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13.2 Using Gas Laws to Solve Problems QuickTime™ and a decompressor are neede d to se e this picture. http://www.phy.cuhk.edu.hk/contextual/heat/tep/trans/kinetic_theory.gif Today… We are going to learn about: the ideal gas law partial pressure molar volume http://chemwiki.ucdavis.edu/@api/deki/files/4262/=SLOWEDEFFUSION.gif The Ideal Gas Law • Boyle’s Law V = k (at constant T and n) P • Charles’s Law V = bT (at constant P and n) • Avogadro’s Law V = an (at constant T and P) We can combine these equations to get The Ideal Gas Law R = the universal gas constant= 0.08206 L atm mol K Rearrange to get the Ideal Gas Law: PV = nRT PV = nRT The ideal gas law involves all the important characteristics of a gas: P - Pressure (in atm) V - Volume (in L) n - number of moles T - Temperature (in K) http://chemwiki.ucdavis.edu/@api/deki/files/4260/=WOOORRRKKKKK.gif PV = nRT Knowing any three of these properties is describe the enough to completely an d a QuickTime™ the gas. conditions ofdecompressor are need ed to see this p icture. The fourth property can be derived. Setbacks to Ideal Gas Law A gas that obeys this equation is said to behave ideally. However, in actuality, no gas is truly ideal. Ideal Gas- A hypothetical gas that exactly obeys the ideal gas law. Why do we use it? Most gases closely obey the ideal gas law at pressures of approximately 1 atm or lower, when the temperature is approximately 0oC or higher. http://chemistry.boisestate.edu/people/richardbanks/inorganic/chemistry/gas_animation.gif Using the Ideal Gas Law A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. Using the Ideal Gas Law A 2.50 mol sample of nitrogen gas has a volume of 5.50 L at a temperature of 27oC. Calculate the pressure of the nitrogen gas. Using the Ideal Gas Law What volume is occupied by 0.250 mol of carbon dioxide gas a 25oC and 371 torr? Ideal Gas and Changing Conditions Suppose we have a 0.240-mol sample of ammonia gas at 25oC with a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at 25oC. Find the final pressure. Ideal Gas and Changing Conditions A sample of methane gas that has a volume of 3.8 L at 5oC is heated to 86oC at constant pressure. Calculate its new volume. Using the Ideal Gas Law The idea behind these exercises is to use the ideal gas law for all types of gas law problems. We don’t have to ask, “Is this a Boyle’s Law problem or a Charles’s Law problem?” http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/atoms_quantum/kinetic%20gas%20animation.gif Dalton’s Law of Partial Pressures We just learned about the different properties of gases: pressure, volume, moles and temperature. But we’ve only been concerned about non-mixtures of gases. What happens if we mix different gases together? http://www.nhn.ou.edu/~jeffery/course/c_energy/energyl/lec004/gas_001_kinetics.gif Dalton’s Law of Partial Pressures Many important gases contain a mixture of components. Air = 78% N2, 21% O2, 0.93% Ar… Gaseous mixtures show that each QuickTime™ an d a decompressor are need ed to see independently of component behaves this p icture . the others. In other words, a given amount of oxygen exerts the same pressure in a 1.0-L container whether it is alone or in the presence of nitrogen or a different gas. http://www.chemistryland.com/CHM107/AirWeBreathe/Comp/AirAtomsMolecules.jpg Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. Ptotal = P1 + P2 + P3… The partial pressure of a gas is the pressure that a gas would exert if it were alone in the container. Each gas is responsible for only a part of the pressure. Dalton’s Law of Partial Pressures Same container = same volume and temperature P1=n1RT/V P2=n2RT/V P3=n3RT/V Ptotal = n1RT/V + n2RT/V… = (n1 + n2 …) (RT/V) QuickTime™ and a decompressor are neede d to see this picture. = ntotal (RT/V) https://reich-chemistry.wikispaces.com/file/view/P3.JPG/34106723/P3.JPG Practice with Partial Pressure Mixtures of helium and oxygen are used in the “air” tanks of underwater divers for deep dives. For a particular dive, 12 L of O2 at 25oC and 1.0 atm and 46 L of He at 25oC and 1.0 atm were pumped into a 5.0-L tank. Calculate the partial pressure of each gas and the total pressure in the tank at 25oC. Practice with Partial Pressure A 2.0-L flask contains a mixture of nitrogen gas and oxygen gas at 25oC. The total pressure of the gaseous mixture is 0.91 atm, and the mixture is known to contain 0.050 mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present. Gas Stoichiometry So far, we have seen how useful the ideal gas equation is. It is useful for finding the number of moles of gas involved. QuickTime™ and a This fact makes it possible to do decompressor are neede d to see this picture. stoichiometric calculations for reactions involving gas. http://staff.um.edu.mt/jgri1/teaching/che2372/notes/10/10_16.gif Practice Calculate the volume of oxygen gas produced at 1.00 atm and 25oC by the complete decomposition of 10.5 g of potassium chlorate. The balanced equation for the reaction is: 2KClO3 2KCl + 3O2 Molar Volume It is useful to define the volume occupied by 1 mol of a gas under certain conditions. 1 mol of an ideal gas at 0oC (273 K) and 1 atm, has a volume of 22.4aL. QuickTime™ and decompressor Standard Temperature and Pressure (STP): 0oC are neede d to se e this picture. and 1 atm Molar Volume of an ideal gas is 22.4 L at STP. 22.4 L contains 1 mol of an ideal gas at STP. http://blog.makezine.com/archive/2009/11/18/molar_beach_ball.jpg STP A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present?