1. Root Mean Square Velocity (urms)
urms = √(3RT/M)
R = J/K(mol)
T = temp in KELVIN
M = mass of one mole in KILOGRAMS (use the molar mass from the periodic table and convert to kg/mol)

2. RMS Example
Calculate the root mean square velocity for the atoms in a sample of oxygen gas at 0ºC.
Answer: 461 m/s
At 300ºC
Answer: 668 m/s

3. Graham’s Law of Effusion
Diffusion: Movement of particles from areas of higher concentration to lower concentration
Effusion: The process where molecules of a gas in a container randomly pass through a hole in the container.

4. Graham’s Law of Effusion
Rate of Effusion for gas 1 = √M2
Rate of Effusion for gas 2 √ M1
M = molar masses of the gases
Example 1: Compare the rate of effusion of carbon dioxide with that of hydrogen chloride at the same temperature and pressure.
Answer: CO2 effuses 0.9X as fast as HCl.

5. Example #2
If a molecule of neon gas travels at an average of 400m/s at a given temp., estimate the average speed of a molecule of butane gas, C4H10, at the same temp.
Answer: 235m/s

6. Larger GFM = slower rate of effusion.
Summary…
Larger GFM = slower rate of effusion.

7. Real Gases No gas actually follows the ideal gas law
Some come close at low pressures and/or high temperatures
Under certain conditions (see above), gases behave more like ideal gases

8. Van der Waals Equation
Corrects the ideal gas equation to take nonideal conditions into account
(P + n2a)(V-nb) = nRT V2
P= pressure of gas (atm)
V = volume of gas (L)
n = moles of gas
T = temperature (K)
R = L(atm)/mol(K)

9. Defining Variables…MORE.
a = a constant, different for each gas, that takes into account the attractive forces between molecules (table 5.3 pg. 216)
b = a constant, different for each gas, that takes into account the volume of each molecule (table 5.3 pg. 216)

10. Example
Calculate the pressure exerted by mol of He in a L container at -25.0ºC
Using the ideal gas law
Answer: atm
Using van der Waal’s equation
Answer: atm
You can calculate percent error: 3%

11. Pollution and Atmospheric Gases
Your book discusses these - you can read about them at the end of chapter 5, but we will not be going over them in class…