Root Mean Square Velocity (urms)
urms = √(3RT/M)
• R = 8.3145 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)
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
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.
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.
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
Summary…
Larger GFM = slower rate of
effusion.
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
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 = 0.08206 L(atm)/mol(K)
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)
Example
• Calculate the pressure exerted by 0.3000 mol
of He in a 0.2000 L container at -25.0ºC
– Using the ideal gas law
– Answer: 30.53 atm
– Using van der Waal’s equation
– Where a = 0.0341 and b = 0.0237
– Answer: 31.60 atm
• You can calculate percent error: 3%
– |experimental – accepted|/accepted = ___ x 100 =
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…