Plan for Fri, 10 Oct 08 Mistake in Exam 1 key –Graphical LR problem: #13 in V1, #5 in V2 –Keys say the answer is B…the answer is really D –Bring your exam to me by Monday to get these points back Office Hours?? Lecture –Dalton’s Law of Partial Pressures (5.4) –Kinetic Molecular Theory of Gases (5.5) Quiz 2

Three 3.0-L flasks, each at a pressure of 878 mmHg, are in a room. The flasks contain He, Ar, and Xe, respectively. Which of the three flasks contain the most atoms of gas? –All flasks contain the same number of atoms. Which of the flasks has the greatest density of gas? –The gas with the greatest M, Xe. If the He flask was heated and the Ar flask cooled, which of the three flasks would be at the highest pressure? –The flask that was heated, He. If the temperature of the He was lowered with the Xe was raised, which of the three flasks would have the greatest number of moles of gas? –They will all have the same number of moles.

Partial Pressures The pressure exerted on the shelves by all of the records is equal to the sum of the pressures exerted by the individual records: …or the pressures exerted by each genre:

Dalton’s Law of Partial Pressures For a mixture of ideal gases in a container, the total pressure exerted by the mixture is the sum of the pressures each gas would exert if it were alone. Recall that according to the ideal gas law, gas molecules are indistinguishable, non-interacting point particles. Increasing the number of point particles increases the pressure an amount proportional to the number of moles.

Proving Dalton’s Law Say we have a container with some amount of three different gases inside, at a certain T and P. Dalton’s Law says that the total pressure exerted by the three gases is the sum of the individual pressures.

Example 5.15, p. 195 Mixtures of He and O 2 are used in scuba tanks to help prevent “the bends.” For a particular dive, 46 L of O 2 at 25 o C and 1.0 atm was pumped along with 12 L of He at 25 o C and 1.0 atm into a 5.0-L tank. What is the partial pressure of each gas? What is the total pressure?

Mole Fraction and Partial Pressure In the last example, we determined the total pressure in two ways: –We calculated the partial pressure of each gas and added them together. –We added up the total number of moles of gas and then calculated the total pressure. These two methods suggest a useful relationship between number of moles of each gas and total pressure.

Mole Fraction and Partial Pressure Mole Fraction (  ): the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. The fraction of moles of a certain gas in a mixture is equal to the ratio of its partial pressure to the total pressure of the mixture.

Collecting gases over water E&G, Fig 5.20

Kinetic Molecular Theory (KMT) The gas laws of Boyle, Charles, and Avogadro are empirical, meaning they are based on observation. –Some guy sitting in a lab and watching how containers full of gases react to different conditions. These laws offer a general description of behavior based on many experiments. –They can tell you what happens to an ideal gas under certain conditions, but not why it happens. KMT is a theoretical, molecular-level model of ideal gases, which can be used to predict the behavior of a gaseous system. Since all matter is composed of atoms an molecules, we want to explain macroscopic behavior in terms of these basic building blocks.

KMT Postulates 1.Gas particles are so small compared to the distances between them that the volume of the individual particles is negligible. 2.Gas particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3.The particles are assumed to exert no forces on each other; they neither attract or repel their neighbors. 4.The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

What can KMT do for you? The main ideas you should take from KMT is that we can describe T and P from a molecular perspective. Pressure: arises from molecules banging into the container walls. Temperature: arises from the kinetic energy of the gas molecules. The more KE they have, the faster they can move around, the “hotter” they are.

Pressure according to KMT Copyright © Houghton Mifflin Company. All rights reserved. Go to Slide Show View (press F5) to play the video or animation. (To exit, press Esc.) This media requires PowerPoint® 2000 (or newer) and the Macromedia Flash Player (7 or higher). [To delete this message, click inside the box, click the border of the box, and then press delete.] One moleculeMany molecules

Microscopic Illustration of Boyle's Law Copyright © Houghton Mifflin Company. All rights reserved. Go to Slide Show View (press F5) to play the video or animation. (To exit, press Esc.) This media requires PowerPoint® 2000 (or newer) and the Macromedia Flash Player (7 or higher). [To delete this message, click inside the box, click the border of the box, and then press delete.] According to KMT, gas pressure is the result of the gaseous molecules colliding with the walls of the container. BOYLE’S LAW: As the volume of a gas is decreased, gas molecules have less distance to travel before they collide with the container, so they collide more often, and the pressure of the system increases. n, T constant

Temperature according to KMT Copyright © Houghton Mifflin Company. All rights reserved. Go to Slide Show View (press F5) to play the video or animation. (To exit, press Esc.) This media requires PowerPoint® 2000 (or newer) and the Macromedia Flash Player (7 or higher). [To delete this message, click inside the box, click the border of the box, and then press delete.] Kinetic energy: The energy an object has by virtue of its motion. Basically, the energy you must apply to an object to accelerate it from rest to a given velocity ( u ): The average E k of a molecule is directly proportional to the absolute temperature in K.

Microscopic Illustration of Charles' Law Copyright © Houghton Mifflin Company. All rights reserved. Go to Slide Show View (press F5) to play the video or animation. (To exit, press Esc.) This media requires PowerPoint® 2000 (or newer) and the Macromedia Flash Player (7 or higher). [To delete this message, click inside the box, click the border of the box, and then press delete.] According to KMT, the temperature of a gaseous system arises from the kinetic energy ( E k ) of the gas molecules. CHARLES’S LAW: As heat is applied, E k of the gas molecules increases, thereby increasing their speed. To maintain constant pressure under these conditions, the volume of the system must increase. n, P constant

Interplay of T & P according to KMT According to KMT, gas pressure is the result of the gaseous molecules colliding with the walls of the container. If the kinetic energy of the molecules is increased, the molecules will collide more often and more forcefully, thereby increasing the pressure. n, V constant