Chem 105 Friday 3 Dec 2010

Transcription

1 Chem 105 Friday 3 Dec 010 Today: Kinetic-molecular theory Diffusion and effusion Course Questionnaires Real gases & Van der Waals equation Hour Exam 4 (Chap 9, 10, 11) Friday. Dec 10 A practice exam will be posted today at 1/3/010 1

2 1. Kinetic-olecular Theory of Gases 1/3/010

3 Precepts of the Kinetic-olecular Theory of Gases 1. Gases (at moderate pressures and temperatures) are mostly empty space. The atoms or molecules are widely spaced. (Air at STP is 99.9% empty space.). Atoms or molecules are in constant motion. They collide randomly in elastic collisions. That is, no energy is lost. (If energy was lost in collisions, gases would cool spontaneously, but they don t.) 3. Average molecular speed = constant * T 1/3/010 3

4 Why are atom atom (or molecule molecule) collisions elastic? Because in a collision, the translational kinetic energy of the molecules is converted to potential energy of nuclear repulsion, then it goes back into kinetic energy. He He He He He He Energy > atoms change direction He He Distance (Å) Kinetic energy Nuclear+electron potential energy When the repulsion energy = initial kinetic energy, the molecules fly apart. The resulting kinetic energy is distributed randomly between the two molecules. 1/3/010 4

5 Elastic collisions closely resemble molecular vibrations: - Collisions and vibrations occur on the same time-scale. That is, the relative motions take place within about 10 femtoseconds (fs) in each case. - Vibrating atoms also lose no energy as they oscillate about their equilibrium positions. 1/3/010 5

6 Gas pressure is due to collisions of gas particles with walls of the container. If you know the average speed of particles, you can calculate the pressure. Atom of mass m moving at speed u Atom bounces off wall Atom now moving at speed u Container wall feels pressure due to elastic collisions of gas molecules with the wall. 1/3/010 6

7 The force of one collision= F = m x acceleration t = average time interval between collisions on either wall. = m x Δu Δt Change in speed = u Average time interval from one collision to the next. t = x length of box = L u u (The faster the atoms are moving, the shorter this time is, and the greater the force.) F m x u L u mu L 1/3/010 7

8 These terms are correct. Keller did not recognize that L and wall area do in fact belong together in the denominator. Pressure force wall area mu L wall area L x mu wall area mu volume Pre Pressure mu So the Kinetic Theory of Gases is actually USEFUL! We can use it to calculate a macroscopic property of gas (P) starting with speed of the particles (u). 1/3/010 8

9 What kind of speeds, u, are we talking about? O This is called the root mean square speed, u rms = 490 m/s (1096 mi/h) 1/3/010 9

10 Boltzmann plots are named for Ludwig Boltzmann, who developed molecular theory in late 1800s. RV heading to Denali Park in July Just came out of the Blue Loon The Boltzmann distribution of molecular speeds is like the distribution of vehicle speeds on the Parks Highway. 1/3/010 10

11 Now if volume = V, then PV = mu And if we recall the Ideal Gas Equation: PV = nrt, then nrt = mu Or u = nrt/m The above derivations were first carried out in 1850s by James Clerk axwell when he derived this temperature dependence of u. This is axwell s Equation for the average speed of gas molecules which is shown more exactly below. Root-meansquare speed u rms u Square root of the average of squared speeds 3RT Gas constant R J/mol-K Absolute Temp (K) olar mass (g/mol) 1/3/010 11

12 Remember that u T 1/ - olecules fly faster at high temperatures. and u 1/ 1/ - Large molecules go slower than small molecules 1/3/010 1

13 ass dependence of molecular speeds at 5 C. Number 1/3/010 13

14 . Diffusion and effusion 1/3/010 14

15 Diffusion = particle movement over large distances in a gas or liquid. Rate of diffusion is proportional to u rms, but is much slower than u rms due to collisions. u rms for NH 3 is about 600 mi/h at room temp. NH 3 diffuses through air at about 5 mi/h. 1/3/010 15

16 Kinetic-olecular Theory of Gases Tracking enabled. This illustrates why, especially at high pressures, diffusion is much slower than u. 1/3/

17 Effusion = escape from a gas container through a pin-hole. This is similar to diffusion, but much easier to measure experimentally. He Rate of effusion u rms Rate of effusion of gas α u rms 3RT 1/3/010 17

18 We commonly measure the RATIO of effusion rates for two gases, 1 and both a same temperature T. Rate of effusion of gas1 α 3RT 1 Rateof effusion of gas α 3RT Rateof effusion of gas1 Rateof effusion of gas 3RT 1 3RT 3RT 1 3RT /3/010 18

19 Application of effusion rate Radioactive uranium isotope U 35 is enriched from stable isotope U 38 by converting to the mixture to UF 6, the forcing it through a metal membrane containing many small orifices. The lighter isotope effuses faster. Rate Rate /3/010 19

20 3. Real gases and van der Waals equation (next week) Course Questionnaires 1/3/010 0