10/15/2015. Why study gases? An understanding of real world phenomena. An understanding of how science works.
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1 0/5/05 Kinetic Theory and the Behavior of Ideal & Real Gases Why study gases? An understanding of real world phenomena. An understanding of how science works.
2 0/5/05 A Gas fills any container. completely with any other gas. Exerts on its surroundings. 760 mm Hg (measured at torr 0,35 Pa 0.35 kpa.03 bar 03 mb 4.7 lb in o C)
3 0/5/05 A manometer is used to measure the pressure inside closed containers Open-end manometer. (a) The pressure of the trapped gas, P gas equals the atmospheric pressure, P atm. Trapped gas pressure (b) higher and (c) lower than atmospheric pressure. 3
4 0/5/05 Compressing a gas increases its pressure. 4
5 0/5/05 Boyle s J-Tube Experiment V P 5
6 0/5/05 Law For constant mols or concentration: Boyle's Law : PV Charles' Law : V / T PV V / T (when T Gay - Lussac's s Law : T (when P ) P ) P / T P / T (when V V ) 6
7 0/5/05 Example: What will be the the final pressure of a sample of oxygen with a volume of 850 m 3 at 655 torr and 5.0 o C if it is heated to o C and given a final volume of 066 m 3? ANALYSIS: Use the combined gas law with temperature in kelvins. SOLUTION: P V P V T T m 655 torr m 69 torr ( )K ( )K)K 7
8 0/5/05 The combined gas law can be generalized to include changes in the number of moles of sample The law is PV nrt R universal gas constant atm L 0.08 mol K One mole of each gas occupies.4 at STP. Carbon dioxide is more dense that oxygen due to molar mass differences. 8
9 0/5/05 Molar Mass of a Gas Molar Mass = drt/p d = density of gas T = temperature in Kelvin P = pressure of gas Copyright Houghton Mifflin Company. All rights reserved Chapter 5 Slide The space above any liquid contains some of the liquid s vapor 9
10 0/5/05 Example: A sample of oxygen is collected over water at 0 o C and a pressure of 738 torr. What is the partial pressure of oxygen? ANALYSIS: The partial pressure of oxygen is less than the total pressure. Get the vapor pressure of water from tables of data or text SOLUTION: P P water vapor gas 7.54 torr ( ) torr 70. torr 0
11 0/5/05 Dalton s Law of Partial Pressures This is possible because the number of moles of each gas is Using the ideal gas equation for each gas n A PAV RT For a given mixture of gases, the volume and temperature for all gases Using C=V/RT gives
12 0/5/05 X A PAC PAC PB C PZ C P A P P P P P A B The partial pressure of a gas can be calculated using the total pressure and mole fraction P A X A P Z total A total Gas volumes can be used in stoichiometry problems H ( g) O ( g) H O(g) volumes volumes H volumes H volumes O moles H moles H mole O volume volumes ( g) volume O ( g) volumes H O( g) ( g) volumes H O( g) just as ( g) mole O ( g) moles H O( g) (same temperature and pressure) ( g) ( g) ( g) moles H O( g)
13 0/5/05 (a) Diffusion (b) Effusion The behavior of ideals gases can be explained Kinetic Molecular Theory So far we have considered what happens, but not why. In science, what always comes before why. 3
14 0/5/05 Postulates: Kinetic Molecular Theory. Gas particles are in motion, colliding with container walls. Kinetic Molecular Theory Postulates:. Gas particles have size compared to the distances between them. 4
15 0/5/05 Postulates: Kinetic Molecular Theory 3. Gas particles have attraction ti for one another. Postulates: Kinetic Molecular Theory 4. Absolute temperature t of the gas is a measure of the average of the gas particles
16 0/5/05 Diffusion is the intermingling of the molecules of one gas with another Effusion is the movement of gas molecules through a into a. The rates of both diffusion and effusion depend on the of the gas molecules l The the molecules, the diffusion and effusion occur Thomas Graham studied effusion He found that the effusion rate of a gas was proportional to the square root of the density (d) This is known as Graham s law effusion rate (constant P and T ) d effusion rate ( A ) effusion rate ( B) d d M M Where M i is the molar mass of species i B A B A 6
