Expand to fill their containers, are highly compressible, have extremely low densities.
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1 Chem150 week6 Handout 1 Gases Characteristics of Gases: Unlike liquids and solids, they Expand to fill their containers, are highly compressible, have extremely low densities. Pressure is the amount of force applied to an area. p = F A Atmospheric pressure is the weight of air per unit of area (Torricelli and Otto von Goerike ). Units of Pressure Pascal 1 Pa = 1 N/m 2 Bar 1 bar = 10 5 Pa = 100 kpa mm Hg or torr, the difference in the heights in mm (h) of two connected columns of mercury. Atmosphere PSI 1.00 atm = 760 torr 1 atm = psi Standard pressure: Normal atmospheric pressure at sea level it is equal to Review of basic Gas Laws: 1.00 atm = 760 torr (760 mm Hg) = kpa Boyle s Law: (Divers law) The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure pv = k
2 Charles s Law: (hot air balloon) The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. V T = constant Gay-Lussac s Law: (pressure cooker) At constant volume, the pressure exerted by a gas is directly proportional to the Kelvin temperature: Avogadro s Law: (Stoichiometry) The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. V = kn One volume of hydrogen + one volume of chlorine gives two volumina of hydrogen chloride: H 2 +Cl 2 2HCl but Avogadro concluded that equal volumina of different gasses must contain the same number of molecules. This molar volume at STP has been found to be V mol = 22.4 l/mol What is the volume of 0.05 mole carbon dioxide at standard temperature and standard pressure (STP)? How many moles of nitrogen are in 1 L of it at STP? What is the volume of 7.14 g of oxygen at STP?
3 Ideal-Gas law: So far we ve seen that the Volume of a gas is: V 1/P (Boyle s law) V T (Charles s law) V n (Avogadro s law) Combining these, we get the ideal gas law: PV = nrt (where R = kpa L/mol K) R is the universal gas constant. Class Exercise: Calculate the volume of sulfur dioxide gas that was released in to the fume hood in the reaction of 1.20 g of sulfur with 1.00 g of copper after the gas had cooled to 25 C. The pressure in the lab at the day of the experiment was kpa. If n does not change (as in the rising balloon (example below) we can compare pressure, volume and temperature of a gas at an initial state ( 1 ) to pressure, volume and temperature of the same gas at a final state ( 2 ) according to: p₁v₁ = p₂v₂ T₁ T₂ Exercise: A weather balloon is filled on site with hydrogen using 200 g calcium hydride and excess water. (Calcium hydroxide is the other product produced) Calculate the volume of the balloon before takeoff (99,5 kpa and 11 C) and after takeoff at an altitude of 3000 m where the pressure is 80.5 kpa and the temperature is -30 C
4 Daltons Law of Partial Pressures The ideal gas law can be applied to pure gases as well as gas mixtures. It treats a litre of hydrogen gas the same as a litre of air (because it has the same number of gas particles in it even though they are different in nature) For stoichiometric problems it is however important to know the pressure of a certain gas in a mixture of gases e.g. How much oxygen is available for combustion when using air? In a mixture of gases each component exerts it s own pressure (its partial pressure) independent of the other components of the mixture The total pressure of the mixture is the sum of the partial pressures of the components Dalton s law: p total = p 1 + p 2 + p Example: A 10 L vessel is filled with 2 mol of argon and 8 mol oxygen at 20 C. What is the total pressure of the gas mixture and what are the partial pressures of argon and oxygen? Kinetic-Molecular Theory 1. Gases consist of large numbers of molecules that are in continuous, random motion. 2. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. 3. Attractive and repulsive forces between gas molecules are negligible. 4. Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. 5. The average kinetic energy of the molecules is proportional to the absolute temperature. Molecular Effusion and Diffusion Effusion Diffusion The escape of gas molecules through a tiny hole into an evacuated space. The spread of one substance throughout a space or throughout a second substance.
5 Effusion (source, Brown LeMay) Real gases: In the real world, the behaviour of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure. Brown LeMay The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature. The ideal-gas equation can be adjusted to take these deviations from ideal behaviour into account.
6 The corrected ideal-gas equation is known as the van der Waals equation. ( n²a )(V nb) = nrt V² The a term takes intermolecular interactions in to account and the b term recognizes the volume of the gas molecules on their own. Note that for an ideal gas a and b approach zero and the van der Waals equation turns in to the ideal gas equation. Consider a sample of 1.00 mol of CO 2 confined to a volume of 3.00L at 273 K. Calculate the pressure of the gas using a) the ideal gas equation and b) the van der Waals equation. a = 364 L 2 kpa/mol 2 b = L/mol Joule-Thomson Effect: most real gasses cool when they expand (BBQ effect) A) Gas at T i and p i B) gas passes through a porous membrane without doing work C) gas has expanded (T f and p f )
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