 7 -300 T (°C) -100100300500 Charles’ Law At Constant P for an Ideal Gas V = kT V1V1 T1T1 V2V2 T2T2 = V  T -273°C Absolute zero

15. 0 1 2 3 4 5 6 Pressure (atm) 7 -300 T (°C) -100100300500 P = kT P1P1 T1T1 P2P2 T2T2 = Gay-Lussac’s Law At Constant V for an Ideal Gas P  T

16. Combined Gas Laws V1V1 T1T1 V2V2 T2T2 = P 2 V 2 T2T2 = P 1 V 1 T1T1 Charles’Boyle’s V 1 P 1 T 2 P 2 T 1 = V2V2 P 1 V 1 = P 2 V 2

17. STP Conditions Standard Temperature: 273.15 K= 0.00°C Standard Pressure: 1 atm Reference Points for T and P for comparison

18. Dalton’s Law of Partial Pressures P tot = P 1 + P 2 + P 3 +... where P 1 is the partial pressure of gas 1, etc... P gas = P total – P H 2 O where P H 2 O is the vapor pressure of water at the specified temperature. Most often used in collection of insoluble gases over water. In open systems, P total = P atm PnPn =XnXn P total XnXn = n n1n1 + n2n2 + n3n3 +... Molar fraction of gas n

19. Gay-Lussac’s Law of combining volumes Avogadro’s Law 18091811 “When measured at the same T and P, the ratios of the V of reacting gases are small whole numbers” “Equal volumes of different gases at the same T and P contain the same number of molecules”

20. Consequences of Avogadro’s Law 1. Explanation of Gay-Lussac’s combining volumes law. Diatomic nature of elemental gases. 2. Method for determining molar masses of gases. The molar Volume. 3. Firm foundation of KMT: gases consists of microscopic particles

21. Density of Gases d V = m But V = f (P, T) GasM(g/mol) d(g/L) STP Gas M(g/mol) STP d(g/L) H2H2 CH 4 NH 3 C 2 H 2 HCN CO N2N2 air H2SH2S HCl F2F2 CO 2 C 3 H 8 O3O3 SO 2 Cl 2 2.016 ) 16.04 17.03 26.04 27.03 28.01 28.02 28.9 32.001.43 70.90 3.17 2.86 2.14 1.97 1.96 1.70 1.63 1.5234.09 36.46 38.00 44.01 44.09 48.00 64.071.25 1.21 1.16 0.760 0.716 0.900 1.29 O2O2

22. 1 P  V Ideal Gas Equation T  V For one mole of a gas at STP, R constant: (1 atm)(22.4L) 273K = R =0.082 L-atm mol-K n  V nT P = VR P  V = R T P V m M = n R T P V = R T M m PV = PM d RT Equation of State

23. Ideal Gas Equation [pressure][Volume] [temperature][mol] = [R] = [force][volume] [area][temperature][mol] = [force][length] [temperature][mol] = [energy] [temperature][mol] R = 8.134 J mol -1 K -1 ~ 2 Cal mol -1 K -1 The ideal gas constant has energy/mol degrees dimensions [R]

24. Gas Stoichiometry Cu(s) + 4H + + 2NO 3 - (aq) Cu +2 (aq) + 2NO 2 (aq) + 2H 2 O Concentrated nitric acid acts on copper and produces nitrogen dioxide and dissolved copper. 6.80 g Cu is consumed and NO 2 is collected at a pressure of.970atm and a temperature of 45°C (318 K). Calculate the volume of NO 2 produced. 63.55 g Cu 1 mol Cu x6.80 g Cux 1 mol Cu 2 mol NO 2 =0.214 mol NO 2 n R T P = V = 5.76 L NO 2NO 2 http://www.sp.uconn.edu/~terry/229sp98/Ncycleanim.html

25. Real Gases Follow the ideal gas law at sufficiently low densities o Gas molecules attract one another Both factors increase in importance when the molecules are close together (high P. low T). o Gas molecules occupy a finite volume n R T P V = z Deviations from ideality are quantified by the Compressibility factor z

26. Real Gases Intermolecular Forces 0 0.5 1.0 1.5 Compresibility ratio 2.0 0 P (atm) 200400600800 Ideal Gas H2H2 CH 4 N2N2

27. 0 0.5 1.0 1.5 Compresibility ratio 2.0 0 P (atm) 200400600800 Ideal Gas 600 °C -100 °C 25 °C Nitrogen at several T

28. Van der Waals Equation b = constant representing volume excluded per mole of molecules a = depends on the strength of attractive forces Proportional to reduction of wall collisions due to cluster formation.

29. Air Pollution O2O2 2O O2O2 O+ O3O3 O2O2 O+ O3O3 +heat CCl 3 F CCl 2 F + Cl. + O3O3 ClO. + O2O2 +OO2O2 +Cl. Allotropic Transformation Ozone shield Ozone destruction