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Chapter 13

Chapter 13. Kinetic Theory (Kinetikos- “Moving”) Based on the idea that particles of matter are always in motion The motion has consequences Behavior of Gases Physical Properties of Gases Ideal Gas – an imaginary gas that conforms perfectly to all assumptions. Five Assumptions of the KMT.

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Chapter 13

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  1. Chapter 13 • Kinetic Theory (Kinetikos- “Moving”) • Based on the idea that particles of matter are always in motion • The motion has consequences • Behavior of Gases • Physical Properties of Gases Ideal Gas – an imaginary gas that conforms perfectly to all assumptions

  2. Five Assumptions of the KMT • Gases consist of large numbers of tiny particles • The Particles are in Constant Motion, moving in straight lines. • The collisions between particles & w/ the container wall are elastic. • There are no forces of attraction or repulsion between the particles of a gas. • The average K.E. of the particles is directly proportional to the Kelvin Temperature. KE = ½ mv2

  3. Measuring Gases • Four factors that can affect the behavior of a gas. • Amount of gas (n) = moles • Volume (V), 1000 cm3 = 1000mL = 1L • Temperature (T), Celsius and Kelvins Kelvins = oC + 273 • Pressure(P), atmospheres(atm), mmHg, or kPa

  4. Atmospheric Pressure • Pressure exerted by the column of air in the atmosphere. • Result of the earth’s gravity attracting the air downward. • Barometer – device used to measure the atmospheric pressure on earth. • Manometer – device used to measure the pressure of a gas in an enclosed container.

  5. Nature of Gases • 1 mole of any gas at STP equals 22.4L of volume. • STP is defined at sea level. • Standard Temperature = 0oC = 273K • Standard Pressure = 1 atm = 101.3 kPa = 760mmHg = 760 torrs • Normal boiling point of water is 100oC at sea level. • Higher elevation lower boiling points. • Less Pressure above the surface of water.

  6. Physical Properties of Gases • Gases have mass • Easily compressed • Fill their containers completely • Different gases move easily through each other. • Diffusion – more mass = slower gas • Gases exert pressure • Pressure of a gas depends on temperature • Volumes of gas particles themselves are assumed to be zero and exert no force on each other.

  7. 13.2 - Summary Pressure = Force / Area P = F/A • Reduce the area - Increase the Pressure • Increase the force - Increase the Pressure S.I Unit for Force - N (Newton) S.I Unit for Area - m2 S.I Unit for Pressure - Pa (Pascal) = 1 N/ m2

  8. Standard Temperature & Pressure The volume of a gas depends upon • Pressure • Temperature In order to do a comparison of the volumes of various gases the gases must have the same temperature and pressure. Scientist agreed upon; STP :Temp. = 0 °C , Press. = 1 atm = 101.3kPa = 760mm Hg

  9. Pressure is exerted by gas particles colliding with wall. What happens when a gas in a one-liter container is placed into a 1/4 liter container? More collisions Greater Pressure Conclusion Volume Decreases - Pressure Increases. Inverse Relationship Pressure and Volume at Constant Temperature

  10. Boyle’s Law - the volume of a fixed gas varies inversely with the pressure at constant temperature. V = k 1/P or PV = k 2 Conditions P1V1 = k (600) P2V2 = k (600) Then P1V1 = P2V2 If you know 3 you can find the 4th 13.3- Boyle’s Law: Pressure-Volume Relationship

  11. P1V1 = P2V2 Algebraic Equations for Boyle

  12. Sample Problem A sample of gas collected occupies a volume of 150mL when its pressure is 720 mmHg. What volume will it occupy if its pressure is changed to 750 mmHg? Given V1 = 150 mL V2 = ? P1 = 720 mmHg P2 = 750 mmHg Equation P1V1 = P2V2

  13. Charles’ Law: Temperature-Volume Relationship The volume of a fixed amount of gas varies directly with the Kelvin temperature at constant pressure. V1 / T1 = V2 / T2 V1 T2 = V2 T1

  14. Charles’ Law Temperature must be in Kelvin! Absolute Zero - lowest possible temperature, all kinetic energy ceases. -273.15 °C

  15. Algebraic Equations for Charles V1 T2 = V2 T1

  16. Sample Problem A sample of neon gas occupies a volume of 752 mL at 25 °C. What volume will it occupy at 50 °C. P, n are constant. V1= 752 mL V2= ? T1 = 25 °C +273 = 298 K T2 = 50 °C + 273 = 323 K

  17. Gay-Lussac’s Law • The pressure of a fixed gas varies directly with the temperature at constant volume. • Mathematically P = k T or P / T = k P1T2 = P2T1

