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##### The Gaseous State of Matter

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**The Gaseous Stateof Matter**Preparation for College Chemistry Columbia University Department of Chemistry**Chapter Outline**KMT Gas Laws Ideal Gas Equation Gas Stoichiometry Air Pollution**Preliminary Observations**Molar mass of water: 18g /mole 6.02x1023 molecules weigh 18g Density of water: 1g/cc 18 g liquid water occupies 18mL 18 g gaseous water occupies 22,400mL**Kinetic Molecular Theory of Gases**2 1 p 2 m c = p = m c KE = 2 2m v=+10cm/s -x +x { v=-10cm/s c=10cm/s c=10cm/s Wall**1.4**# Molecules 1.2 1.0 0.8 0.6 0.4 0 200 600 1000 1400 1800 Molecular Speed (ms-1) Distribution of Molecular SpeedsMaxwell-Boltzmann Distribution O2 at 25°C O2 at 1000°C**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.**(g)**235 238 235 UF UF UF 6 6 6 3rd step: 235 U Naturally occurring Uranium : U-235 / U238 = 1 / 140 1st step: U + 6 F 2nd step: Diffusion through thousands of membranes (cascades) Vacuum Gas Fully enriched weapons-grade Uranium**State Variables**V = volume (liters, cm3, m3) T = temperature (in K) P = pressure (atmospheres, mmHg, kPa)**Torricelli’s barometer**760 torr 760 mmHg 76 cmHg 101.325 mbar 29.9 in. Hg 14.7 lb/in2 (PSI) 1 atm At sea level**Atmospheric Pressure**150 km Hg height air**7**6 5 Pressure (atm) 4 3 2 1 0 9 0 1 3 5 7 Volume (L) Boyle’s Law At Constant TFor an Ideal Gas PV = C P1 V1 = P2 V2 P2 P1 = V1 V2 **7**6 5 Pressure (atm) 4 3 2 1 0 9 0 1 3 5 7 1/V (L-1) Boyle’s Law At Constant TFor an Ideal Gas**7**6 5 4 3 PV 2 1 0 9 0 1 3 5 7 P Boyle’s Law At Constant TFor an Ideal Gas**7**6 5 4 Volume (L) 3 2 1 0 -300 -100 100 300 500 T (°C) At Constant P for an Ideal Gas Charles’ Law V T Absolute zero -273°C**7**6 5 Pressure (atm) 4 3 2 1 0 -300 -100 100 300 500 T (°C) Gay-Lussac’s Law P2 P1 At Constant V for an Ideal Gas P T = T2 T1 P = CT**V2**V1 = T2 T1 P1 V1 P2 V2 = T1 T2 V1 P1 T2 V2 = P2 T1 Combined Gas Laws Charles’ Boyle’s P1V1 = P2 V2**STP Conditions**Reference Points for T and P for comparison Standard Temperature: 273.15 K= 0°C Standard Pressure: 1 atm**Dalton’s Law of Partial Pressures**Ptot = P1 + P2 + P3 + ... where P1 is the partial pressure of gas 1, etc... Pn = Xn Ptotal nn Molar fraction of gasn Xn = n1 n2 n3 + ... + + Pgas = Ptotal – PH2O (table 11.3 p. 387) where PH2O is the vapor pressure of water at the specified temperature. Most often used in collection of insoluble gases over water. In open systems,Ptotal = Patm**1809**1811 Gay-Lussac’s Law of combining volumes “When measured at the same T and P, the ratios of the V of reacting gases are small whole numbers” Avogadro’s Law “Equal volumes of different gases at the same T and P containthe same number of molecules”**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**m**d = V STP STP Gas Gas M(g/mol) M(g/mol) d(g/L) d(g/L) H2 H2S 2.016 0.900 34.09 1.52 CH4 HCl 16.04 0.716 36.46 1.63 17.03 NH3 F2 0.760 38.00 1.70 26.04 C2 H2 CO2 1.16 44.01 1.96 27.03 1.21 44.09 C3 H8 1.97 HCN 28.01 48.00 CO O3 1.25 2.14 N2 28.02 1.25 64.07 2.86 SO2 28.9 3.17 air 1.29 Cl2 70.90 O2 32.00 1.43 Density of Gases But V = f (P, T)**V**n nT 1 nT V V V R = V P V T n R T = P P P PM L-atm (1 atm)(22.4L) m R T = d m R T P V = = 0.082 RT M R = = PV M mol-K 273K Equation of State Ideal Gas Equation For one mole of a gas at STP, R constant:**[pressure][Volume]**= [temperature][mol] [energy] [force][length] = = [temperature][mol] [temperature][mol] [force][volume] = [area][temperature][mol] Ideal Gas Equation The ideal gas constant has energy/mol degrees dimensions [R] [R] R = 8.134 J mol-1 K-1 ~ 2 Cal mol -1 K-1**Cu(s) + 4H+ + 2NO3- (aq)Cu+2 (aq)+2NO2 (aq) + 2H2O**1 mol Cu 2 mol NO2 1 mol Cu 63.55 g Cu n R T = V P Gas Stoichiometry Concentrated nitric acid acts on copper and produces nitrogen dioxide and dissolved copper. 6.80 g Cu is consumed and NO2 is collected at a pressure of .970atm and a temperature of 45°C (318 K) . Calculate the volume of NO2 produced. 6.80 g Cu x x = 0.214 mol NO2 = 5.76 L NO2**P V**= z n R T Real Gases Follow the ideal gas law at sufficiently low densities • Gas molecules attract one another • Gas molecules occupy a finite volume Both factors increase in importance when the molecules are close together (high P. low T). Deviations from ideality are quantified by the Compressibility factor z**2.0**1.5 Compressibility factor 1.0 0.5 0 0 200 400 600 800 P (atm) Real Gases Intermolecular Forces N2 H2 Ideal Gas CH4**2.0**1.5 Compressibility factor 1.0 0.5 0 0 200 400 600 800 P (atm) Nitrogen at several T 25 °C 600 °C Ideal Gas -100 °C**Van der Waals Equation (1873)**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.**Air Pollution**Upper and Lower Atmosphere Ozone Sulfur Dioxide Nitrogen Oxides Green House Effect**Upper atmosphere Ozone**hn 2O O2 O3 Allotropic Transformation O2 + O hn Ozone shield + O + heat O3 O2 hn Ozone Layer Destruction CCl3F CCl2F . Cl . + Chain propagation + Cl . ClO . O2 O3 + ClO . + O O2 + Cl .**hn**NO2 NO + O O2 + O + M O3 SO2 + OH SO2OH SO2OH + O2 SO3 + OOH OOH O+ OH Tropospheric Chemistry Photochemical Smog < 3 ppm Ozone alert, M= N2 or O2 Radical Oxidation Acid Rain Precursor**http://news6.thdo.bbc.co.uk/hi/english/special_report/1997/sci/tech/global_warming/newsid_33000/33557.stm**http://news6.thdo.bbc.co.uk/hi/english/special_report/1997/sci/tech/global_warming/newsid_33000/33557.stm