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Lesson 5.5 Law of Partial Pressures Suggested ReadingZumdahl Chapter 5 Sections 5.5Essential QuestionsHow is Dalton's law of partial pressures applied?Learning ObjectivesApply Dalton's law of partial pressures. ?IntroductionWhile studying the composition of air, John Dalton concluded in 1801 that each gas in a mixture of unreactive gases acts, as far as the pressure is concerned, as though it were the only gas in the mixture. Thus, each gas exerts the same pressure it would exert if it were the only gas in the flask and the total pressure of the gas mixture is the sum of the pressure exerted by each component gas in the mixture. Although this sounds pretty straightforward, students tend to struggle with this content. Don't rush through this lesson. Study the material and use your textbook to support your learning.?Partial Pressures and Mole FractionsThe pressure exerted by a particular gas in a mixture is the partial pressure of that gas. According to Dalton's law of partial pressures, the sum of the partial pressures of all the different gases in a mixture is equal to the total pressure of the mixture. ?If you let P be the total pressure and PA, PB, PC, ... be the partial pressures of the component gases in a mixture, then the law of partial pressures can be written as?Dalton's law of partial pressure: PTotal = ?PA +?PB?+ PC?+...The individual partial pressures follow the ideal gas law. For gas A in a mixture,?PAV = nART?where PA is the partial pressure of component A and nA is the number of moles of gas A.?The composition of a gas mixture is often described in terms of the mole fractions of a component gases with respect to the total moles of gas mixture.?Because the pressure of a gas is proportional to moles, for a fixed volume and temperature (P = nRT/V ∝ n), the mole fraction also equals the partial pressure divided by total pressure.Mole percent equals mole fraction x 100. Mole percent is equivalent to the percentage of the molecules that are component molecules.?Example: Calculating Partial Pressures and Mole Fractions of a Gas in a MixtureA 1.00 L sample of dry air at 25°C and 786 mmHg contains 0.925 g N2 plus other gases including oxygen, argon, and carbon dioxide. a) What is the partial pressure (in mmHg) of N2 in the air sample? b) What is the mole fraction and mole percent of N2 in the mixture? ??Solution:?a) Each gas in a mixture is assumed to behave ideally, so you can used the ideal gas to determine partial pressure. First,?you convert 0.925 g N2 to moles of N2,?using basic stoichiometry.Then, after putting the data in tabular form, rearrange for the unknown, substitute, and solve.?PN2 = ?V = 1.00 LnN2 = 0.0330 molT = 25 + 273 = 298 KBy checking the prompt (working method!), we see that the prompt specifies units of mmHg, so we must convert as follows.b) Since the temperature and volume are constant, the mole fraction of N2 in air is?Air contains 78.0 mole percent N2.?Collecting Gases over WaterThe law of partial pressure is useful when collecting gases over water. Gases can be collected over water when they do not dissolve appreciably in water. The figure shows how a gas, produced by chemical reaction in a test tube, is collected by leading it to an inverted tube where it displaces water. You should be familiar with this procedure from your earlier chemistry course. As gas bubbles through the water, the gas picks up molecules of water vapor that mix with it. The partial pressure of water vapor in the gas mixture in the collection tube depends only on the temperature. The table below shows the pressure of water at different temperatures.??This partial pressure of water is called the vapor pressure of water. The following example shows how to find the partial pressure and then the mass of the collected gas.Example: Calculating the Amount of Gas Collected Over WaterHydrogen gas is produced by the reaction of HCl, on zinc metal.2HCl(aq) + Zn(s) → ZnCl2(aq) + H2(g)The gas is collected over water. If 156 mL of gas is collected at 19°C and 769 mmHg total pressure, what is the mass of the hydrogen collected?Solution: ?The gas collected is hydrogen mixed with water vapor. To obtain the amount of hydrogen, you must first find its partial pressure in the mixture, using Dalton's law (Step 1). Then you calculate the moles of hydrogen using the ideal gas law (Step 2). Finally you obtain the mass of hydrogen from the moles of hydrogen (Step 3).Step 1: The vapor pressure of water at ?19°C is 16.5 mmHg (see table). From Dalton's law of partial pressures, you know that the total gas pressure equals the partial pressure of hydrogen plus the partial pressure of water.Substituting and solving for the partial pressures of hydrogen, you getStep 2: Now use the ideal gas law to find the moles of hydrogen collected. Putting the data in tabular form you have:P = 752 mmHg x 1 atm / 760 mmHg = 0.989 atmV = 156 mL = 0.156 LT = (19 + 273) = 292 Kn = ?Rearranging the ideal gas law and substituting givesStep 3: Convert moles of H2 to grams of H2.?HOMEWORK: Review the power point notes slides and example problems for Dalton’s Law of Partial Pressures. ................
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