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Understanding Gas Laws: Properties, Behaviors & Applications

Explore the unique properties and behaviors of gases, fluids, and liquids. Learn about the fundamental laws governing gas behavior, including Boyle's Law, Dalton's Law of Partial Pressures, and more. Gain insights into concepts like molecular motion, ideal gases, and the impact of temperature and pressure. Enhance your knowledge of important topics in chemistry with practical examples and explanations.

jamal-richard
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Understanding Gas Laws: Properties, Behaviors & Applications

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  1. Gases & Liquids Ch.12

  2. (12-1) Properties of Gases • Fluids • Low density • Compressible • Fill a container & exert P equally in all directions • Influenced by T

  3. Kinetic-Molecular Theory • Explains behavior of gases • 2 major assumptions: • Collisions are elastic • V of individual gas molecules is negligible KE is lost KE is maintained

  4. Ideal Gas • Describes the behavior of gases under most conditions • High T & low P gases act more ideal

  5. Kinetic Energy • T of a gas determines the avg. KE of its particles • KE = ½ mv2 • Where, m = mass, v = speed

  6. Pressure • Pressure (P) = force (F) area (A) • SI units: • F: newtons (N) • P: pascal (Pa) = 1 N/m2

  7. Standard Temp. & Pressure • STP: std. conditions for a gas • Temp. (T): 0 °C (273 K) • Pressure (P): 1 atm (101.325 kPa) • See Table 12-1, p.428 for more P units

  8. Greenhouse Effect • Inc. in the T of Earth caused by reflected solar radiation that’s trapped in the atmosphere • Inc. in greenhouse gases such as CO2 & CFCs

  9. Free Radical • Atom or molecule that has 1 or more unpaired e- & is very reactive • UV radiation breaks apart CFCs, making Cl• • Chain rxn: self-sustaining rxn in which the product from 1 step acts as a reactant for the next step • Cl• + O3 ClO + O2 + O • ClO + O  Cl• + O2

  10. (12-2) The Gas Laws • Symbols: • P = pressure • T = temp in K • V = volume • n = # of moles

  11. Boyle’s Law • At constant T: • Inc. P, dec. V • Dec. P, inc. V • P1V1 = P2V2

  12. Boyle’s Law Practice If the P exerted on a 300 mL sample of H2 gas at constant T is inc. from 0.500 atm to 0.750 atm, what will be the final V of the sample? • List known V1 = 300 mL P1 = 0.500 atm V2 = ? mL P2 = 0.750 atm

  13. Boyle’s Law Practice • Write eq. P1V1 = P2V2 V2 = P1V1 P2 3. Substitute & solve V2= (0.500 atm)(300 mL) = 200 mL 0.750 atm

  14. Dalton’s Law of Partial P’s • Total P in a gas mixture is the sum of the partial P’s of the individual components • Ptotal = PA + PB + PC… • Where, Ptotal = total P, PA = partial P of A

  15. Dalton’s Law Practice A mixture of O2, N2, & H2 gases exerts a total P of 278 kPa. If the partial P’s of O2 & H2 are 112 kPa & 101 kPa respectively, what would be the partial P of the N2? • List the known Ptotal = 278 kPa PN2 = ? kPa PO2 = 112 kPa PH2 = 101 kPa

  16. Dalton’s Law Practice • List the eq. & rearrange Ptotal = PO2 + PH2 + PN2 PN2 = Ptotal - PO2 - PH2 • Substitute & solve PN2 = 278 kPa – 112 kPa – 101 kPa = 65 kPa

  17. Mole Fraction • # of moles of 1 component compared w/ the total # of moles in the mixture • Mole fraction (X) = ____mol A___ total mols • To calc. partial P: • PA = PTXA

  18. Mole Fraction Example The total P of a mixture of gases is 0.97 atm. The mole fraction for N2 is 0.78. What’s the partial P of N2? • List the known Ptotal = 0.97 atm XN2 = 0.78

  19. Mole Fraction Example • Write the eq. PN2 = Ptotal XN2 • Substitute & solve PN2 = (0.97 atm)(0.78) = 0.76 atm

  20. Charles’ Law • At constant P: • V inc., T inc. • V dec., T dec. • V1 = V2 T1 T2

  21. Charles’ Law Practice Gas in a balloon occupies 2.5 L at 300 K. The balloon is dipped into liquid N2 at 80 K. What V will the gas in the balloon occupy at this T? • List known V1 = 2.5 L T1 = 300 K V2 = ? L T2 = 80 K

