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Gas Laws

Gas Laws. Kinetic Theory. True for ideal gases. 1. Gas molecules don’t attract or repel each other 2. Particles are smaller than the space between them They don’t have volume. Kinetic Theory. 3. Constant Random motion

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Gas Laws

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  1. Gas Laws

  2. Kinetic Theory True for ideal gases. 1. Gas molecules don’t attract or repel each other 2. Particles are smaller than the space between them • They don’t have volume

  3. Kinetic Theory 3. Constant Random motion 4. No kinetic energy is lost when molecules collide—elastic collision • All gases have same energy at a particular temperature. **Actual gases don’t really obey all of these assumptions—But it’s close enough!!**

  4. B. Real Gases • Particles in a REAL gas… • have their own volume • attract each other • Gas behavior is most ideal… • at low pressures • at high temperatures • in nonpolar atoms/molecules

  5. C. Characteristics of Gases • Gases expand to fill any container. • random motion, no attraction • Gases are fluids (like liquids). • no attraction • Gases have very low densities. • no volume = lots of empty space

  6. C. Characteristics of Gases • Gases can be compressed. • no volume = lots of empty space • Gases undergo diffusion & effusion. • random motion

  7. The Gas Laws • Describe HOW gases behave. • Can be predicted by the theory. • Amount of change can be calculated with mathematical equations.

  8. E. Pressure Which shoes create the most pressure?

  9. Aneroid Barometer Mercury Barometer E. Pressure • Barometer • measures atmospheric pressure

  10. U-tube Manometer Bourdon-tube gauge E. Pressure • Manometer • measures contained gas pressure

  11. E. Pressure • KEY UNITS AT SEA LEVEL 101.325 kPa (kilopascal) 1 atm 760 mm Hg 760 torr 14.7 psi

  12. Standard Temperature & Pressure 0°C273 K 1 atm101.325 kPa -OR- F. STP STP

  13. The effect of adding gas. • Doubling the the number of gas particles doubles the pressure. (of the same volume at the same temperature).

  14. Pressure and the number of molecules are directly related • More molecules means more collisions. • Fewer molecules means fewer collisions. • Gases naturally move from areas of high pressure to low pressure because there is empty space to move in.

  15. If you double the number of molecules 1 atm

  16. If you double the number of molecules • When we blow up a balloon we are adding gas molecules. • You double the pressure. 2 atm

  17. 4 atm • As you remove molecules from a container

  18. 2 atm • As you remove molecules from a container the pressure decreases

  19. 1 atm • As you remove molecules from a container the pressure decreases • Until the pressure inside equals the pressure outside • Molecules naturally move from high to low pressure

  20. Changing the size of the container • In a smaller container molecules have less room to move. • Hit the sides of the container more often. • As volume decreases pressure increases.

  21. 1 atm • As the pressure on a gas increases 4 Liters

  22. 2 atm • As the pressure on a gas increases the volume decreases • Pressure and volume are inversely related 2 Liters

  23. Temperature • Raising the temperature of a gas increases the pressure if the volume is held constant. • The molecules hit the walls harder. • The only way to increase the temperature at constant pressure is to increase the volume.

  24. 300 K • If you start with 1 liter of gas at 1 atm pressure and 300 K • and heat it to 600 K one of 2 things happens

  25. 600 K 300 K • Either the volume will increase to 2 liters at 1 atm

  26. 600 K 300 K • Or the pressure will increase to 2 atm. • Or someplace in between

  27. Daltons’ Law of Partial Pressures • The total pressure inside a container is equal to the partial pressure due to each gas. • The partial pressure is the contribution by that gas. • PTotal = P1 + P2 + P3 • For example

  28. We can find out the pressure in the fourth container. • By adding up the pressure in the first 3. 6 atm 1 atm 2 atm 3 atm

  29. Examples • What is the total pressure in a balloon filled with air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg? • In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

  30. Boyle’s Law • At a constant temperature pressure and volume are inversely related. • As one goes up the other goes down • P1 x V1=P2 x V2

  31. Think about it mathematicallyPressure and Volume are INVERSELY proportional • P1 x V1=P2 x V2 • Pressure is 2 atm at 10L and increases to 4 atm. • (2 atm)(10L) = (4 atm)(X) • 20 = (4) (X)

  32. P V

  33. Examples • A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume? • A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to volume to 43 L?

  34. Charles’ Law • The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. • V1 = V2 T1 T2

  35. Think about it mathematically Volume and Temperature are DIRECTLY proportional • V1 = V2 T1 T2 • Volume is 4L and Temp is 8K and Temp is lowered to 4K. What does the volume have to be???? • 4 = ? 8 4 What number does it take to keep both sides equal

  36. V T

  37. Examples • What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure. • What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC?

  38. Gay Lussac’s Law • The temperature and the pressure of a gas are directly related at constant volume. • P1 = P2 T1 T2

  39. P T

  40. Examples • What is the pressure inside a 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? • At what temperature will the can above have a pressure of 2.2 atm?

  41. Putting the pieces together • The Combined Gas Law Deals with the situation where only the number of molecules stays constant. • P1 x V1 = P2 x V2 T1 T2 • Lets us figure out one thing when two of the others change.

  42. Examples • A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 1.7 atm. What is the new volume? • If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?

  43. The combined gas law contains all the other gas laws! • If the temperature remains constant. P1 V1 P2 x V2 x = T1 T2 Boyle’s Law

  44. The combined gas law contains all the other gas laws! • If the pressure remains constant. P1 V1 P2 x V2 x = T1 T2 Charles’ Law

  45. The combined gas law contains all the other gas laws! • If the volume remains constant. P1 V1 P2 x V2 x = T1 T2 Gay-Lussac Law

  46. The Fourth Part • Avagadro’s Hypothesis • Volume is proportional to number of molecules (or moles) at constant T and P. • V is proportional to moles. • Gets put into the combined gas Law

  47. For an ideal gas at STP • P=101KPa • T=273K • V=22.4L • n=1mole P1 x V1 = P2 x V2 T1x n1 T2x n2

  48. These numbers are constant, so put them into the equation!!! P2 x V2 101.3KPa 22.4L x = 273K x 1 mol T2 x n The left side = 8.31 KPa x L K x mole Let’s assign it a letter-----R---------called the ideal gas constant

  49. What if we use a different number for standard pressure? • Instead of 101.3KPa use 1atm… 1 atm x 22.4L P2 x V2 = 1 mole 273K n2xT2 x So R = .0821 atm x L mole x K

  50. What if we use a different number for standard pressure? • Instead of 101.3KPa use 760mHg… 760mm x 22.4L P2 x V2 = 1 mole 273K n2xT2 x So R = 62.4mmHg x L mole x K

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