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Chapter 13: Gases

Chapter 13: Gases. Kinetic Molecular Theory (KMT). Kinetic Molecular Theory. Kinetic Molecular Theory (KMT): Model used to explain the properties of solids, liquids, and gases in terms of the energy of particles and the forces that act between them.

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Chapter 13: Gases

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  1. Chapter 13: Gases

  2. Kinetic Molecular Theory (KMT)

  3. Kinetic Molecular Theory • Kinetic Molecular Theory (KMT):Model used to explain the properties of solids, liquids, and gases in terms of the energy of particles and the forces that act between them. • The KMT is based on the idea that particles of matter are always in motion.

  4. The kinetic-molecular theory of gases is based on these five postulates: • Gases consist of large numbers of tiny particles that are far apart • Most of the volume occupied by a gas is empty space • Collisions between gas particles and between particles and container walls are elastic collisions. These collisions result in the pressure exerted by gases. • An elastic collision is one in which there is no net loss of total kinetic energy.

  5. Gas particles are in continuous, rapid, random motion. Therefore, they possess kinetic energy. • There are no forces of attraction between gas particles. • The temperature of a gas depends on the average kinetic energy of the particles of the gas.

  6. All gases at the same temperature have the same average kinetic energy. • At the same temperature, lighter gas particles have higher average speeds than do heavier gas particles. • Hydrogen molecules will have a higher speed than oxygen molecules; however, both possess the same kinetic energy • The average speeds and kinetic energies of gas particles increase with an increase in temperature and decrease with a decrease in temperature.

  7. Properties of Gases Expansion • Gases completely fill any container in which they are enclosed. • Gas particles move rapidly in all directions without significant attraction between them. Fluidity • Because liquids and gases flow, they are both referred to as fluids. • Because the attractive forces between gas particles are insignificant, gas particles glide easily past one another.

  8. Low Density • The density of a gaseous substance is about 1/1000 the density of the same substance in the liquid or solid state. • The reason is that the particles are so much farther apart in the gaseous state. Compressibility • During compression, the gas particles, which are initially very far apart, are crowded closer together.

  9. Diffusion • Gases spread out and mix with one another, even without being stirred. • Such spontaneous mixing of the particles of two substances caused by their random motion is called diffusion. • The random and continuous motion of the gas molecules carries them throughout the available space.

  10. Effusion • A process by which gas particles pass through a tiny opening • Molecules of low mass effuse faster than molecules of high mass.

  11. Deviations of Real Gases from Ideal Behavior • An ideal gas is a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory. • A real gas is a gas that does not behave completely according to the assumptions of the kinetic-molecular theory. • Under most normal conditions (not high pressures or low temperatures), real gases behave very similar to those of ideal gases

  12. At high pressures and low temperatures, real gases deviate significantly from behavior of ideal gases because particles are closer together and their kinetic energy is insufficient to overcome the attractive forces. • KMT is more likely to hold true for gases whose particles have little attraction for each other. • The more polar the molecules of a gas, the greater the attractive forces between them, and the more the gas will deviate from ideal gas behavior.

  13. Pressure & Dalton’s Law of Partial Pressure

  14. Gas Pressures • Gas pressure is caused by collisions of the gas molecules with each other and with surfaces with which they come into contact. • The pressure exerted by a gas depends on volume, temperature, and the number of molecules present. • The greater the number of collisions of gas molecules, the higher the pressure will be. • Atmospheric Pressure: The sum of the individual pressures of the various gases that compose the atmosphere.

  15. Other Units of Pressure • Atmosphere (atm) • 1 atm defined to be the pressure at sea level when temperature is 0°C. • 1 atm = 760 mm Hg • Torr (torr) • 1 torr represents the same amount of pressure as 1 mm Hg 1 atm = 760 mm Hg = 760 torr = 101.325 kPa

  16. Gas Mixtures and Partial Pressures • First studied by John Dalton in 1803 • Each gas in mixture exerts a pressure called a partial pressure • Dalton’s Law:For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas exerts PTOTAL = P1 + P2 + P3 + …

  17. Partial Pressures: Sample Problem A mixture of three gases – He, CO2, and NH3 – is at a total pressure of 6.11 atm. The partial pressure of the He is 1.68 atm and the partial pressure of the CO2 is 3.89 atm. What is the partial pressure of gas NH3?

