Kinetic Molecular Theory (KMT)

Kinetic Molecular Theory (KMT) Speculates about the behavior about individual gas particles

Kinetic Molecular Theory • The volume of individual gas molecules are so small, we say they = 0.

Kinetic Molecular Theory • The volume of individual gas molecules are so small, we say they = 0. • Particles are in constant motion-collisions exert pressure.

Kinetic Molecular Theory • The volume of individual gas molecules are so small, we say they = 0. • Particles are in constant motion-collisions exert pressure. • Particles are assumed to exert no attraction to each other.

Kinetic Molecular Theory • The volume of individual gas molecules are so small, we say they = 0. • Particles are in constant motion-collisions exert pressure. • Particles are assumed to exert no attraction to each other. • Ave KE(speed) is directly proportional to temperature in Kelvin

Kinetic Molecular Theory • The volume of individual gas molecules are so small, we say they = 0. They have volume. • Particles are in constant motion-collisions exert pressure. No collisions if they show attraction. • Particles are assumed to exert no attraction to each other. They have mass so they show attraction. • Ave KE(speed) is directly proportional to temperature in Kelvin. Huge! Remember

Therefore • Real gases act like ideal gases when they are at low pressure and high temperature. • Helps tremendously if they have a small atomic mass. Why?

The building of van der Waals eqn Real gases have volume, therefore volume available in container is less. These molecules take up some of the space that we calculated for volume of the container.

The building of van der Waals eqn Real gases have volume, therefore volume available in container is less. These molecules take up some of the space that we calculated for volume of the container. Correction factor for the Ideal Gas Law P (V-nb) = nRT n= # of moles b=correction factor (pg 224: Table 5.3)

The building of van der Waals eqn Real gases attract each other (law of universal gravitation), therefore not all of them are colliding with container. Pressure is less than what we calculated it to be.

The building of van der Waals eqn Real gases attract each other (law of universal gravitation), therefore not all of them are colliding with container. Pressure is less than what we calculated it to be. Correction factor for the Ideal Gas Law. (P + a(n/V)2) (V-nb) = nRT a=pressure correction factor n/V = amount of gas you have; you increase the amount, you increase the attraction

The building of van der Waals eqn Johannes van der Waal won the Nobel Prize for his work on this equation in 1910.

Van der Waals • Calculate the pressure exerted by 0.5000 mol N2 in a 10.000 L container at 25C, a) using the ideal gas law b) using van der Waals eqn c) Compare the results

Let’s talk about the speed of gas molecules. • The meaning of temperature. Kelvin temperature indicates the average kinetic energy of the gas molecules. (KMT)

Let’s talk about the speed of gas molecules. • The meaning of temperature. (KE)avg = 3/2 RT Work R = 8.31 J/K x mole

Lecture Ave KE • Calculate the average kinetic energy of the N2 molecules in a sample of N2 gas at 273 K and 546 K.

Let’s talk about the speed of gas molecules. The average kinetic energy of any gas (1/2mv2) has a specific value at a given temperature! Doesn’t matter what the gas is, it will have the same average KE at a given temp. How can that be?

Let’s talk about the speed of gas molecules. Mass is smaller in He than in Xe. Same temperature==same ave KE Only way tha could be is that the velocity of He has to be greater than Xe. (Mathematical explanation)

Let’s talk about the speed of gas molecules. Equation: Root mean square velocity u = 3RT MM where u= root mean square velocity R= work R T = temp in K M = mole mass of gas in kg

Lecture-root mean square • Consider separate 1.0 L samples of He(g) and UF6(g), both at 1.00 atm and containing the same number of moles. What ratio of temperatures for the two samples would produce the same root mean square velocity?

Let’s talk about the speed of gas molecules. Equation: Root mean square velocity u = 3RT M M(molar mass in kg) is in denominator, what does that mean?

Let’s talk about the speed of gas molecules. Equation: Root mean square velocity u = 3RT M => the less massive the molecule, the higher the rms speed(u).

Lecture-Table of all Ave KE Ave Velocity freq Collisions A B C D

Lecture – RMS, KE • Consider a 1.0 L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease or stay the same under each of the following conditions: a) The temperature is increased to 100C. b) The temperature is decreased to -50C. c) The volume is decreased to 0.5 L. d) The number of moles of neon is doubled.

Let’s talk about the speed of gas molecules Diffusion • Describes the mixing of gases=Smells • The rate of Diffusion is the rate of mixing of gases. EQN: The distance traveled by gas 1 = Mole Mass Gas 2 The distance traveled by gas 2 Mole Mass Gas 1

Let’s talk about the speed of gas molecules Diffusion • Distance and Diffusion • Makes sense Problem: Lecture Q#4

Problem • An unknown diatomic molecule effuses at a rate that is only 0.355 times that of O2 at the same temperature. What is the identity of the unknown gas?

Let’s talk about the speed of gas molecules Graham’s Law of Effusion Describes the passage of a gas through tiny holes Demo: Smelly Balloons The rate of effusion is how fast it goes through a tiny hole. EQN: Rate of effusion for gas 1 = Mole Mass Gas 2 Rate of effusion for gas 2 Mole Mass Gas 1

Let’s talk about the speed of gas molecules • All about mole masses. • Doesn’t always work as well as it should. Too many things in the way including other air molecules!

Problem Set 4 due tomorrow

Kinetic Molecular Theory (KMT)