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Molecular Kinesis. CM2004 States of Matter: Gases. Molecules on the Move. In 17 th and 18 th centuries many scientists believed that molecules stayed in one place; repelling each other in the “ether”.
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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) http://mc2.cchem.berkeley.edu/Java/molecules/index.html SIMULATION
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: HIGH LOW 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 Collisions v=distance/time Therefore: Unit Check: 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 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 <v> (Population)
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.
