Kinetic Molecular Theory KMT Chapter 10 Gas Laws

Gases  Atmospheric gases are made up of :  N 2 78%  O 2 21%  Other He, CO 2, H 2 etc  What are the GREENHOUSE gases?  CO 2  CH 4 H2OH2OH2OH2O  Other (CFC’s, NOx, ozone)

Pressure GGGGases fill a container uniformly. PPPPressure is Force per unit area PPPP= F x A TTTThe force of the collisions of the gas particles with the wall of their container. PPPPressure is measured by a barometer, or manometer. UUUUnits???

Models vs Laws  So far we have looked at Gas laws to predict the behavior of gases.  Scientists have also developed a model that helps to explain the behavior of gases.  Models are an approximation!!

Kinetic Molecular Theory KKKKMT attempts to explain the properties of an ideal gas. KKKKMT is based on speculations of the behavior of individual gas particles.

States of Matter  Gas  Liquid  Solid

States of Matter

KMT of gases  The particles are so small compared with the distance between then that the volume of the individual particles can assumed to be zero. (demo)  The particles are in constant motion. The collisions of the particles with the wall of the container are the cause of the pressure exerted by the gas.

KMT of gases  The particles are assumed to exert no force on one another. (neither attracted nor repelled).  The average Kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.  Why Kelvin????

Pressure and Volume (Boyles)  For a given sample of gas at constant moles and temperature, pressure and volume are inversely related.  With KMT, a decrease in volume increases the number of collisions increasing the pressure.

Pressure and Temperature  For an Ideal gas pressure is directly related to temperature.  In KMT, An increase in temperature increases the speed of the particles allowing the particles to hit the wall with greater force and greater frequency.

Volume and Temperature  The ideal Gas at a constant pressure, the volume is directly proportional to temperature.  In KMT, as the temperature increases, the speed and force of the particles increases. The only way to keep pressure constant is to increase the volume.

Volume and the number of moles  Ideal gas predicts the volume of a gas at constant temperature and pressure depends directly on the number of gas particles present.  KMT, points out that the number of collisions is the pressure and if there is an increase in the number of particles that increases the number of collisions and pressure. To keep the pressure constant the volume must increase.

The Meaning of Temperature  The Kelvin scale indicates the average Kinetic energy of gas particles. WHY average?  The exact relationship is PV/n=RT=2/3(KE) ave  Or (KE) ave =3/2RT

Average Kinetic energy

Root Mean Square  The average velocity of gas particles is special.  The symbol u 2(with a line over it) is the average squares of the particle velocities.  The square root of the number is the Root Mean Square velocity.  u rms

So what do we use RMS for?  RMS is used to find the velocity of gas particles based on their mass.  The units for R in this case are:  J/K mol  Take home: speed is determined by both Temperature and Mass of particle

Average speed of certain gas molecules at the same temperature

Effusion and Diffusion  Effusion:  The passage of a gas through a tiny orifice.  Diffusion:  The rate at which a gas moves from area of high concentration to low concentration  Demo!

Graham’s law of effusion  Larger molecules will migrate slower than a smaller molecule under a constant temperature.  This is in direct violation of the KMT.  REAL GASES

Graham’s Law and Diffusion  In diffusion, one may expect the gases to act similarly to effusion.  NH 3 (g)+HCl(g)  NH 4 Cl(s)  Plug into Graham’s Law and find the relative rates of effusion to be 1.5  The actual ratio is less. Distance NH 3 =u rms NH 3 Distance HCl u rms HCl Sq root M NH3 M HCl M HCl Sq root =1.5

Diffusion of a gas is more complicated than its rate.