Molecular Kinesis Molecular Kinesis

CM2004 CM2004 States of Matter: States of Matter: Gases Gases

Molecules on the MoveMolecules on the Move

http://mc2.cchem.berkeley.edu/Java/molecules/index.html

SIMULATION

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)

What Happens when the What Happens when the Pressure is On?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 ConceptJohn 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 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 WallHitting the WallPressure 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 PressureWall Pressure

Hence:

Collision Rate (Z) per unit area

Time is proportional to distance. Therefore a TIME x AREA product is equivalent to VOLUME

Collision Rates, ZCollision Rates, ZCollision rates depend upon: LOW

HIGH

PARTICLE VELOCITY (v)

NUMBER OF PARTICLES (AVOGADRO’S NUMBER, No)

VOLUME (V)

http://www.phy.ntnu.edu.tw/java/idealGas/idealGas.html

Pressure of the CollisionsPressure of the Collisions

Therefore:

Unit Check: Pressure

v=distance/time

Speed and StatisticsSpeed 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 ProbabilitiesPopulations and Probabilities (1859-1871)(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 disordered state

• In other words hot does not always flow to cold: there is a distribution of probability in large populations

• This statistical idea was quantified by the Maxwell-Boltzmann theory

(Population)

<v>

Maxwell-Boltzmann FractionsMaxwell-Boltzmann Fractions

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.

Exponential Function