  18. Gas Laws

  19. Boyle’s Law: Pressure-Volume Relationship • Boyle’s Law states that the volume of a gas varies inversely with the pressure at a constant temperature. • Plotting the values of volume versus pressure for a gas gives a curve like that shown at right.

  20. Boyle’s Law: Pressure-Volume Relationship • Boyle’s Law can also be expressed mathematically as: P1V1 = P2V2 • P1 and V1 represent original conditions, and P2 and V2 represent new set of conditions • As pressure increases, volume decreases; as pressure decreases, volume increases

  21. Boyle’s Law: Sample Problem • A sample of helium gas collected at 750 mm Hg occupies a volume of 250 mL. What pressure does the gas exert if the volume increases to 300 mL?

  22. Charles’s Law: Volume-Temperature Relationship • Charles’s Law states that the volume of a gas varies directly with the Kelvin temperature at a constant pressure. • (K = °C + 273) • Gas volume and Kelvin temperature are directly proportional to each other as shown at right.

  23. Charles’s Law: Volume-Temperature Relationship • Charles’s Law can be expressed mathematically as: V1 = V2 T1 T2 • V1 and T1 represent original conditions, and V2 and T2 represent new set of conditions • As temperature increases, volume increases; as temperature decreases, volume decreases • In order to use this equation the temperature MUST be in Kelvin (K = C + 273)

  24. Charles’s Law: Sample Problem A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?

  25. Gay-Lussac’s Law: Pressure-Temperature Relationship • Gay-Lussac’s Law states that the pressure of a gas varies directly with the Kelvin temperature at a constant volume. • Gas pressure and Kelvin temperature are directly proportional to each other as shown at right.

  26. Gay-Lussac’s Law: Pressure-Temperature Relationship P1 = P2 T1 T2 • Gay-Lussac’s law can be mathematically expressed as: • P1 and T1 represent original conditions, and P2 and T2 represent new set of conditions • As temperature increases, pressure increases; as temperature decreases, pressure decreases • Temperatures must be in Kelvin(K = C + 273)

  27. Gay-Lussac’s Law: Sample Problem The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C?

  28. The Combined Gas Law • Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law can be combined into a single equation that can be used for situations in which temperature, pressure, and volume all vary at the same time. • The Combined Gas Law can be written as: P1V1 = P2V2 T1 T2

  29. Standard Temperature and Pressure • As a reference point used for comparing gases, scientists have agreed on standard conditions. • Standard Temperature – 0°C or 273 K • Standard Pressure – 1 atm • These conditions are commonly abbreviated as STP

  30. The Ideal Gas Law • Ideal Gas Law: Mathematical relationship among pressure, volume, temperature, and number of moles (n) of a gas. PV = nRT • R is known as the ideal gas constant • The value of R will usually be one of the following: • 0.0821 L x atm/mol x K • 8.314 L x kPa/mol x K • Check to see your units of pressure in the problem (either atm or kPa) to determine which value of R to use)

  31. Ideal Gas Law: Sample Problems 1.) What is the pressure exerted by a 0.475 mol sample of nitrogen gas in a 10.0 L container at 25°? 2.) Calculate the volume of a 0.323 mol sample of a gas at 265 K and 0.900 atm.

  32. Gas Stoichiometry

  33. Avogadro’s Principle • Avogadro’s Principle: At STP, 1 mol of ANY gas occupies a volume of 22.4 L Example: What is the number of moles in a sample of gas that has a volume of 3.72 L at STP? 3.72 L X 1 mol = 0.166 mol x 22.4 L

  34. Avogadro’s Principle: Sample Problems 1.) What size (volume) container do you need to hold 0.0459 mol of N2 gas at STP? 2.) What volume will 0.416 g of krypton gas occupy at STP?

  35. Gas Stoichiometry • For gases, the coefficients in a balanced chemical equation represent not only molar amounts/ratios, but also volumes (and volume ratios) N2(g) + 3H2(g) → 2 NH3(g) • In the chemical equation above, 1 L of N2 reacts with 3 L of H2 to yield 2 L of NH3 • If 20.0 mol of nitrogen (N2) is available, how many liters of NH3 can be produced at STP?

  36. Gas Stoichiometry: Sample Problem The complete combustion of propane, C3H8, occurs according to the following balanced equation. C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g) How many liters of oxygen (O2) will be required for the complete combustion of 0.350 L of propane?

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