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Published byMarsha Francis Modified over 9 years ago
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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!
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Measuring Pressure Barometer Manometer
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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
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Ideal Gas Law Avogadro’s Principle The Ideal Gas Equation PV = nRT
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” = L•atm/mole•K memorize! {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 L/mol)
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Example Problems Now use ideal gas law to find volume of C2H2:
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:
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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 = torr at 50 °C, Pwater = torr
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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 torr Pgas = 732 torr (732 torr) x (1 atm/760 torr) x (0.310 L) n = = mol N2 ( L atm/mol K) x (288 K) mass N2 = ( mol N2) x ( g N2/mol N2) = g N2
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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
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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 = J/mol∙K = L∙atm/mol∙K urms = 3RT M
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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 rateB = MB MA
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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 P + a (V – nb) = nRT n V
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Sample Problems Hydrogen gas is produced when metals such as aluminum are treated with acids. Calculate the volume (in mL) of 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?
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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.
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