17 0/5/05 Diffusion The movement of one gas through another by thermal random motion. Diffusion is a very slow process in air because the mean free path is very short (for N at STP it is 6.6x0-8 m). Given the nitrogen molecule s high velocity, the collision frequency is very high also (7.7x0 9 collisions/s). Diffusion also follows Graham's law: Rate of diffusion M Diffusion of a gas particle through a space filled with other particles 7
18 0/5/05 NH 3 (g) + HCl(g) = NH 4 Cl(s) The inverse relation between diffusion rate and molar mass. Due to it s light mass, ammonia travels.46 times as fast as hydrogen chloride NH 3 (g) + HCl(g) NH 4 Cl(s) 8
19 0/5/05 Relative Diffusion Rates of NH 3 and HCl A Practical Example of Using Gas Density, Diffusion, Separation and Purification for Enriched Uranium Gaseous Diffusion Separation of Gaseous Diffusion Separation of Uranium 35 / 38 9
20 0/5/05 Gaseous Diffusion Separation of Uranium 35 / 38 Purified solid mixed U 3 O 8,UO 3,and, UO containing all uranium isotopes are converted to all isotopic forms of UF 6 (g) Gaseous Diffusion Separation of Uranium 35 / 38 Purified solid mixed U 3 O 8,UO 3,and, UO containing i all uranium isotopes are converted to all isotopic forms of UF 6 (g) At Start: 35 UF 6 vs 38 UF % 99.8 % after approximately 000 runs 35 UF 6 is > 99% Purity 0
21 0/5/05 The Gas Laws Can Be Explained by KMT When the gas volume is made When the gas volume is made smaller going from (a) to (b), the frequency of collisions per unit area of the containers wall increases. Thus the pressure increases.
22 0/5/05 The kinetic theory and the pressure-temperature law (Gay-Lussac s law). The pressure increases from (a) to (b) as measured by the amount of mercury that must be added to maintain a constant volume. The kinetic theory and the temperature-volume law (Charles law). The pressure is the same in both (a) and (b). At higher temperatures the volume increases because the gas molecules have higher velocities.
23 0/5/05 Kinetic Molecular Theory Particles are masses in constant, random, straight line motion. Particles are separated by distances. Collisions are and. No between particles. Total energy remains. Slide 45 of 46 General Chemistry: Chapter 6 Prentice-Hall 007 Pressure Assessing Collision Forces Translational kinetic energy, Frequency of collisions, Impulse or momentum transfer, Pressure proportional to impulse times frequency ek mu N v u V I mu N P mu V Slide 46 of 46 General Chemistry: Chapter 6 Prentice-Hall 007 3
24 0/5/05 Pressure and Molecular Speed Three dimensional systems lead to: P N m u 3 V u m is the modal speed u av is the simple average u rms u Slide 47 of 46 General Chemistry: Chapter 6 Prentice-Hall 007 Assume one mole: PV=RT so: N A m = M: Rearrange: Pressure PV N A m u 3 3RT N m u 3RT A M u 3RT u rms M Prentice-Hall 007 General Chemistry: Chapter 6 Slide 48 of 46 4
25 0/5/05 Distribution of Molecular Speeds u rms 3RT M Prentice-Hall 007 General Chemistry: Chapter 6 Slide 49 of 46 Determining Molecular Speed Prentice-Hall 007 General Chemistry: Chapter 6 Slide 50 of 46 5
26 0/5/05 Modify: PV=RT so: Solve for e k : Temperature PV N 3 e A m u RT k 3 N 3 3 R N N A A e k A (T) ( m u ) Conclusion: Average is directly proportional to Prentice-Hall 007 General Chemistry: Chapter 6 Slide 5 of Gas Properties Relating to the Kinetic-Molecular Theory Diffusion Net rate is proportional to molecular speed. Effusion A related phenomenon. Slide 5 of 46 General Chemistry: Chapter 6 Prentice-Hall 007 6
27 0/5/05 Plots of PV/nRT Versus P for Several Gases (00 K) Copyright Houghton Mifflin Company. All rights reserved 5 53 J. D. van der Waals corrected the ideal gas equation in a simple, but useful, way 7
28 0/5/05 8 nrt nb V a n P measured measured value gas ideal to measured reduces : value gas to ideal up measured brings : V nb P V a n V measured measured measured measured constants Van der Waals the as known b are and a He Helium, mol L mol atm L Substance b a O H Water, NH Ammonia, H Hydrogen, Ne Neon, He Helium, 3
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