Chapter 10 Gases: Their Properties and Behavior

Chapter 9: Gases: Their Properties and Behavior 11/8/2018 Copyright © 2008 Pearson Prentice Hall, Inc.

The Kinetic-Molecular Theory of Gases Chapter 9: Gases: Their Properties and Behavior 11/8/2018 The Kinetic-Molecular Theory of Gases A gas consists of tiny particles, either atoms or molecules, moving about at random. The volume of the particles themselves is negligible compared with the total volume of the gas; most of the volume of a gas is empty space. there is a lot of empty space between the particles compared to the size of the particles The gas particles act independently of one another; there are no attractive or repulsive forces between particles. like billiard balls 4. Collisions of the gas particles, either with other particles or with the walls of a container, are elastic (constant temperature). The average kinetic energy of the gas particles is proportional to the Kelvin temperature of the sample. as you raise the temperature of the gas, the average speed of the particles increases Copyright © 2008 Pearson Prentice Hall, Inc.

Gas Laws Explained – Dalton’s Law of Partial Pressures Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy since the average kinetic energy is the same, the total pressure of the collisions is the same

Kinetic Energy and Molecular Velocities average kinetic energy of the gas molecules depends on the average mass and velocity KE = ½mv2 gases in the same container have the same temperature, the same average kinetic energy if they have different masses, the only way for them to have the same kinetic energy is to have different average velocities lighter particles will have a faster average velocity than more massive particles molar mass average speed 5

The Kinetic-Molecular Theory of Gases Chapter 9: Gases: Their Properties and Behavior 11/8/2018 The Kinetic-Molecular Theory of Gases Copyright © 2008 Pearson Prentice Hall, Inc.

Diffusion and Effusion the process of a collection of molecules spreading out from high concentration to low concentration is called diffusion the process by which a collection of molecules escapes through a small hole into a vacuum is called effusion both the rates of diffusion and effusion of a gas are related to its rms average velocity

Graham’s Law of Effusion for gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of the molar mass for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

Example Determine how much faster Helium atoms moves, on average, than a carbon dioxide molecule at the same temperature Determine the molar mass and identity of a gas that moves 4.67 times as fast as CO2

Ideal vs. Real Gases Real gases often do not behave like ideal gases at high pressure or low temperature Ideal gas laws assume no attractions between gas molecules gas molecules do not take up space based on the kinetic-molecular theory at low temperatures and high pressures these assumptions are not valid

The Behavior of Real Gases Chapter 9: Gases: Their Properties and Behavior 11/8/2018 The Behavior of Real Gases The volume of a real gas is larger than predicted by the ideal gas law. Copyright © 2008 Pearson Prentice Hall, Inc.

The Effect of Molecular Volume at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume the molecular volume makes the real volume larger than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the molecular volume b is called a van der Waals constant and is different for every gas because their molecules are different sizes

Real Gas Behavior because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures

The Effect of Intermolecular Attractions Attractive forces between particles become more important at higher pressures. at low temperature, the attractions between the molecules is significant the intermolecular attractions makes the real pressure less than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the intermolecular attractions a is called a van der Waals constant and is different for every gas because their molecules are different sizes

Real Gas Behavior because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

The Behavior of Real Gases Chapter 9: Gases: Their Properties and Behavior 11/8/2018 The Behavior of Real Gases van der Waals equation Correction for intermolecular attractions. a n2 P + V - n b = nRT V2 Correction for molecular volume. Copyright © 2008 Pearson Prentice Hall, Inc.

Example A sample of 3.50 moles of NH3 gas occupies 5.20 L at 47oC. Calculate the pressure of the gas (in atm) using A) the ideal gas equation B) the van der Waals equation a = 4.17 atm •L2/mol2 b = 0.0371 L/mol