Transcript Gases - Weebly
Gases
GASES Kinetic theory of gases Behavior of gases pressure manometers Units of pressure Partial pressure of a gas Pressure vs.
volume Pressure vs.
temperature Combined gas law Ideal gas law Temperature vs. volume Diffusion/effusion
Diffusion and Effusion
• Diffusion – 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
Graham’s Law
Graham’s Law
• Conceptual: • Lighter gases travel quicker at the same temp • Consider H 2 vs. Cl 2 Which would diffuse at the greater velocity?
Graham’s Law
• Calculating the speed of a molecule can be done using the following equation
Graham’s Law
• Calculate the rms speed of an N 2 molecule at 25 o C • Convert temp to Kelvin • MM = 28 • R= 8.314 J/mol.K ( 0.0821 x 101.3) • •
Graham’s Law
• The relative rates of diffusion of two gases vary inversely with the square roots of the gram formula masses.
• Mathematically:
rate
1
rate
2
gfm
2
gfm
1
Graham’s Law Problem
• A helium atom travels an average 1000. m/s at 250 temperature?
o C. How fast would an atom of radon travel at the same • Solution: – Let rate 1 – Gfm 1 = x rate 2 = 1000. m/s = radon 222 g/mol – Gfm 2 = helium = 4.00 g/mol
Solution (cont.)
• Rearrange:
x rate
2
gfm
2
gfm
1
x
rate
2
gfm
2
gfm
1 • Substitute and evaluate:
x
1000 .
m s
4 .
00
g
/
mol
134
m
/
s
222
g
/
mol
Applications of Graham’s Law
• Separation of uranium isotopes – 235 U – 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
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?
Solution
• Let gfm 2 gfm 1 = x rate 2 = 4.00 rate 1 = 1 = 3.16
• From Graham’s Law,
rate rate
2 1 2
gfm
2
gfm
1
Solution, cont.
• Rearrange (
rate
1 ) 2 (
rate
2 ) 2
gfm
1
gfm
2 • Substitute and evaluate: ( 3 .
16 ) 2 4 39 .
9
g
/
mol
1 2
WWWW we do
• What is the rms speed of an He atom at 40oC
• 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