Transcript Law and Chaos - Chemistry Department, University College Cork

Molecular Kinesis
CM2004
States of Matter:
Gases
Molecules on the Move
In 17th and 18th centuries many scientists believed that
molecules stayed in one place; repelling each other in
the “ether”
In contrast Daniel
Bernoulli believed
that air contained
“..very minute
corpuscles which
are driven hither
and thither with a
very rapid motion”
(1738)
SIMULATION
http://mc2.cchem.berkeley.edu/Java/molecules/index.html
What Happens when the
Pressure is On?
• Bernoulli suggested (in 1734)
that the pressure of the gas on
the walls of its container is the
sum of the many collisions
made by the individual particles
all moving independently
• From this idea and Newton’s
Law it can be reasoned that the
pressure is proportional to
developed momentum (mv)
and frequency and therefore
the particle density
John Herapath’s Concept
• In 1820, John
Herapath suggested
that temperature
was equated with
motion
• The concept was
rejected by the
famous scientist
Humphrey Davy
who pointed out
that it would imply
an absolute zero in
temperature.
• Oops!
Davy studied the oxides of
nitrogen and discovered the
physiological effects of nitrous
oxide, which became known as
laughing gas. In 1815 he invented
a safety lamp for use in gassy
coalmines, allowing deep coal
seams to be mined despite the
presence of methane.
Molecular Motion and Pressure
• About 120 years after the original
suggestion, Bernoulli’s kinetic
theory of gases was revisited by
scientists such as Rudolf Clausius
(1857)
• The main questions posed were
related to Newton’s Laws:
• Do molecules move through space
at constant velocity
(encountering no resistance
except when they collide with
each other or effect a pressure on
a wall)?
Or is there an average velocity?
Hitting the Wall
Pressure on the wall depends on the force delivered
with each impact and the number of collisions per
unit area.
Force = mass x acceleration
m.vs-1
= momentum x frequency
mv.s-1
= momentum x 1/time
mv.s-1
Momentum of
particle changes
each time it hits
the wall
Magnitude of
momentum
transfer is 2mv
Wall Pressure
Hence:
Time is proportional to distance.
Therefore a TIME x AREA product
is equivalent to VOLUME
Collision Rate (Z)
per unit area
Collision Rates, Z
Collision rates depend upon:
PARTICLE VELOCITY
(v)
NUMBER OF PARTICLES
(AVOGADRO’S NUMBER, No)
VOLUME
(V)
http://www.phy.ntnu.edu.tw/java/idealGas/idealGas.html
LOW
HIGH
Pressure of the Collisions
Therefore:
Unit Check:
v=distance/time
Pressure
Speed and Statistics
• Clearly very large numbers of
molecules could potentially be
involved for collisions in small
volumes
• Would the molecules all be
travelling at the same speed?
• James Clerk Maxwell applied
the increasingly fashionable
mathematical science of the
collection, organization, and
interpretation of numerical
data (statistics) to the
problem
• In 1866, he established a
distribution of gas speeds as
a function of molecular weight
Populations and Probabilities
(1859-1871)
• Ludwig Boltzmann knew that
the random motion of atoms
gives rise to pressure
• He also knew that the process
makes heat and leaves the
atoms, generally, in a more
<v>
disordered state
• In other words hot does not
always flow to cold: there is a
distribution of probability in
large populations
(Population)
• This statistical idea was
quantified by the MaxwellBoltzmann theory
Maxwell-Boltzmann Fractions
Exponential Function
The importance of the Maxwell-Boltzmann
distribution is that it allows us to calculate the
Fraction (probability) of molecules (F1-F2)
travelling with Speeds (v1-v2)....and the
speeds are related to molecular energies.