graham’s law of diffusion hcl nh 3 100 cm nh 4 cl(s) choice 1: both gases move at the same speed...
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Graham’s Law of Diffusion
Graham’s Law of Diffusion
HCl NH3
100 cm 100 cm
NH4Cl(s)
Choice 1: Both gases move at the same speed and meet in the middle.
Diffusion
HCl NH3
81.1 cm 118.9 cm
NH4Cl(s)
Choice 2: Lighter gas moves faster; meet closer to heavier gas.
Graham’s Law
2
21
222
2112
21 v m
1v mv m
v m
1
1
22
2
21
mm
v
v
1
2
2
1
mm
vv
Consider two gases at same temp.Gas 1: KE1 = ½ m1 v1
2
Gas 2: KE2 = ½ m2 v22
Since temp. is same, then… KE1 = KE2
½ m1 v12 = ½ m2 v2
2
m1 v12 = m2 v2
2
Divide both sides by m1 v22…
Take square root of both sides to get Graham’s Law:
Graham’s Law
DiffusionDiffusion– Spreading of gas molecules throughout
a container until evenly distributed.
EffusionEffusion– Passing of gas molecules through a tiny
opening in a container
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Graham’s Law
KE = ½mv2
Speed of diffusion/effusionSpeed of diffusion/effusion– Kinetic energy is determined by the temperature of
the gas.
– At the same temp & KE, heavier molecules move more slowly.
• Larger m smaller v
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Graham’s Law
Graham’s LawGraham’s Law– Rate of diffusion of a gas is inversely related to the
square root of its molar mass.
– The equation shows the ratio of Gas A’s speed to Gas B’s speed.
A
B
B
A
m
m
v
v
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Determine the relative rate of diffusion for krypton and bromine.
1.381
Kr diffuses 1.381 times faster than Br2.
Kr
Br
Br
Kr
m
m
v
v2
2
A
B
B
A
m
m
v
v
g/mol83.80
g/mol159.80
Graham’s Law
The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “vA/vB”.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Kr83.80
36
Br79.904
35
A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions?
A
B
B
A
m
m
v
v
2
2
2
2
H
O
O
H
m
m
v
v
g/mol 2.02
g/mol32.00
m/s 12.3
vH 2
Graham’s Law
3.980m/s 12.3
vH 2
m/s49.0 vH 2
Put the gas with the unknown
speed as “Gas A”.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
O15.9994
8
H1.00794
1
An unknown gas diffuses 4.0 times faster than O2. Find its molar mass.
Am
g/mol32.00 16
A
B
B
A
m
m
v
v
A
O
O
A
m
m
v
v2
2
Am
g/mol32.00 4.0
16
g/mol32.00 mA
2
Am
g/mol32.00 4.0
g/mol2.0
Graham’s Law
The first gas is “Gas A” and the second gas is “Gas B”. The ratio “vA/vB” is 4.0.
Square both sides to get rid of the square
root sign.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
O15.9994
8
H2.0
1
http://www.unit5.org/christjs/tempT27dFields-Jeff/GasLaw1.htm
Graham's Law
Graham's Law
Graham's Law
Diffusion
Gas Diffusion and Effusion
Graham's law governs effusion and diffusion of gas molecules.
Thomas Graham(1805 - 1869)
Rate of effusion is inversely proportional to its molar mass.
Rate of effusion is inversely proportional to its molar mass.
Aof massB of mass
B of Rate Aof Rate
NETNET MOVEMENT
To use Graham’s Law, both gases must be at same temperature.
diffusiondiffusion: particle movement from
high to low concentration
effusioneffusion: diffusion of gas particles
through an opening
For gases, rates of diffusion & effusion obey Graham’s law: more massive = slow; less massive = fast
Diffusion
Particles in regions of high concentrationspread out into regions of low concentration,
filling the space available to them.
Weather and Diffusion
Map showing tornado risk in the U.S.
HighestHigh
LOWAir Pressure
HIGHAir Pressure
Calculation of Diffusion Rate
NH3V1 = XM1 = 17 amu
HCl V2 = XM2 = 36.5 amu
Substitute values into equation
V1 moves 1.465x for each 1x move of V2
NH3 HCl
1.465 x + 1x = 2.465
200 cm / 2.465 = 81.1 cm for x
1 2
2 1
v m
v m
1
2
36.5
17
v
v
1
2
1.465v
xv
Calculation of Diffusion Rate
V1 m2
V2 m1
= NH3V1 = XM1 = 17 amu
HCl V2 = XM2 = 36.5 amu
Substitute values into equation
V1 36.5V2 17
=
V1 V2
= 1.465
V1 moves 1.465x for each 1x move of v2
NH3 HCl
1.465 x + 1x = 2.465
200 cm / 2.465 = 81.1 cm for x