Behavior of Gases

1. Behavior of Gases

2. Example of Importance of Gases Airbags fill with N2 gas in an accident. Gas is generated by the decomposition of sodium azide Gas molecules save your life! 2 NaN3 ---> 2 Na + 3 N2

3. Kinetic Molecular Theory (KMT) Particles in an ideal gas… have no volume. have elastic collisions. are in constant, random, straight-line motion. don’t attract or repel each other. have an avg. KE directly related to Kelvin temperature.

4. 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 when very small in size when nonpolar PLIGHT

6. Characteristics of Gases Gases expand to fill any container uniformly. Are in random motion, have no attraction Gases have very low densities. Particles have no volume = lots of empty space

7. Characteristics of Gases There is a lot of “free” space in a gas. Gases can be compressed. no volume = lots of empty space

8. Gases undergo diffusion & effusion. • Are always in random motion • Smaller and lighter gas particles do this faster

9. Gas Pressure Which shoes create the most pressure?

10. What Causes Pressure? • http://www.chm.davidson.edu/vce/kineticmoleculartheory/Pressure.html

11. Factors Affecting Gas Pressure • Number of Moles (Amount of gas) • As # of particles increase, the number of collisions with the container wall increases. • Volume • Smaller the volume, the greater the pressure exerted on the container. • Temperature • As temp. increases, KE increases, this increases frequency of collisions making pressure increase.

12. Measuring Gas Pressure Barometer measures atmospheric pressure (developed by Torricelli in 1643) Aneroid Barometer Mercury Barometer

13. Standard Pressure (Sea Level) 101.3 kPa (kilopascal) 1 atm 760 mm Hg (also called torr) You may be asked to convert between units of pressure!

14. Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in soft drink) Column height measures pressure of atmosphere 1 standard atmosphere (atm) = 760 mm Hg (or torr)

15. Measuring Gas Pressure Manometer measures contained gas pressure U-tube Manometer

16. Working withFormulas The Gas Laws V T P

17. Temperature Always use absolute temperature (Kelvin) when working with gases. K = ºC + 273 ºC -273 0 100 K 0 273 373

18. Gas properties can be modeled using math. Model depends on: • V = volume of the gas (L) • T = temperature (K) • ALL temperatures MUST be in Kelvin!!! • n = amount (moles) • P = pressure (atmospheres or kPa)

19. Standard Temperature & Pressure 0°C1 atm 273 K101.325 kPa 760 mmHg -OR- STP

20. Boyle’s Law The pressure and volume of a gas are inversely related at constant mass & temp P V Robert Boyle (1627-1691). Son of Earl of Cork, Ireland. PV = k

21. Boyle’s Law • Since P x V is always a constant: P1 x V1 = P2 x V2

22. Pressure and Volume Relationship http://www.chm.davidson.edu/vce/kineticmoleculartheory/PV.html

23. If Mass and Temp are Constant

24. Boyle’s Law Balloon in a Vacuum

25. Charles’ Law The volume and absolute temperature (K) of a gas are directly related at constant mass & pressure V T Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist.

26. Charles’ Law • Since V/T is always a constant: V1 = V2 T1 T2

27. If Mass and Pressure are Constant

28. Charles’ Law Pour Liquid Nitrogen on Balloon!! http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flashfiles/gaslaw/charles_law.html http://www.pinnaclescience.com/demo.htm

29. Gay-Lussac’s Law The pressure and absolute temperature (K) of a gas are directly related at constant mass & volume P T

30. Gay – Lussac’s Law • Since P/T is always a constant: P1 = P2 T1 T2

31. Pressure and Temperature Relationship • http://www.chm.davidson.edu/vce/kineticmoleculartheory/PT.html

32. Review of 3 Gas Laws Summary of Changing Variables http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/gasesv6.swf

33. P1V1 T1 P2V2 T2 = Combined Gas Law (on Ref Table) The good news is that you don’t have to remember all three gas laws! We can combine them into a single equation. 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! P1V1T2 =P2V2T1

36. Example 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 .090 L and a pressure of 3.20 atm? Set up Data Table P1 = 0.800 atm V1 = .180 L T1 = 302 K P2 = 3.20 atm V2= .090 L T2 = ??

37. Gas Law Problems A gas occupies 473 ml at 36°C. Find its volume at 94°C. CHARLES’ LAW GIVEN: V1 = 473 ml T1 = 36°C = 309K V2 = ? T2 = 94°C = 367K T V WORK: P1V1T2 = P2V2T1 (473 ml )(367 K)=V2(309 K) V2 = 562 ml

38. Gas Law Problems A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLE’S LAW GIVEN: V1 = 100. mL P1 = 150. kPa V2 = ? P2 = 200. kPa P V WORK: P1V1T2 = P2V2T1 (150.kPa)(100.mL)=(200.kPa)V2 V2 = 75.0 mL

39. Gas Law Problems A gas occupies 7.84 ml at 71.8 kPa & 25°C. Find its volume at STP. COMBINED GAS LAW P T V GIVEN: V1=7.84 ml P1=71.8 kPa T1=25°C = 298 K V2=? P2=101.325 kPa T2=273 K WORK: P1V1T2 = P2V2T1 (71.8 kPa)(7.84 ml)(273 K) =(101.325 kPa)V2 (298 K) V2 = 5.09 ml

40. Gas Law Problems A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSAC’S LAW GIVEN: P1 = 765 torr T1 = 23°C = 296K P2 = 560. torr T2 = ? P T WORK: P1V1T2 = P2V2T1 (765 torr)T2 = (560. torr)(309K) T2 = 226 K = -47°C

41. Dalton’s Law of Partial Pressures • Ptotal = P1+P2+…. • Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone. • This is often useful when gases are collected “over water”

42. Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. Ptotal = P1 + P2 + ... Patm = PH2 + PH2O

43. Dalton’s Law Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor. GIVEN: PH2 = ? Ptotal = 94.4 kPa PH2O = 2.72 kPa WORK: Ptotal = PH2 + PH2O 94.4 kPa = PH2 + 2.72 kPa PH2 = 91.7 kPa Look up water-vapor pressure on for 22.5°C. Sig Figs: Round to least number of decimal places.

44. A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? Dalton’s Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor. DALTON’S LAW GIVEN: Pgas = ? Ptotal = 742.0 torr PH2O = 42.2 torr WORK: Ptotal = Pgas + PH2O 742.0 torr = PH2 + 42.2 torr Pgas = 699.8 torr Look up water-vapor pressure for 35.0°C. Sig Figs: Round to least number of decimal places.

45. 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

46. Graham’s Law Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly.

47. Avogadro’s Principle Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas V n Equal volumes of gases at the same T and P have the same number of molecules.