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Exploring Gas Laws: Mathematics and Applications in Modern Balloons

Learn the fundamental gas laws, such as Boyle's Law, Charles's Law, and the Ideal Gas Law, and their mathematical expressions. Discover key concepts like partial pressures and the Kinetic Molecular Theory. Dive into Graham's Law of Effusion and compare ideal vs. real gas behaviors. Practice calculations and experiment interpretations to solidify your understanding of gas properties and behaviors.

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Exploring Gas Laws: Mathematics and Applications in Modern Balloons

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  1. Chapter 5 Gases

  2. Chapter 5 Gases

  3. WHY?

  4. Sketch of ModernBalloons

  5. WHY?

  6. Mathematics • V/T = constant

  7. 1.00 PSI

  8. 8.00 PSI

  9. 8.00 PSI WHY?

  10. Mathematics • PV = constant

  11. Mathematics • V/n = constant • (n = moles)

  12. Moles

  13. 273 1.00 K ATM

  14. 804 9.79 K ATM

  15. (atm)

  16. Mathematics • P/T= constant

  17. MathematicsSummary • V/n = constant • V/T = constant • P/T = constant • PV = constant

  18. MathematicsSummary • V/nT = constant • P/T = constant • PV/nT = constant

  19. MathematicsSummary • PV/nT = constant • PV = nTconstant • constant = R • PV = nRT Ideal Gas Law

  20. Conditions of Use • PV = nRT Ideal Gas Law • P units must be atm’s • V units must be liters • T must be in Kelvin

  21. Gas Law ResourcesPressures equivalent to the standard 1.00 ATM • 28.3 ft. H2O • 29.92 in. Hg • 76.0 cm Hg • 760.0 mm Hg • 760.0 torr • 14.7 psi. • 1.013 bar • 1.013 x 105 Pa • 101.3 kPa • (1 Pa = 1 Nt/M2)

  22. Practice • Fill out the following chart. • mm Hg. atm. kPa. bar • 1215 . • 0.714 . • 143 . • 0.904 .

  23. Gas Law ResourcesTemperature - must be absolute - never negative • Temperature must be in Kelvin • K = oC + 273

  24. Practice • Calculate the volume of 1.0 mole of a gas at Standard Temperature and Pressure.

  25. Practice • Fill out the following chart for C4H10 • Press. Vol. Temp. Moles Grams • 1.75 L 19 oC 1.66 . • 0.895 atm 6.0 oC 14.0 . • 433 mm Hg 92.4 mL 0.395 . • 1.74 bar 8.66 L 310 K .

  26. Experiment

  27. Experiment

  28. Experiment 4 Fe + 3 O2→ 2 Fe2O3 Fe + N2→ NR

  29. Interpretation • Air contains both N2 and O2 • Each gas has its own independent pressure. • “The sum of all individual gas pressures in a gas mixture is equal to the total pressure” DALTON • Dalton’s Law of Partial Pressures

  30. (go to video)

  31. KMT • Kinetic Molecular Theory of gases • Gases consist of very tiny particles in continuous random motion. • Particle collisions are elastic(no energy lost). • Particle volume is negligible. • Particle interaction is negligible. • molecular speed causes both pressure and volume of gases

  32. Graham’s Law • Often called Grahams’ Law of Diffusion - in error • Diffusion - movement of gas down an open tube • complex and influenced by many factors. • Effusion - movement of gas through small holes. • Graham’s Law of Effusion of Gases • “At a given temperature and pressure, gaseous effusion rate in moles per time unit, is inversely proportional to the square root of the molar mass of the gases”. • effusion rate of B = √mm B • effusion rate of A √mm A

  33. Ideal vs Real • Review KMT. Obvious non-realities. • Some gas molecules are NOT tiny. • Many gas collisions DO lose energy • Gas molecules HAVE a noticeable volume • Some molecules have SIGNIFICANT interaction.

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