GAS LAWS WRAP-UP 4/26/2012. Chapter 11. Dalton s Law of Partial Pressures. Chapter 11

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1 GAS LAWS WRAP-UP Dalton s Law of Partial Pressures The pressure of each gas in a mixtureis calledthe partialpressure of thatgas. John Dalton, the English chemist who proposed the atomictheory, discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present. Dalton slaw of partial pressures statesthatthe totalpressure of a gas mixtureis the sum of the partialpressures of the componentgases. Dalton s Law of Partial Pressures, continued Gases Collected by Water Displacement Gases producedin the laboratoryare often collectedover water. Thegas producedby the reactiondisplaces thewater in thereactionbottle. Dalton s law of partial pressures can be applied to calculate the pressures of gases collected in this way. Water molecules at the liquid surface evaporate and mix with the gas molecules.water vapor, like othergases, exerts a pressure known as vapor pressure. 1

2 Dalton s Law of Partial Pressures, continued Gases Collected by Water Displacement, continued To determinethepressure of a gas inside a collectionbottle, you woulduse the following equation, which is an instance of Dalton slaw of partialpressures. P atm = P gas + If you raise the bottleuntil the waterlevels inside and outsidethe bottleare the same, the totalpressure outside and inside thebottlewill be thesame. Reading the atmosphericpressure from a barometerand looking up the value of at the temperature of the experiment in a table, you can calculate P gas. Section 1 Gases and Pressure Particle Model for a Gas Collected Over Water Objectives State the law of combining volumes. State Avogadro s law and explain its significance. Define standard molar volume of a gas and use it to calculate gas masses and volumes. State theideal gas law. Using the idealgas law, calculatepressure, volume, temperature, or amountof gas when the otherthreequantitiesare known. 2

3 Measuring and Comparing the Volumes of Reacting Gases In the early 1800s, French chemistjosephgay-lussacobserved that2 L of hydrogen can react with 1 L of oxygen to form 2 L of water vapor. hydrogen gas + oxygen gas water vapor 2 L (2 volumes) 1 L (1 volume) 2 L (2 volumes) The reactionshows a simple 2:1:2 ratio in thevolumes of reactantsand products.this sameratio applies to any volumeproportions: for example, 2 ml, 1 ml, and 2 ml; or 600 L, 300 L, and 600 L. Measuring and Comparing the Volumes of Reacting Gases The samesimple anddefinite volume proportionscan be observed in othergas reactions. hydrogen gas + chlorine gas hydrogen chloride gas 1 L (2 volumes) 1 L (1 volume) 2 L (2 volumes) Gay-Lussac slaw of combiningvolumesof gases statesthatat constant temperatureand pressure, thevolumes of gaseous reactantsand products can be expressed as ratiosof smallwhole numbers. Avogadro s Law In 1811, AmedeoAvogadroexplainedGay-Lussac slaw of combining volumes of gases without violating Dalton s idea of indivisible atoms. Avogadroreasoned that, instead of always being in monatomicform when they combineto form products, gas moleculescan containmore thanone atom. He also statedan idea known todayas Avogadro s law. Thelaw states that equal volumesof gases at the same temperature and pressure contain equal numbers of molecules. 3

4 Avogadro s Law, continued Avogadro s law also indicates that gas volume is directly proportional to the amount of gas, at a given temperature and pressure. The equationfor this relationshipis shown below, where V is the volume, k is a constant, and n is the amountof moles of the gas. V = kn Molar Volume of a Gas Recall thatone mole of a substance containsa numberof particles equal to Avogadro s constant ( ). example: one mole of oxygen, O 2, contains diatomic molecules. AccordingtoAvogadro slaw, one mole of any gas will occupy thesame volume as one moleof any othergas at the sameconditions, despite mass differences. The volumeoccupied by one moleof gas atstp is known as the standard molar volume of a gas, which is L (rounded to 22.4 L). Molar Volume of a Gas, continued Knowing thevolume of a gas, youcan use the conversion factor1 mol/22.4l to find the moles (and therefore also mass) of a given volume of gas at STP. example: at STP, You can also use themolarvolume of a gas to find the volume, atstp, of a known number of moles or a known mass of gas. example: at STP, 4

5 Gas Stoichiometry Gay-Lussac slaw of combiningvolumes of gases andavogadro slaw can be applied in calculating the stoichiometry of reactions involving gases. The coefficients in chemicalequationsof gas reactions reflect not only molar ratios, but also volume ratios (assuming conditionsremain thesame). example reaction of carbon dioxide formation: 2CO(g) + O 2 (g) 2CO 2 (g) 2 molecules 1 molecule 2 molecules 2 mole 1 mole 2 mol 2 volumes 1 volume 2 volumes Gas Stoichiometry, continued 2CO(g) + O 2 (g) 2CO 2 (g) 2 molecules 1 molecule 2 molecules 2 mole 1 mole 2 mol 2 volumes 1 volume 2 volumes You can use thevolume ratiosas conversion factors in gas stoichiometryproblems as you would moleratios: etc. The Ideal You have learnedaboutequationsdescribing the relationshipsbetween two or three of the four variables pressure, volume, temperature, and moles needed to describe a gas sample at a time. All of the gas laws you havelearned thus far can be combinedinto a single equation, theideal gas law: the mathematicalrelationshipamongpressure, volume, temperature, and number of moles of a gas. It is stated as shown below, where R is a constant: PV = nrt 5

6 The Ideal, continued The Ideal Gas Constant In the equationrepresenting theideal gas law, theconstant R is known as the ideal gas constant. Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation. Measured values of P, V, T, and n for a gas at near-ideal conditions can be used to calculate R: The Ideal, continued The Ideal Gas Constant, continued The calculatedvalue of R is usuallyroundedto (L atm)/(mol K). Use this value in ideal gas law calculations when the volume is in liters, the pressure is in atmospheres, and the temperature is in kelvins. The ideal gas law can be applied to determine the existing conditions of a gas sample when three of the four values, P,V,T, and n, are known. Be sure to match the units of the known quantities and the units of R. Numerical Values of the Gas Constant 6

7 The Ideal, continued Sample Problem I What is the pressure in atmospheres exerted by a mol sample of nitrogen gas in a 10.0 L container at 298 K? The Ideal, continued Sample Problem I Solution Given: V of N 2 = 10.0 L n of N 2 = mol T of N 2 = 298 K Unknown: P of N 2 in atm Solution: Use the ideal gas law, which can be rearranged to find the pressure, as follows. The Ideal, continued Sample Problem I Solution, continued Substitute the given values into the equation: 7

8 Objectives Describe theprocess of diffusion. State Graham slaw of effusion. State therelationshipbetween the averagemolecularvelocities of two gases and their molar masses. Diffusion and Effusion The constant motion of gas molecules causes them to spread out to fill any containerthey arein. The gradualmixing of two or more gases due to their spontaneous, random motion is known as diffusion. Effusion is the process whereby the molecules of a gas confined in a container randomlypass through a tiny opening in the container. Graham s Law of Effusion Rates of effusion and diffusion depend on the relative velocities of gas molecules. The velocity of a gas varies inversely with the square root of its molar mass. Recall that the average kinetic energy of the molecules in any gas depends only the temperature and equals. For two different gases, A and B, at the same temperature, the following relationship is true. 8

9 Graham s Law of Effusion From the equation relating the kinetic energy of two different gases at the same conditions, one can derive an equationrelating the rates of effuses of two gases with their molecular mass: This equationis known as Graham slaw of effusion, which states thatthe rates of effusion of gases at the same temperature and pressure are inversely proportionalto the square rootsof their molar masses. Graham s Law 9