2. Graham’s Law of Diffusion

3. HCl NH 3 100 cm NH 4 Cl(s) Choice 1: Both gases move at the same speed and meet in the middle.

4. Diffusion HCl NH 3 81.1 cm 118.9 cm NH 4 Cl(s) Choice 2: Lighter gas moves faster; meet closer to heavier gas.

5. Graham’s Law Consider two gases at same temp. Gas 1: KE 1 = ½ m 1 v 1 2 Gas 2: KE 2 = ½ m 2 v 2 2 Since temp. is same, then… KE 1 = KE 2 ½ m 1 v 1 2 = ½ m 2 v 2 2 m 1 v 1 2 = m 2 v 2 2 Divide both sides by m 1 v 2 2 … Take square root of both sides to get Graham’s Law:

6. Graham’s Law Diffusion –Spreading of gas molecules throughout a container until evenly distributed.Effusion –Passing of gas molecules through a tiny opening in a container Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

7. Graham’s Law KE = ½mv 2 Speed of diffusion/effusion –Kinetic energy is determined by the temperature of the gas. –At the same temp & KE, heavier molecules move more slowly. Larger m  smaller v Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

8. Graham’s Law –Rate of diffusion of a gas is inversely related to the square root of its molar mass. –The equation shows the ratio of Gas A’s speed to Gas B’s speed. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

9. Determine the relative rate of diffusion for krypton and bromine. Kr diffuses 1.381 times faster than Br 2. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “v A /v B ”. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem Kr 83.80 36 Br 79.904 35

10. A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Graham’s Law Put the gas with the unknown speed as “Gas A”. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem O 15.9994 8 H 1.00794 1

11. An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. The ratio “v A /v B ” is 4.0. Square both sides to get rid of the square root sign. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem O 15.9994 8 H 2.0 1

12. http://www.unit5.org/christjs/tempT 27dFields-Jeff/GasLaw1.htm Graham's Law

13. Diffusion

14. Gas Diffusion and Effusion Graham's law governs effusion and diffusion of gas molecules. Thomas Graham (1805 - 1869) Rate of effusion is inversely proportional to its molar mass. Rate of effusion is inversely proportional to its molar mass.

15. NET NET MOVEMENT To use Graham’s Law, both gases must be at same temperature. diffusion diffusion: particle movement from high to low concentration effusion effusion: diffusion of gas particles through an opening For gases, rates of diffusion & effusion obey Graham’s law: more massive = slow; less massive = fast

16. Diffusion Particles in regions of high concentration spread out into regions of low concentration, filling the space available to them.

17. Weather and Diffusion Map showing tornado risk in the U.S. Highest High LOW Air Pressure HIGH Air Pressure

18. Calculation of Diffusion Rate NH 3 V 1 = X M 1 = 17 amu HCl V 2 = X M 2 = 36.5 amu Substitute values into equation V 1 moves 1.465x for each 1x move of V 2 NH 3 HCl 1.465 x + 1x = 2.465 200 cm / 2.465 = 81.1 cm for x

19. Calculation of Diffusion Rate V 1 m 2 V 2 m 1 = NH 3 V 1 = X M 1 = 17 amu HCl V 2 = X M 2 = 36.5 amu Substitute values into equation V 1 36.5 V 2 17 = V1V1 V2V2 = 1.465 V 1 moves 1.465x for each 1x move of v 2 NH 3 HCl 1.465 x + 1x = 2.465 200 cm / 2.465 = 81.1 cm for x