2. Graham’s Law of Diffusion

3. 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

4. Derivation of Graham’s Law The average kinetic energy of gas molecules depends on the temperature: where m is the mass and v is the speed Consider two gases:

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. On average, carbon dioxide travels at 410 m/s at 25 o C. Find the average speed of chlorine at 25 o C. **Hint: Put whatever you’re looking for in the numerator.

7. At a certain temperature fluorine gas travels at 582 m/s and a noble gas travels at 394 m/s. noble gas What is the noble gas?

8. CH 4 moves 1.58 times faster than which noble gas? Governing relation:

9. So HCl dist. = 1.000 m/s (0.487 s) = 0.487 m HClNH 3 1.20 m DISTANCE = RATE x TIME HCl and NH 3 are released at same time from opposite ends of 1.20 m horizontal tube. Where do gases meet? Velocities are relative; pick easy #s:

10. 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: “mouse in the house”

11. 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.

12. 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

13. Graham’s Law The rate of diffusion/effusion is proportional to the mass of the molecules –The rate is inversely proportional to the square root of the molar mass of the gas 250 g 80 g Large molecules move slower than small molecules

14. Step 1) Write given information GAS 1 = helium M 1 = 4.0 g v 1 = x GAS 2 = chlorine M 2 = 71.0 g v 2 = x HeCl 2 Step 2) Equation Step 3) Substitute into equation and solve v1v1 v2v2 = 71.0 g 4.0 g 4.21 1 Find the relative rate of diffusion of helium and chlorine gas He diffuses 4.21 times faster than Cl 2 Cl 35.453 17 He 4.0026 2

15. If fluorine gas diffuses at a rate of 363 m/s at a certain temperature, what is the rate of diffusion of neon gas at the same temperature? Step 1) Write given information GAS 1 = fluorine M 1 = 38.0 g v 1 = 363 m/s GAS 2 = Neon M 2 = 20.18 g v 2 = x F2F2 Ne Step 2) Equation Step 3) Substitute into equation and solve 363 m/s v2v2 = 20.18 g 38.0 g 498 m/s Rate of diffusion of Ne = 498 m/s Ne 20.1797 10 F 18.9984 9

16. Find the molar mass of a gas that diffuses about 4.45 times faster than argon gas. What gas is this? Hydrogen gas: H 2 Step 1) Write given information GAS 1 = unknown M 1 = x g v 1 = 4.45 GAS 2 = Argon M 2 = 39.95 g v 2 = 1 ?Ar Step 2) Equation Step 3) Substitute into equation and solve 4.45 1 = 39.95 g x g 2.02 g/mol H 1.00794 1 Ar 39.948 18

17. Where should the NH 3 and the HCl meet in the tube if it is approximately 70 cm long? 41.6 cm from NH 3 28.4 cm from HCl Ammonium hydroxide (NH 4 OH) is ammonia (NH 3 ) dissolved in water (H 2 O) NH 3 (g) + H 2 O (l) NH 4 OH (aq) Stopper 1 cm diameter Cotton plug Stopper Clamps 70-cm glass tube

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

19. 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.

20. 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

21. 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

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23. 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

24. 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

25. 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 1.0 1 H 2 = 2 g/mol

26. Graham's Law Keys Graham's Law http://www.unit5.org/chemistry/GasLaws.html