Kinetic theory

Kinetic theory of GasesBy: Dr. Robert D. Craig, Ph.D

discrepencies between the theoretical and experimental

• In 1873, J.D. Van der Waals published his "Essay on Continuity of the Liquid and Solid States" which profoundly affected the study of Kinetic Molecular Theory. In this literature, he proposed a radical change to the hypothetical Ideal Gas Law that accounted for discrepencies between the theoretical and experimental behavior of gases. His work quickly became accepted by his peers, and thus the Van der waals equation of state was born.

Brownian motion-melting ice video

Gases and the stock marker exhibit Brownian motion

• Do atoms(molecule)Take orbit around other gas molecules?

• Do atoms Feel repulsion from one another?• Do atoms Feel attraction from one another?• Would I take up space?• How fast can I move-How far can I travel,

before I bump into another atom (molecule)

Please record-and condense vapor!!!

Please record-boiling point of water to the nearest ±0.1 oC.• Please record-MASS OF FLASK, FOIL , • RUBBER BAND- ±0.001 Gram

*****must condense vapor to let 0.3 grams of air back in!!!!!!!!!!!!!!!!!!!!!!!

Important step

• Remove the flask and allow it cool to room temperature. Dry the outside of the flask and mass it along with its contents, the aluminum foil and rubber band.

• Puts air back in vessel you weighted at first• Demo this Rob!!!

Do this first thing!!!!

• Do this first thing!!!! (and second tip)• The mass of the vapor , m vapor is determined by• M vapor = • m flask + vapor - m flask 12.2• • Other labs-Better to determine the mass of air!!!!• Mair = density of air x volume of flask• Mair = 1.2 g/L x 0.250L = 0.3 g is significant

Do this first thing!!!!

• So convenient to use:• 1A = m flask +m air + m foil + m rubber • 3A = m flask +m vapor+ m foil + m rubber • 3A - 1A = or better yet-condense• 3A - 1A - m air = m vapor-not needed!!• Can also find density of vapor• Mair = density of air x volume of flask• Mvapor = density of air x volume of flask

How scientific theory is constructed

• Over time-this theory took 200 years!!!• Through a collection scientific views.• By many symposium and colloquia!!!

Why dates are important?

• Robert Boyle• Lord Kelvin• Charles’ Law• 200 Years later• Van der waals • John Dumas

Every once and a while . . .

• Jane Goddal• Steve Jobs• Bill Gates• Stephen Hawkins

Van der Waals-200 years after Issac Newton, Lord Kelvin, and Robert Boyle

Corrected “empirically” PV=nRT

Van der Waals Constantsfor Common Gases

Compound a (L2-atm/mol2) b (L/mol)He 0.03412 0.02370Ne 0.2107 0.01709H2 0.2444 0.02661Ar 1.345 0.03219O2 1.360 0.03803N2 1.390 0.03913CO 1.485 0.03985CH4 2.253 0.04278CO2 3.592 0.04267NH3 4.170 0.03707

Used this theory –Very important !!!

• According to the kinetic theory of gas,• - Gases are composed of very small molecules

and their number of molecules is very large.- These molecules are elastic.- They are negligible size compare to their container.- Their thermal motions are random.

Please review for exam

• To begin, let’s visualize a rectangular box with length L, areas of ends A1 and A2. There is a single molecule with speed vx traveling left and right to the end of the box by colliding with the end walls

3D Demonstration of Ideal Gas

3D Demonstration of Ideal Gas

• The time between collisions with the wall is the distance of travel between wall collisions divided by the speed

• 1.

3D Demonstration of Ideal Gas

• The frequency of collisions with the wall in collisions per second is

• 2.

3D Demonstration of Ideal Gas

• According to Newton, force is the time rate of change of the momentum

• 3.

3D Demonstration of Ideal Gas

• The momentum change is equal to the momentum after collision minus the momentum before collision.

• Since we consider the momentum after collision to be mv, the momentum before collision should be in opposite direction and therefore equal to -mv

3D Demonstration of Ideal Gas

• The momentum change is equal to the momentum after collision minus the momentum before collision.

mv2-mv1 =Dmv (x-direction)

3D Demonstration of Ideal Gas

• According to equation #3, force is the change in momentum divided by change in time . To get an equation of average force in term of particle velocity , we take change in momemtum multiply by the frequency from equation #2.

3D Demonstration of Ideal Gas

3D Demonstration of Ideal Gas“nike box”

• The pressure, P, exerted by a single molecule is the average force per unit area, A. Also V=AL which is the volume of the rectangular box.

• 6.

3D Demonstration of Ideal Gas

• Let’s say that we have N molecules (say 1 mol =6.022 x 10e23)of gas traveling on the x-axis. The pressure will be

mean square speed

• To simplify the situation we will take the mean square speed of N number of molecules instead of summing up individual molecules. Therefore, equation #7 will become

• *8.

3 possible components

• Earlier we are trying to simplify the situation by only considering that a molecule with mass m is traveling on the x axis.

•

3 possible components

• . To make a more accurate derivation we need to account all 3 possible components of the particle’s speed, vx, vy and vz.

• #9

• Since there are a large number of molecules we can assume that there are equal numbers of molecules moving in each of co-ordinate directions.

• #10.

thermal motion creates pressure

• Because the molecules are free too move in three dimensions, they will hit the walls in one of the three dimensions one third as often. Our final pressure equation becomes

• #11.

thermal motion of gas particles

• However to simplify the equation further, we define the temperature, T, as a measure of thermal motion of gas particles because temperature is much easier to measure than the speed of the particle.

thermal motion of gas particles

• The only energy involve in this model is kinetic energy and this kinetic enery is proportional to the temperature T.

• #12.

solve kinetic energy equation

• To combine the equation #11 and #12 we solve kinetic energy equation #12 for mv2.

• #13.

solve kinetic energy equation

• Since the temperature can be obtained easily with simple daily measurement like a thermometer, we will now replace the result of kinetic equation #13 with with a constant R times the temperature, T.

T is proportional to the kinetic energy

• Again, since T is proportional to the kinetic energy it is logical to say that T times k is equal to the kinetic energy E. k, however, will currently remains unknown.

• #14.

T is proportional to the kinetic energy

• Combining equation #14 with #11, we get:• #15.

• Because a molecule is too small and therefore impractical we will take the number of molecules, N and divide it by the Avogadro’s number, NA= 6.0221 x 1023/mol to get n (the number of moles)

• #16.

• Since N is divided by Na, k must be multiply by Na to preserve the original equation. Therefore, the constant R is created

• #17.

• Now we can achieve the final equation by replacing N (number of melecules) with n (number of moles) and k with R.

• #18.

Calculation of R & k

• Calculation of R & k• According to numerous tests and

observations, one mole of gas is a 22.4 liter vessel at 273K exerts a pressure of 1.00 atmosphere (atm). From the ideal gas equation above:

Calculation of R & k

• A.

• B.

Calculation of R & k

• C.

Molecular Weight of a Volatile Liquid

• Molecular Weight of a Volatile Liquid • Objectives

To determine the molecular weight of a volatile liquid.

• Discussion