# KMT, Graham’s Law & Real Gases

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KMT, Graham’s Law & Real Gases

Kinetic Molecular Theory
1. Volume of individual particles is  zero. 2. Collisions of particles with container walls cause pressure exerted by gas.

Kinetic Molecular Theory
3. Particles exert no forces on each other. 4. Average kinetic energy  Kelvin temperature of a gas.

Equations Related to KMT
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.) (The derivation of this equation can be found in many college physics texts)

Average velocity of the gas particles uRMS = (3RT/M)1/2
Root Mean Square Speed Average velocity of the gas particles uRMS = (3RT/M)1/2 M is in Kg R = J/K mol

Diffusion: describes the mixing of gases
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Effusion: describes the passage of gas into an evacuated chamber.

The Effusion of a Gas into an Evacuated Chamber

Diffusion: HCI(g) and NH3(g) Meet in a Tube

Graham’s Law Effusion: Diffusion:

Real Gases Must correct ideal gas behavior when at high pressures and low temperatures -volume of molecules becomes significant -attractive forces become important

Gas at Low (a) and High (b) Concentration

Volume Taken up by Gas Particles

Plots of PV/nRT Versus P for Several Gases (200 K)

Plots of PV/nRT Versus P for Nitrogen Gas at Three Temperatures

Calculate the relative rates of diffusion of H2(g) and Br2(g) at the same conditions.

The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane gas is 47.8 mL/min. What is the molar mass of the unknown gas?

Real Gases – van der Waal’s Equation
corrected pressure corrected volume Van der Waal’s constants, a and b, are dependent on the type of gas molecule (see table 5.3)

Practice Problems Which gas will diffuse faster, ammonia (NH3) or carbon dioxide (CO2)? What are their relative rates of diffusion? Freon-12 is used as a refrigerant in central home air-conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass = g/mol) is 1.07:1. The formula of Freon-12 is one of the following: CF4, CF3Cl, CF2Cl2, CFCl3 or CCl4

Answers NH3 diffuses 1.6 times faster CF2Cl2