Properties of Gases

1. Properties of Gases Important properties of a Gas Quantity n = moles Volume V = container size (usually L or mL) Temperature T ≈ average kinetic energy of molecules (must be in K for all “gas laws”) Pressure P = force/area Units of pressure: SI unit is the pascal (Pa) • 1 atm = 101,325 Pa (not commonly used) = 14.7 psi More important: 1 mm Hg = 1 torr 1 atm = 760 torr = 760 mm Hg Exact!

2. Measuring Pressure Barometer Manometer

3. Pressure - Volume - Temperature Relationships • Boyle’s Law (at constant T and n) V ∝ 1/P or PV = constant • Charles’ Law (at constant P and n) V ∝ T or V/T = constant • Gay-Lussac’s Law (at constant V and n) P ∝ T or P/T = constant • Combined Gas Law (for constant n) PV/T = constant or (remember that T must be in units of K -- practice problems in book!) P1V1 P2V2 = T1 T2

4. Ideal Gas Law • Avogadro’s Principle • At constant P and T, V ∝ n • i.e. at constant T and P, equal volumes of gases contain equal numbers of moles • The Ideal Gas Equation PV = nRT where R = “universal gas constant” = 0.0821 L•atm/mole•Kmemorize! {useful in many different kinds of calculations involving gases!} • Standard Molar Volume • At Standard Temperature and Pressure (0 °C and 1 atm), 1 mole of any gas occupies 22.4 L (i.e. 22.4 L/mol)

5. Example Problems • At STP, the density of a certain gas is 4.29 g/L. What is the molecular mass of the gas? (4.29 g/L) x (22.4 L/mol) = 96.1 g/mol • Acetylene (welding gas), C2H2, is produced by hydrolysis of calcium carbide. CaC2(s) + 2 H2O --> Ca(OH)2(s) + C2H2(g) Starting with 50.0 g of CaC2, what is the theoretical yield of acetylene in liters, collected at 24 °C and a pressure of 745 torr? 1st find yield in moles: Now use ideal gas law to find volume of C2H2:

6. Dalton’s Law of Partial Pressures • For a mixture of gases: Ptotal = Pa + Pb + Pc + … • Mole fraction: Xa = moles a/total moles = Pa/Ptotal • Gases are often prepared and collected over water: Ptotal = Pgas + Pwater where Pwater = vapor pressure of water (depends on temperature) e.g. at 25 °C, Pwater = 23.8 torr at 50 °C, Pwater = 92.5 torr

7. Example Problem A sample of N2 gas was prepared and collected over water at 15 °C. The total pressure of the gas was 745 torr in a volume of 310 mL. Calculate the mass of N2 in grams. (vapor pressure of water at 15 °C = 12.8 torr) Answer: Ptotal = Pgas + Pwater 745 torr = Pgas + 12.8 torr Pgas = 732 torr (732 torr) x (1 atm/760 torr) x (0.310 L) = 0.012624 mol N2 n = (0.0821 L atm/mol K) x (288 K) mass N2 = (0.012624 mol N2) x (28.014 g N2/mol N2) = 0.354 g N2

8. Kinetic Theory of Gases -- READ BOOK Basic Postulate -- A gas consists of a very large number of very small particles, in constant random motion, that undergo perfectly elastic collisions with each other and the container walls. There is a distribution of kinetic energies of the particles. Temp ∝ average KE The kinetic theory “explains” the gas laws, pressure, etc. based on motion and kinetic energy of gas molecules. e.g. Boyle’s Law (P = 1/V) ~ at constant Temp (same average KE) If volume of container is reduced, there are more gas particles per unit volume, thus, more collisions with the container walls per unit area.  higher pressure

9. Temperature & Molecular Velocities • Kinetic molecular theory states that all particles have the same average kinetic energy at a given temperature. KE = ½mv2 • If m is smaller, v is bigger! i.e. small particles move faster. Quantitatively, where urms = root mean square velocity (a kind of average), M = formula mass (in kg/mol!), and R = universal gas constant, but in J/mol∙K rather than L∙atm/mol∙K! R = 8.314 J/mol∙K = 0.0821 L∙atm/mol∙K urms = 3RT M

10. Graham’s Law of Effusion • diffusion “mixing” of gases throughout a given volume • effusion “leaking” of a gas through a small opening • mean free path average distance between collisions Graham’s Law: effusion rate ∝ 1/√ M where M = formula mass So, effusion rates of two gases can be compared as a proportion: e.g. He (FM = 4.0 g/mol) effuses 2 times faster than CH4 (FM = 16.0) rateA MB = MA rateB

11. Real Gases -- Deviations from Ideal Gas Law For real gases, small corrections can be made to account for: • Actual volume of the gas particles themselves, and • intermolecular attractive forces One common approach is to use the Van der Waals’ Equation: Don’t memorize! where a and b are empirical parameters that are dependent on the specific gas (e.g. Table 5.5) a ≈ intermolecular attractive forces b ≈ molecular size 2 n P + a (V – nb) = nRT V

12. Sample Problems Hydrogen gas is produced when metals such as aluminum are treated with acids. Calculate the volume (in mL) of 0.500 M HCl solution that is required to produce a total gas pressure of 725 torr in a 2.50-L vessel if the hydrogen gas (H2) is collected over water at 25 °C. (The vapor pressure of water at 25 °C is 24 torr.) 2 Al(s) + 6 HCl(aq) --> 2 AlCl3(s) + 3 H2(g) A gas mixture contains 25.0 g of CH4, 15.0 g of CO and 10.0 g of H2. If the total pressure of the mixture is 1.00 atm, what is the partial pressure of CH4 in torr?

13. Chemistry in the Atmosphere • Air Pollutants • SOx • e.g 2 SO2(g) + O2(g) + 2 H2O(g) 2 H2SO4(aq)acid rain • NOx • e.g. 4 NO2(g) + O2(g) + 2 H2O(g) 4 HNO3(aq)acid rain • O3 (ozone) • CO • solid particles • Ozone Layer • Stratospheric ozone ≠ ground-level ozone • CFC’s produce Cl, and • O3(g) + UV light  O2(g) + O(g) • Cl(g) + O3(g) ClO(g) + O2(g) • ClO(g) + O(g)  Cl(g) + O2(g) • Freons are being replaced by other less harmful refrigerants.