Kinetic Molecular Theory

Energy Kinetic Potential Energy of motion Energy due to position SI unit: joules ( J ) 1J = 1kgm2/s2 = 1Nm Equation: KE = ½ mu2

KMT Assumptions Gas molecules are separated from each other by distances far greater than their own dimensions Gas molecules are in constant motion in random directions, & frequently collide with one another in perfectly elastic collisions Gas molecules exert neither attractive nor repulsive forces on one another Average kinetic energy of the molecules is proportional to temperature of the gas in kelvin; any two gases at the same temp will have the same KE

Distribution of Molecular Speeds

Gas Behavior Ideal Real Hypothetical P-V-T behavior can be completely accounted for by ideal gas equation No attraction or repulsion Volume is negligible Behave like an ideal gas, but not under all conditions Do attract one another and have a finite volume conditions under which a gas will deviate: High pressure Low temperature

Gas Behavior Diffusion Effusion Gradual mixing of the molecules of one gas with the molecules of another by virtue of their kinetic properties High to low Gradual not instant Lighter gases diffuse through a certain space more quickly Process by which a gas under pressure escapes from one compartment of a container to another by passing through a small opening molecular path

r1 r2 M2 M1  =

Example 1 Under the same conditions of temperature and pressure, how many times faster will helium diffuse compared to nitrogen?

Example 2 What is the relative rate of diffusion of carbon dioxide compared to hydrogen? Does carbon dioxide effuse faster or slower than hydrogen?

Example 3 An unknown gas diffuses 0.25 times faster than helium. What is the molar mass of the unknown gas?