  22. Charles’ Law Practice 2. Write eq. V1 = V2 V2 = V1T2 T1 T2 T1 3. Substitute & solve V2 = (2.5 L)(80 K) = 0.67 L (300 K)

  23. Pressure & Temp. • P inc. w/ inc. in T at constant V • P1 = P2 T1 T2

  24. P & T Practice Gas in a sealed can has a P of 3.00 atm at 25°C. A warning says not to store the can in a place where the T will exceed 52°C. What would the gas P in the can be at 52°C? • List known P1 = 3.00 atm T1 = 25°C = 298 K P2 = ? atm T2 = 52°C = 325 K

  25. P & T Practice 2. Write eq. P1 = P2 P2 = P1T2 T1 T2 T1 3. Substitute & solve P2 = (3.00 atm)(325 K) = 3.27 atm (298 K)

  26. Avogadro’s Law • V’s of different gases under the same T & P’s have the same # of molecules • V1 = V2 n1 n2

  27. Gay-Lussac’s Law • Law of Combining Volumes: at constant T & P, gases react in whole # V proportions • H2 + Cl2 2 HCl • 1 V + 1 V  2 V

  28. Effusion • Motion of a gas through a small opening • Diffusion: gas particles disperse from areas of high to low conc.

  29. Graham’s Law of Effusion • At the same T & P, 2 gases rates of effusion can be measured by: • ½ MAvA2 = ½ MBvB2 or vA = MB vB MA • Where: • v = speed of effusion (2 gases, A & B) • M = molar mass

  30. Graham’s Law Practice O2 has an avg. speed of 480 m/s at room T. On avg., how fast is SO3 traveling at the same T? • List known vO2 = 480 m/s MO2 = 32 g/mol vSO3 = ? m/s MSO3 = 80.07 g/mol

  31. Graham’s Law Practice • Write eq. vSO3 = MO2 vSO3 =vO2MO2 vO2 MSO3 MSO3 3. Substitute & solve vSO3 = (480 m/s) (32 g/mol) (80.07 g/mol) = 300 m/s

  32. More Graham’s Practice Compare the rate of effusion of H2O vapor w/ O2 gas at the same T & P. 1. List known MH2O = 18.02 g/mol MO2 = 32 g/mol

  33. More Graham’s Practice 2. Write eq. vH2O = MO2 vO2 MH2O 3. Substitute & solve vH2O = 32 g/mol = 1.33 vO2 18.02g/mol H2O effuses 1.33X faster than O2

  34. (12-3) Ideal Gas Law • PV = nRT • Where: • R = 8.314 L•kPa / mol•K or • R = 0.0821 L•atm / mol•K

  35. Ideal Gas Law Practice Calculate the V of 1.00 mol of CO2 gas at STP. • List known P = 1.00 atm V = ? L n = 1.00 mol R = 0.0821 L•atm/mol•K T = 273 K

  36. Ideal Gas Law Practice • Write eq. PV = nRT  V = nRT P • Substitute & solve V = (1.00 mol)(0.0821 L•atm/mol•K)(273 K) (1.00 atm) = 22.4 L

  37. Combined Gas Law • Moles remain constant, but other conditions change • P1V1 = P2V2 T1 T2

  38. Combined Gas Law Practice A sample of CO2 gas occupies 45 L at 750 K & 500 kPa. What’s the V of this gas at STP? • List known P1 = 500 kPa P2 = 101.325 kPa V1 = 45 L V2 = ? L T1 = 750 K T2 = 273 K

  39. Combined Gas Law Practice • Write eq. P1V1 = P2V2 V2 = P1V1T2 T1 T2 T1P2 3. Substitute & solve V2 = (500 kPa)(45 L)(273 K) (750 K)(101.325 kPa) = 81 L

  40. Gas Stoichiometry • Gas V’s can be determined from mole ratios in bal. eqs. • 3H2 + N2 2NH3 3 L 1 L 2 L 22 L N2 x 3 L H2 = 66 L H2 1 L N2

  41. (12-4) Changes of State • Evaporation: l g • Condensation: g  l • Sublimation: s  g

  42. Vapor Pressure • P exerted by a vapor in equilibrium w/ its liquid state at a given T • H2O(l) H2O(g)

  43. Phase Diagrams • Shows T’s & P’s at which a substance exists in different phases • Phases are at equilibrium along the lines • Phase: substance has uniform composition & properties

  44. Phase Diagrams (cont.) • Normal bp: boiling T at 1 atm • Critical point: T & P above which the properties of vapor can’t be distinguished from a liquid • Supercritical fluids • Triple point: T & P where 3 phases exist in equil.

  45. C.P. N.M.P. N.B.P.

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