1. U NIT 4 G AS L AWS Chemistry CDO High School

2. Important Characteristics of Gases 1) Gases are highly compressible An external force compresses the gas sample and decreases its volume, removing the external force allows the gas volume to increase. 2) Gases are thermally expandable When a gas sample is heated, its volume increases, and when it is cooled its volume decreases. 3) Gases have high viscosity Gases flow much easier than liquids or solids. 4) Most Gases have low densities Gas densities are on the order of grams per liter whereas liquids and solids are grams per cubic cm, 1000 times greater. 5) Gases are infinitely miscible Gases mix in any proportion such as in air, a mixture of many gases.

3. T HE N ATURE OF G ASES Three basic assumptions of the kinetic theory as it applies to gases: 1. Gas is composed of particles- usually molecules or atoms Small, hard spheres Insignificant volume; relatively far apart from each other No attraction or repulsion between particles

4. T HE N ATURE OF G ASES 2. Particles in a gas move rapidly in constant random motion Move in straight paths, changing direction only when colliding with one another or other objects Average speed of O 2 in air at 20 o C is an amazing 1660 km/h! (1.6km=1mile)

5. T HE N ATURE OF G ASES 3. Collisions are perfectly elastic- meaning kinetic energy is transferred without loss from one particle to another- the total kinetic energy remains constant

6. THE KINETIC THEORY OF GASES Gas consists of large number of particles (atoms or molecules) Particles make elastic collisions with each other and with walls of container There exist no external forces (density constant) Particles, on average, separated by distances large compared to their diameters No forces between particles except when they collide Remember the assumptions

7. V ARIABLES THAT DESCRIBE A G AS The four variables and their common units: 1. pressure (P) in kilopascals 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. amount (n) in moles

8. 1. P RESSURE OF G AS a measure of the force exerted by the gas on the walls of a container The greater the number of collisions between gas particles and the wall the greater the pressure

9. P RESSURE C ONVERSIONS 1 atm = 101.3 kPa = 760 mmHg = 760 torr The pressure in Tucson 668 mmHg, what is that pressure in: atm kPa torr

10. 2. A MOUNT OF G AS Increasing the number of gas particles increases the number of collisions thus, the pressure increases

11. P RESSURE AND THE NUMBER OF MOLECULES ARE DIRECTLY RELATED Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into

12. 3. V OLUME OF G AS As volume decreases, pressure increases. Thus, volume and pressure are inversely related to each other

13. 4. T EMPERATURE OF G AS Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related)

14. D ENSITY OF G AS AT STP One mole of any gas at STP occupies 22.4 L. The mass of one mole of a substance can be used with the molar volume to calculate the density of the gas as a g/L value. What is the density of SO 2 gas at STP, in g/L?

15. P RACTICE What is the density, in g/L, of C 2 H 6 at STP?

16. P RACTICE What is the molar mass of a gas that has a density of 0.890 g/L at STP?

17. T HE G AS L AWS

18. #1. B OYLE ’ S L AW Gas pressure is inversely proportional to the volume, when temperature is held constant.

19. #2. C HARLES ’ S L AW The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.

20. C ONVERTING C ELSIUS TO K ELVIN Gas law problems involving temperature will always require that the temperature be in Kelvin. Kelvin =  C + 273 °C = Kelvin - 273 and

21. #3. G AY -L USSAC ’ S L AW The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.

22. #5. T HE C OMBINED G AS L AW The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. P 1 = Initial Pressure V 1 = Initial Volume T 1 = Initial Temperature in Kelvin P 2 = Final Pressure V 2 = Final Volume T 2 = Final Temperature in Kelvin

23. The combined gas law contains all the other gas laws! If the temperature remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

24. The combined gas law contains all the other gas laws! If the pressure remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Charles’s Law

25. u The combined gas law contains all the other gas laws! u If the volume remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac’s Law

26. E XAMPLES The volume of some amount of a gas was 1.00 L when the pressure was 10.0 atm; what would the volume be if the pressure decreased to 1.00 atm?

27. The volume of some amount of a gas was 1800 mL when the pressure was 98 kPa; what would the volume be if the pressure decreased to 400 mmHg?

28. A gas occupied a volume of 6.54 mL at 25°C what would its volume be at 100°C?

29. A gas occupied a volume of 3.2 L at 90 o C what would be the temperature of the gas if the volume is increased to 5.0L ?

30. A gas has a pressure of 750 torr at 15 o C. If the pressure is increased 1025 torr, what is the new temperature?

31. A gas has a pressure of 250 kPa at 100 K. If the pressure is increased 3.5 atm, what is the new temperature?

32. A 1.00 L balloon at 25.0 o C has a pressure of 750 mmHg. If the temperature is increased to 37.0 o C and the pressure is decreased to 740 mmHg, what is the new volume?

33. 0.85 L of a gas 125.0 o C has a pressure of 1.25 atm. If the temperature is increased to 237.0 o C and the pressure is decreased to 0.85 atm, what is the new volume?

34. A VOGADRO ' S L AW The amount of gas, in moles, is directly related to the volume of the gas. n 1 = Initial amount of gas in moles n 2 = Final amount of gas in moles

35. 1.75 mol of gas occupies a volume of 1.5 L what would be the volume if the amount of gas is decreased to 0.68 mol?

36. 3.5 mol of gas occupies a volume of 300 mL what would be the volume if the amount of gas is increased to 5.8 mol?

37. #6. T HE I DEAL G AS L AW #1 Equation: PV = nRT Ideal Gas Constant (R) R = 0.08206 (L atm) / (mol K) The other units must match the value of the constant, in order to cancel out.

39. #7. I DEAL G AS L AW 2 PVmm = gRT g = mass, in grams mm = molar mass, in g/mol

41. I DEAL G AS E QUATION #3 Density is mass divided by volume PM r = dRT d = density M r = Molar Mass

43. #8 D ALTON ’ S L AW OF P ARTIAL P RESSURES For a mixture of gases in a container, P Total = P 1 + P 2 + P 3 +... P 1 represents the “partial pressure”, or the contribution by that gas. Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.

44. Collecting a gas over water – one of the experiments in this unit involves this. Connected to gas generator

45. If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: 2 atm + 1 atm + 3 atm = 6 atm Sample Problem 14.6, page 434 1 2 3 4

47. I DEAL G ASES DON ’ T EXIST, BECAUSE : 1. Molecules do take up space 2. There are attractive forces between particles - otherwise there would be no liquids formed

48. R EAL G ASES BEHAVE LIKE I DEAL G ASES... When the molecules are far apart. The molecules do not take up as big a percentage of the space We can ignore the particle volume. This is at low pressure

49. R EAL G ASES BEHAVE LIKE I DEAL G ASES … When molecules are moving fast This is at high temperature Collisions are harder and faster. Molecules are not next to each other very long. Attractive forces can’t play a role.

50. D IFFUSION IS : Effusion: Gas escaping through a tiny hole in a container. Both of these depend on the molar mass of the particle, which determines the speed. u Molecules moving from areas of high concentration to low concentration. u Example: perfume molecules spreading across the room.

51. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Molecules move from areas of high concentration to low concentration. Fig. 14.18, p. 435

52. Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire… Diffusion and effusion are explained by the next gas law: Graham’s