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Chapter 5: Gases

Chapter 5: Gases. CHE 123: General Chemistry I Dr. Jerome Williams, Ph.D. Saint Leo University. Overview. Gas Laws Ideal Gas Law Example Problems General Gas Law Example Problem. Boyle’s Law. Robert Boyle (1627–1691). Pressure of a gas is inversely proportional to its volume

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Chapter 5: Gases

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  1. Chapter 5: Gases CHE 123: General Chemistry I Dr. Jerome Williams, Ph.D. Saint Leo University

  2. Overview • Gas Laws • Ideal Gas Law • Example Problems • General Gas Law • Example Problem

  3. Boyle’s Law Robert Boyle (1627–1691) • Pressure of a gas is inversely proportional to its volume • constant T and amount of gas • graph P vs V is curve • graph P vs 1/V is straight line • As P increases, V decreases by the same factor • P x V = constant • P1 x V1 = P2 x V2 Tro: Chemistry: A Molecular Approach, 2/e

  4. Boyle’s Experiment, P x V Tro: Chemistry: A Molecular Approach, 2/e

  5. Tro: Chemistry: A Molecular Approach, 2/e

  6. Tro: Chemistry: A Molecular Approach, 2/e

  7. Boyle’s Law: A Molecular View • Pressure is caused by the molecules striking the sides of the container • When you decrease the volume of the container with the same number of molecules in the container, more molecules will hit the wall at the same instant • This results in increasing the pressure Tro: Chemistry: A Molecular Approach, 2/e

  8. V1, P1, P2 V2 Example 5.2: A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm? Given: Find: V1 =7.25 L, P1 = 4.52 atm, P2 = 1.21 atm V2, L Conceptual Plan: Relationships: P1∙ V1 = P2∙ V2 Solution: Check: because P and V are inversely proportional, when the pressure decreases ~4x, the volume should increase ~4x, and it does Tro: Chemistry: A Molecular Approach, 2/e

  9. Practice – A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78 x 103 mL, what was it originally? Tro: Chemistry: A Molecular Approach, 2/e

  10. V2, P1, P2 V1 A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78x 103 mL, what was it originally? Given: Find: V2 =2780 mL, P1 = 782 torr, P2 = 0.500 atm V1, mL Conceptual Plan: Relationships: P1∙ V1 = P2∙ V2 , 1 atm = 760 torr (exactly) Solution: Check: because P and V are inversely proportional, when the pressure decreases ~2x, the volume should increase ~2x, and it does Tro: Chemistry: A Molecular Approach, 2/e

  11. Charles’s Law Jacques Charles (1746–1823) • Volume is directly proportional to temperature • constant P and amount of gas • graph of V vs. T is straight line • As T increases, V also increases • Kelvin T = Celsius T + 273 • V = constant x T • if T measured in Kelvin Tro: Chemistry: A Molecular Approach, 2/e

  12. If you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line If the lines are extrapolated back to a volume of “0,” they all show the same temperature, −273.15 °C, called absolute zero Tro: Chemistry: A Molecular Approach, 2/e

  13. V1, V2, T2 T1 Example 5.3: A gas has a volume of 2.57 L at 0.00 °C. What was the temperature in Celsius at 2.80 L? Given: Find: V1 =2.57 L, V2 = 2.80 L, t2 = 0.00 °C t1, K and °C Conceptual Plan: Relationships: Solution: Check: because T and V are directly proportional, when the volume decreases, the temperature should decrease, and it does Tro: Chemistry: A Molecular Approach, 2/e

  14. Practice – The temperature inside a balloon is raised from 25.0 °C to 250.0 °C. If the volume of cold air was 10.0 L, what is the volume of hot air? Tro: Chemistry: A Molecular Approach, 2/e

  15. The temperature inside a balloon is raised from 25.0 °C to 250.0 °C. If the volume of cold air was 10.0 L, what is the volume of hot air? V1, T1, T2 V2 Given: Find: V1 =10.0 L, t1 = 25.0 °C L, t2 = 250.0 °C V2, L Conceptual Plan: Relationships: Solution: Check: when the temperature increases, the volume should increase, and it does Tro: Chemistry: A Molecular Approach, 2/e

  16. Avogadro’s Law Amedeo Avogadro (1776–1856) • Volume directly proportional to the number of gas molecules • V = constant x n • constant P and T • more gas molecules = larger volume • Count number of gas molecules by moles • Equal volumes of gases contain equal numbers of molecules • the gas doesn’t matter Tro: Chemistry: A Molecular Approach, 2/e

  17. V1, V2, n1 n2 Example 5.4:A 0.225 mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L? Given: Find: V1 = 4.65 L, V2 = 6.48 L, n1 = 0.225 mol n2, and added moles Conceptual Plan: Relationships: Solution: Check: because n and V are directly proportional, when the volume increases, the moles should increase, and they do Tro: Chemistry: A Molecular Approach, 2/e

  18. Ideal Gas Law • Ideal gases obey an equation incorporating the laws of Charles, Boyle, and Avogadro. P V = n R T • 1 mole of an ideal gas occupies 22.414 L at STP • STP conditions are 273.15 K and 1 atm pressure • The gas constant R = 0.08206 L·atm·K–1·mol–1

  19. P, V, T, R n Example 5.6: How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25°C? Given: Find: V = 3.24 L, P = 24.3 psi, t = 25 °C n, mol Conceptual Plan: Relationships: Solution: 1 mole at STP occupies 22.4 L, because there is a much smaller volume than 22.4 L, we expect less than 1 mole of gas Check: Tro: Chemistry: A Molecular Approach, 2/e

  20. Example Problems • Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.5°C. • Answer = 9.42 atm

  21. Example Problems • What is the volume (in liters) occupied by 7.40 g of CO2 at STP? • Answer = 3.77 L

  22. Ideal Gas Law: Application • Density and Molar Mass Calculations • Given the following: Note: MM = molar mass • Density d = mass/volume • No. moles n n = mass / MM • Show that MM = dRT / P

  23. Ideal Gas Law: Application Examples • What is the molar mass of a gas with a density of 1.342 g/L–1 at STP? • What is the density of uranium hexafluoride, UF6, (MM = 352 g/mol) under conditions of STP? • The density of a gaseous compound is 3.38 g/L–1 at 40°C and 1.97 atm. What is its molar mass?

  24. Ideal Gas Law: Application Answers • Molar mass = 30.08 g/mole • Density of UF6 = 15.7 g/mL • Molar mass = 44.09 g/mole

  25. General Gas Law Equation • (P1V1 / T1 )= (P2V2 / T2 ) • Only equation that uses two sets of data for V, P, and T.

  26. Example Problem • Oxygen gas is normally sold in 49.0 L steel containers at a pressure of 150.0 atm. What volume would the gas occupy if the pressure was reduced to 1.02 atm and the temperature raised from 20oC to 35oC?

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