1. Gases

2. GASES manometers pressure Kinetic theory of gases Units of pressure
Behavior of gases
Partial pressure
of a gas
Pressure vs.
volume
Pressure vs.
temperature
Temperature vs.
volume
This is the path we have taken so far
We have studied the kinetic theory of gases
Behavior of gases
Pressure vs volume keeping temp constant
Whose law is this
When comparing P and T what is kept constant
Combined gas law
Ideal gas equation
What is
It choral response for value of the gas constant
Now over to pressure monometer are used to measure presuure
There are many ways of measuring pressure name units
We looked at partial pressure who had a law about this what was the law
Now we will look at the last section
Diffusion and Effusion
Diffusion/effusion
Combined gas law
Ideal gas law

3. Diffusion and Effusion
The gradual mixing of 2 gases due to random spontaneous motion
Effusion
When molecules of a confined gas escape through a tiny opening in a container
Read definitions

4. Graham’s Law Thomas Graham (1805-1869)
Do all gases diffuse at the same rate?
Graham’s law discusses this quantitatively.
Technically, this law only applies to gases effusing into a vacuum or into each other

5. Graham’s Law Conceptual: Lighter gases travel quicker at the same temp
Consider H2 vs. Cl2
Which would diffuse at the greater velocity?
At the same temperature, molecules with a smaller gfm travel at a faster speed than molecules with a larger gfm.
As gfm , v 

6. Note here that the average speed of H2 is much quicKer than the average speed of molecules of O2 at the same temp
Graham actually quantified the relationship between speed of molecule temperature and mass

7. Graham’s Law
Calculating the speed of a molecule can be done using the following equation
U is the average speed of molecules
R is the gas constant but here the value is 8.314
This the gas constant in j/mol K and is times the atm’s gas constant

8. Graham’s Law Calculate the rms speed of an N2 molecule at 25oC
Convert temp to Kelvin
MM = 28
R= J/mol.K ( x 101.3)
I will now run through the calculations of average speed of a gas and then grahams law of comparative masses
Although the equation looks quite fieghtful it is actually quite staright forward

9. Graham’s Law
The relative rates of diffusion of two gases vary inversely with the square roots of the gram formula masses.
Mathematically:
This second equation relates the masses to the speed of different gases

10. Graham’s Law Problem
A helium atom travels an average m/s at 250oC. How fast would an atom of radon travel at the same temperature?
Solution:
Let rate1 = x rate2 = m/s
Gfm1 = radon 222 g/mol
Gfm2 = helium = 4.00 g/mol
Example question

11. Solution (cont.)
Rearrange:
Substitute and evaluate:

12. Applications of Graham’s Law
Separation of uranium isotopes
235U
Simple, inexpensive technique
Used in Iraq in early 1990’s as part of nuclear weapons development program
Identifying unknowns
Use relative rates to find gfm

13. Problem 2
An unknown gas effuses through an opening at a rate 3.16 times slower than that of helium gas. What is the gfm of this unknown gas?

14. Solution Let gfm2 = x rate2 = 1 gfm1 = 4.00 rate1 = 3.16
From Graham’s Law,
If we square both side of the equation we would get

15. Solution, cont. Rearrange Substitute and evaluate:
If we square both side

16. WWWW we do
What is the rms speed of an He atom at 40oC

17. Runknown /R He = 0.1 what is the molecular mass of the unknown gas
The rate of effusion was measured for an unknown gas is 10 time slower than helium so
Runknown /R He = 0.1 what is the molecular mass of the unknown gas
What equation do we use?
How do we rearrange this to isolate mass of the unknown
Remember mass one is the mass of the unkn
What is the rms speed of an He atom at 40oC
3 x J/Kmol.x 313 4
44.1 m/s
The rate of effusion was measured for an unknown gas and for He
R unknown /R he = 0.1 what is the molecular mass of the unknown gas
Runknown
0.1 = = = 4/ M1
M1 = 4/0.01
400
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