  18. Gay-Lussac’s Law P1T2 = P2T1

  19. Sample Problem The gaseous contents in an aerosol can are under a pressure of 3.00 atm at 25 °C. If the temperature is increased to 52 °C, what would the pressure of the can be? P1= 3.00 atm T1 = 25 + 273 = 298 K P2= ? T2 = 52 + 273 = 325 K P1T2 = P2T1

  20. Avogadro’s Law • Equal volumes of gases at the same temperature and pressure contain equal number of gas particles. • At STP, 22.4L = 1 mol • V1n2 = V2n1

  21. Equations

  22. Sample Problem • Determine the number of moles of helium that are held in a 250mL container. Consider that 2.0 moles can be held in a 3L container. V1 = 250mL V2 = 3000mL n1 = ? N2 = 2.0moles

  23. The Combined Gas Law • Expresses the relationship between P,T, & V of a fixed amount of gas. • Mathematically PV/T = k P1V1 = P2V2 T1 T2 P1V1T2 = P2V2T1

  24. The Combined Gas Law V2 = P1V1T2 T1 P2 P2 = P1V1T2 T2 = P2 V2T1 T1V2 P1V1

  25. Sample Problem A helium-filled balloon has a volume of 50.0 L at 25°C and 820 mmHg. What volume will it occupy at 650 mmHg and 10 °C? P1 = 820 mmHg P2 = 650 mmHg V1 = 50 L V2 = ? T1 = 298 K T2 = 283 K

  26. Dalton’s Law of Partial Pressure • The total pressure of a mixture of gases is equal to the sum of all the partial pressures. Partial pressure - pressure of one gas in a mixture of gases PT = P1 + P2 + P3 + …

  27. Sample Problem Determine the pressure of oxygen gas in a container that is under 1 atm of pressure and contains carbon dioxide and nitrogen. Note: PCO2 = .285mmHg, PN2 = 594mmHg

  28. 13-4 : Ideal Gas Law • Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature and number of moles. • The combination of all 4 gas laws from the previous section.

  29. Derived Equation for the Ideal Gas Law • Needed an Ideal Gas Law Constant (R). • The second conditions were set at STP to equal the ideal behavior.

  30. Ideal Gas Constant

  31. Practice Problem • A camping stove uses a 5.0L propane tank that holds 4.0 moles of liquid C3H8. How large a container would be needed to hold the same amount of propane at 25oC and 3atm? V = ? n = 4 mol T = 25oC = 298K P = 3 atm R = .0821

  32. Gas Density at STP • The density of a gas at STP is constant, due to the standard molar volume of a gas. • However the density of a gas changes with temperature and pressure, due to the volume in the equation.

  33. Gas Density Problems • Determine the density of CO2 at STP. • What is the molar mass of gas that has a density of 1.28g/L at STP?

  34. Molar Mass and Ideal Gas Law • Considering that moles are in the Ideal Gas Law equation, we can substitute the equivalent of moles(n) into the equation.

  35. Density and the Ideal Gas Law • Now that mass(m) is in the equation we can substitute density(d) into the equation.

  36. Ratm = .0821 RmmHg = 62.4 RkPa = 8.314

  37. Molar Mass not at STP • Using the previous equations : Example: A 1.25g sample of gas was found to have a volume of 350mL at 20oC and 750mmHg. What is the molar mass of this gas?

  38. Classwork • What is the molar mass of a gas that has a density of 2.08g/L at STP? • What is the density at STP of NO2? • What is the molar mass of a gas, if a 1.39g sample of gas has a volume of 375mL at 22oC and 755mmHg?

  39. Corrected Vapor Pressure • When a gas is collected through water displacement, there is always a trace of water vapor in the container. • To correctly use the gas laws you must subtract the water vapor pressure from the atmospheric pressure. • Pgas = Patm – PH2O

  40. Water Displacement • A sample of methane gas that was collected through water displacement had a volume of 350mL at 27.0oC and 720mmHg. What is the volume at 2.0oC and 600.2mmHg? T1 = 300 K T2 = 275K P1 = 720mmHg P2 = 600.2mmHg V1 = 350mL V2= ? V2 = P1V1T2 T1 P2

  41. Solution

  42. Graham’s Law • Diffusion – Tendency of gas particles to travel toward areas of lower concentration. • Effusion – Gas escapes a tiny opening in a container. (one way diffusion) • Graham’s Law • Rate of effusion of a gas is inversely proportional to the square root of it’s molar mass. • Less mass = faster gas

  43. Graham’s Law Problems • Which gas will diffuse into a container faster? CO2 or NH3? Why? • Compare the rates of effusion for F2 and Cl2.

  44. At a certain temperature and pressure, Cl2 has a velocity of .038m/s. What is the velocity of SO2 at the same condition?

  45. Determining the Molar Mass • An unknown gas was placed into a container with N2 gas. The nitrogen was found to travel 1.2 times faster than the unknown gas. What is the molar mass of this unknown gas?

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