1. Chapter 14 “The Behavior of Gases”

2. Section14-1 Properties of Gases

3. Compressibility Gases can expand to fill its container, unlike solids or liquids Gases can expand to fill its container, unlike solids or liquids The reverse is also true: The reverse is also true: They are easily compressed, or squeezed into a smaller volume They are easily compressed, or squeezed into a smaller volume Compressibility is a measure of how much the volume matter decreases under pressure Compressibility is a measure of how much the volume matter decreases under pressure

4. Compressibility This is the idea behind placing “air bags” in automobiles This is the idea behind placing “air bags” in automobiles In an accident, the air compresses more than the steering wheel or dash when you strike it In an accident, the air compresses more than the steering wheel or dash when you strike it

5. Compressibility Airbags fill with N 2 gas in an accident. Airbags fill with N 2 gas in an accident. Gas is generated by the decomposition of sodium azide, NaN 3. Gas is generated by the decomposition of sodium azide, NaN 3. 2 NaN 3 ---> 2 Na + 3 N 2 2 NaN 3 ---> 2 Na + 3 N 2 The impact forces the gas particles closer together, because there is a lot of empty space between them The impact forces the gas particles closer together, because there is a lot of empty space between them

6. Variables that describe a Gas The four variables and their common units: 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 The amount of gas, volume, and temperature are factors that affect gas pressure.The amount of gas, volume, and temperature are factors that affect gas pressure.

7. 1. Amount of Gas When we inflate a balloon, we are adding gas molecules. When we inflate a balloon, we are adding gas molecules. Increasing the number of gas particles increases the number of collisions Increasing the number of gas particles increases the number of collisions thus, the pressure increases thus, the pressure increases If temperature is constant- doubling the number of particles doubles the pressure If temperature is constant- doubling the number of particles doubles the pressure

8. Pressure and the number of molecules are directly related More molecules means more collisions. More molecules means more collisions. Fewer molecules means fewer collisions. Fewer molecules means fewer collisions. Gases naturally move from areas of high pressure to low pressure because there is empty space to move into – a spray can is example. Gases naturally move from areas of high pressure to low pressure because there is empty space to move into – a spray can is example.

9. Common use? Aerosol (spray) cans Aerosol (spray) cans gas moves from higher pressure to lower pressure gas moves from higher pressure to lower pressure a propellant forces the product out a propellant forces the product out whipped cream, hair spray, paint whipped cream, hair spray, paint Is the can really ever “empty”? Is the can really ever “empty”? Gas Propellant Paint Gas pressure forces paint up tube

10. 2. Volume of Gas In a smaller container, the molecules have less room to move. In a smaller container, the molecules have less room to move. The particles hit the sides of the container more often. The particles hit the sides of the container more often. As volume decreases, pressure increases. (think of a syringe) As volume decreases, pressure increases. (think of a syringe)

11. 3. Temperature of Gas Raising the temperature of a gas increases the pressure, if the volume is held constant. Raising the temperature of a gas increases the pressure, if the volume is held constant. The molecules hit the walls harder, and more frequently! The molecules hit the walls harder, and more frequently! Should you throw an aerosol can into a fire? What could happen? Should you throw an aerosol can into a fire? What could happen? When should your automobile tire pressure be checked? When should your automobile tire pressure be checked?

12. Sec. 14-2 The Gas Laws These will describe HOW gases behave. These will describe HOW gases behave. Gas behavior can be predicted by the theory. Gas behavior can be predicted by the theory. The amount of change can be calculated with mathematical equations. The amount of change can be calculated with mathematical equations. You need to know both of these: the theory, and the math You need to know both of these: the theory, and the math

13. Robert Boyle (1627-1691) Boyle was born into an aristocratic Irish family Became interested in medicine and the new science of Galileo and studied chemistry. A founder and an influential fellow of the Royal Society of London Wrote extensively on science, philosophy, and theology.

14. #1. Boyle’s Law - 1662 Pressure x Volume = a constant Pressure x Volume = a constant Equation: P 1 V 1 = P 2 V 2 (T = constant) Equation: P 1 V 1 = P 2 V 2 (T = constant) Gas pressure is inversely proportional to the volume, when temperature is held constant.

15. Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

16. P 1 x V 1 = P 2 x V 2 Boyle’s Law Constant temperature Constant amount of gas

17. A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg

18. Practice Problems 1.00 L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas? 1.00 L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas?

19. Practice Problems In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 10 6 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion? In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 10 6 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion?

20. Practice Problems Synthetic diamonds can be manufactured at pressures of 6.00 x 10 4 atm. If we took 2.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 10 4 atm, what would the volume of that gas be? Synthetic diamonds can be manufactured at pressures of 6.00 x 10 4 atm. If we took 2.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 10 4 atm, what would the volume of that gas be?

21. Jacques Charles (1746-1823) French Physicist French Physicist Part of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humansPart of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans This is how his interest in gases startedThis is how his interest in gases started It was a hydrogen filled balloon – good thing they were careful!It was a hydrogen filled balloon – good thing they were careful!

22. As T increasesV increases

23. #2. Charles’s Law - 1787 The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. This extrapolates to zero volume at a temperature of zero Kelvin.

24. Converting Celsius to Kelvin Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.) Reason? There will never be a zero volume, since we have never reached absolute zero. Kelvin =  C + 273 °C = Kelvin - 273 and

25. Variation of gas volume with temperature at constant pressure. V  TV  T V = constant x T V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C) + 273.15 Charles’ Law Temperature must be in Kelvin

26. 26 The Kelvin Temperature Correction: absolute zero = -273.15 0 C K = o C + 273 (use for all Gas Law problems)

27. A sample of carbon monoxide gas occupies 3.20 L at 125 0 C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = 398.15 K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V1 1.54 L x 398.15 K 3.20 L = = 192 K V 1 /T 1 = V 2 /T 2

28. Joseph Louis Gay-Lussac (1778 – 1850)  French chemist and physicist  Known for his studies on the physical properties of gases.  In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

29. #3. Gay Lussac’s Law - 1802 The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. How does a pressure cooker affect the time needed to cook food? How does high altitude affect cooking?

