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Chapter%205%20Student%20Notes%20Part%202%20PHW

# Chapter%205%20Student%20Notes%20Part%202%20PHW - Mixtures...

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Unformatted text preview: Mixtures of Gases Dalton ’s Law of Partial Pressures The pressure exerted by a mixture of ideal gases is the sum of the pressures that each one would exert if it occupied the container alone. RT ml =P1+P2+P3 =(nl—rn2+n3 l—V 5: Mole Fractions and Partial Pressures The mole fraction of a component in a mixture is deﬁned as the number of moles of the component divided by the total number of moles present. Mole Fraction of A = X A n n XA = _A = mus— ntot nA +11B +...+nN For ideal gases: PAV = nART PIOIV E ntOIRT divide equations -—-—> PAV = nART or PA =n—A or PA =k—Pmt P V n RT P n n tot tot E_________—__ Sample Problem A solid hydrocarbon is burned in air in a closed container, producing a mixture of gases having a total pressure of 3.34 atm. Analysis of the mixture shows it to contain 0.340 g of water vapor, 0.792 g of carbon dioxide, 0.288 g of oxygen, 3.790 g of nitrogen, and no other gases. Calculate the mole fraction and partial pressure of carbon dioxide in this mixture. ntot = “H20 + not)2 + no2 + an 0.34 0.792 0.288 3.790 r1tot = —---—+ + + = 0.1809 18 44 32 28 n 0.018 X a C02 = =0.0995 C02 11 0.1809 tot PCOZ = XCOZPtot = 0.0995 X 3.34 atm 0.332 atm The Kinetic Molecular Theory of Gases The Ideal Gas‘ Law is an empirical relationship based on experimental observations (Boyle, Charles, & Avogadro). The Kinetic Molecular Theory is a simple theoretical model that attempts to explain the behavior of gases. The Kinetic Molecular Theory of Gases 1. The molecules of an ideal gas are constantly moving in random directions with a distribution of speeds. Collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. The gas molecules occupy a negligibly small fraction of the total volume. 2. The molecules of a gas exert no forces on one another except during collisions, so that between collisions they move in straight lines with constant velocities. The gases are assumed to neither attract or repel each other. The collisions of the molecules with each other and with the walls of the container are elastic, i.e., no energy is lost during a collision. Essentially, the gas molecules behave like tiny billiard balls undergoing ceaseless random motion. 3. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the temperature of the gas in degrees Kelvin. See pages 156 — 162 in for donation of key results ,_____—_wm_sm—______Mﬁw__ EPressure 0: (impulse per collision) x (rate ofcollisions with walls) Poc(mxu)><(N/V)xu => But, the molecules of a gas are constantly moving in random directions with a distribution of speeds. m 2 :5 L3 O E O I... O I— .3 E = E .‘é’ E 52 with given velocity = Mean-square speed , a of all molecules 0 4 x 10- 8 x lO' Molecular velocity (mis) Temperature and Molecular Motion As shown in the text derivation, the ro ortionali constant relating PV to thmgis 1/3, i.e., PV = Nana/s = nNAmil-i/S Therefore, PV/n = RT = _ _ 2 ideal gas law molar ' kinetic energy The Meaning of Temperature The temperature of a gas in degrees K is a measure of the random motions of the gas atoms. Higher T => greater random motion Maxwell-Boltzmann Distribution of Speeds N2 one ﬂu) '(xﬁlz'ié'lénTrﬁjuz éxm—muZ/zkn’r) y,” '5; iii NA? =‘jf'1;_;;8 g-;.o+za-J:.x+1 molecule”1 o 500 1000 " Isa-u 2000 7 ' ' 3500 “mpg-I Speed. I: (m ar‘) I‘m-me- 44mg o 200:! Thomson-Breakch- Temperature is a measure of the average kinetic energy of molecules when their speeds have a Maxwell-Boltmann distribution. i.e., when the molecules are at themed equilibrium. Distributions of Molecular Speeds :1: 2. :3 u 2 o E e. Z t.— a 2 E g; 2. E u m with given veloc'ny 500 I000 1500 4‘“ ___ H [mm 1000 2000 3000 r"- llll In Vetociry (W‘s) umID : uavg : urms = 1.000 : 1.128: 1.225 Sample Problem At a certain speed, the root—mean—square-speed 0f the molecules of hydrogen in a sample of gas is 1055 m 5". Compute the root-mean square speed of molecules of oxygen at the same temperature. Strategy 1. Find T for the H2 gas with a u“ms = 1055 m S“1 2. Find arms of 02 at the same temperature Strategy 1. Find T for the H2 gas with 2 arms = 1055 m S'1 = (1055 m s-1)2 (0.002016 kg mol'1)/3 (3.315 J K-1 mol-l) ,——__%w—__ : Strategy 2. Find arms of 02 at the same temperature At a constant temperature, arms is proportional to M‘W. Therefore, for 02 ﬁrms 1055 m s‘1 x urms for 02 = 264.8 m S'1 Gaseous Diffusion and Eﬁusion Diffusion: Mixng of gases via their ceaseless random motions Col W W Distance diffused by HC] uavg(HCl) “ MBCI 1/2 __ 1 5 approximately _ MNHs _ ' correct Rate of effusion of gas 1 _ u“ (I) = (—5” M2 Rateof ---- M1 Graham’s Law of Effusion lisions of Gas Molecules with Container Walls See Text, pages 1 66-1 6 7 for details ZA no. of collisions per unit time of gas molecules with an area A of container wall 1.00 atm of 02 at T = 27 °C makes 2.72 x 1023 collisions per second per cm2 of container surface Intermolecular Collisions See Text, pages 1 68-1 70 for details Z Ill no. of collisions per unit time between gas molecules Z = (d 5 molecular diameter) Z”1 = mean time between collisions l. E = mean distance traveled between collisions For 02 atT =27 °C and P= 1 atm: Z'I = 2.5x 10-10s Z = 4.9 x 109 collisions/s Real Gases Ideal Gas behavior is generally observed under conditions of low pressure and high temperature. 0 200 400 600 800 1000 P(am:) F Or an ideal gas, PV/nRT = 1 at all pressures. F or real gases, attractive forces dominate at intermediate pressures and repulsive forces dominate at high pressures I - Van der Waals Equation of State Johannes van der Waals (18 73) - Correction to ideal gas equation of state for attractive forces in gases (and liquids) — Correction to ideal gas equation of state to account for volume occupied by the molecules The Person Behind the Science H ighlig hts — 1873 ﬁrst to realize the necessity of taking into account the volumes of molecuies and — intermolecular forces (now generally called "van der Waals forces") in establishing the relationship between the pressure, volume and temperature of gases and liquids. Moments in a Life — 1910 awarded Nobel Prize in Physics 10 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. Chapter 5: Gases Early Experiments The Gas Laws of Boyle, Charles and Avogadro The ideal Gas Law Gas Stoichiometry Dalton's Laws of Partial Pressure The Kinetic Molecular Theory of Gases Effusion and Diffusion Collisions of Gas Particles with the Container Walls Intermolecular Collisions 5.10. Real Gases 5.11. Chemistry in the Atmosphere 11 ...
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Chapter%205%20Student%20Notes%20Part%202%20PHW - Mixtures...

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