30. Practice Problems Determine the pressure change when a constant volume of gas at 1.00 atm is heated from 20.0 °C to 30.0 °C. Determine the pressure change when a constant volume of gas at 1.00 atm is heated from 20.0 °C to 30.0 °C. 1.00 atm / 293 K = x / 303 K; x = 1.03 atm.

31. Practice Problems A gas has a pressure of 699.0 mm Hg at 40.0 °C. What is the temperature at standard pressure? A gas has a pressure of 699.0 mm Hg at 40.0 °C. What is the temperature at standard pressure? 699.0 mm Hg / 313 K = 760 mm Hg / x 699.0 mm Hg / 313 K = 760 mm Hg / x

32. #4 Combined Gas Law The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P 1 V 1 P 2 V 2 = T 1 T 2 T 1 T 2 No, it’s not related to R2D2

33. Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyle’s Law Charles’ Law Gay-Lussac’s Law

34. Combined Gas Law Problem A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P 1 = 0.800 atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ??

35. Calculation P 1 = 0.800 atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ?? P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 = P 1 V 1 T 2 = P 2 V 2 T 1 T 1 T 2 T 1 T 2 T 2 = P 2 V 2 T 1 P 1 V 1 P 1 V 1 T 2 = 3.20 atm x 90.0 mL x 302 K 0.800 atm x 180.0 mL T 2 = 604 K - 273 = 331 °C = 604 K

36. Learning Check A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg? A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

37. One More Practice Problem A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

38. Section 14.3 Ideal Gases

39. Avogadro’s Hypothesis Equal volumes of gases at the same T and P have the same number of molecules. V and n are directly related. twice as many molecules

40. 40 14.3: The Ideal Gas Law Boyle’s Law - V  1/P (constant T & n (amount)) Boyle’s Law - V  1/P (constant T & n (amount)) Charles’ Law – V  T (at constant P & n) Charles’ Law – V  T (at constant P & n) Avogadro’s Law – V  n (at constant T & P) Avogadro’s Law – V  n (at constant T & P) Gay-Lussac’s Law – P  T (with constant V & n) Gay-Lussac’s Law – P  T (with constant V & n) Combine these four laws into one statement Combine these four laws into one statement V  nT/P Convert the proportionality into an equality Convert the proportionality into an equality V = nRT/P

41. IDEAL GAS LAW Brings together gas properties. Can be derived from experiment and theory. BE SURE YOU KNOW THIS EQUATION! P V = n R T

42. Using PV = nRT P = Pressure V = Volume T = Temperature N = number of moles R is a constant, called the Ideal Gas Constant Instead of learning a different value for R for all the possible unit combinations, we can just memorize one value and convert the units to match R. R = 0.0821 R = 0.0821 L atm Mol K

43. We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: P x V P x V R x T R x T The Ideal Gas Law n =

44. Ideal Gases We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure An ideal gas does not really exist, but it makes the math easier and is a close approximation. An ideal gas does not really exist, but it makes the math easier and is a close approximation. Particles have no volume? Wrong! Particles have no volume? Wrong! No attractive forces? Wrong! No attractive forces? Wrong!

45. Ideal Gases There are no gases for which this is true; however, There are no gases for which this is true; however, Real gases behave this way at a) high temperature, and b) low pressure. Real gases behave this way at a) high temperature, and b) low pressure. Because at these conditions, a gas will stay a gas! Because at these conditions, a gas will stay a gas!

46. #6. Ideal Gas Law 2 P x V = m x R x T M P x V = m x R x T M Allows LOTS of calculations, and some new items are: Allows LOTS of calculations, and some new items are: m = mass, in grams m = mass, in grams M = molar mass, in g/mol M = molar mass, in g/mol Molar mass = m R T P V Molar mass = m R T P V

47. Density Density is mass divided by volume Density is mass divided by volume m Vso, m M P m M P V R T V R T D = =

49. Ideal Gases don’t exist, because: 1. Molecules do take up space 2. There are attractive forces between particles - otherwise there would be no liquids formed

50. Real Gases behave like Ideal Gases... When the molecules are far apart. When the molecules are far apart. The molecules do not take up as big a percentage of the space The molecules do not take up as big a percentage of the space We can ignore the particle volume. We can ignore the particle volume. This is at low pressure This is at low pressure

51. Real Gases behave like Ideal Gases… When molecules are moving fast When molecules are moving fast This is at high temperature This is at high temperature Collisions are harder and faster. Collisions are harder and faster. Molecules are not next to each other very long. Molecules are not next to each other very long. Attractive forces can’t play a role. Attractive forces can’t play a role.

52. Section 14.4 Gases: Mixtures and Movements

53. Dalton’s Law of Partial Pressures Dalton’s Law of Partial Pressures 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. 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.

54. 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: 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

55. Diffusion is: Effusion: Gas escaping through a tiny hole in a container. 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. 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.

56. 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

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

58. Graham’s Law Graham’s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Derived from: Kinetic energy = 1/2 mv 2 Derived from: Kinetic energy = 1/2 mv 2 m = the molar mass, and v = the velocity. m = the molar mass, and v = the velocity. Rate A  Mass B Rate B  Mass A =

59. Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 With effusion and diffusion, the type of particle is important: With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Graham’s Law