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Gas Laws

Learn about the principles of gas laws, including the concept of pressure, measurement techniques, pressure conversions, and the relationships between pressure, volume, and temperature. Discover how to use the ideal gas law and solve gas law problems. Explore Dalton's law, mole fraction, and the impact of water vapor on gas collection.

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Gas Laws

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  1. Gas Laws Remember that gas has mass

  2. F A P = Pressure • Pressure is the amount of force applied to an area. • Atmospheric pressure is the weight of air per unit of area.

  3. Pressure • What is pressure? • Accumulated force of the collisions of atoms • Pascals (Pa) or kilopascals (kPa) • 1 Pa = 1 newton/square meter = 1 N/m2 • Bar • 1 bar = 105 Pa = 100 kPa • mm Hg or torr • These units are literally the difference in the height measured in mm of a mercury barometer. Atmospheres (atm) • Average value of atmospheric pressure at sea level 1 atm = 760 torr = 101.325 kPa

  4. How is Pressure Measured • Barometers and manometers • Use pressure to elevate a liquid • An open-end manometer is used to measure the difference between atmospheric pressure and that of a gas in a vessel. • A closed-end manometer will only measure the pressure of the gas inside the vessel. • Piezoelectric chips

  5. Pressure Conversions • Normal atmospheric pressure at sea level and room temperature is referred to as standard temperature and pressure, or STP. • 1 atm = 760 torr = 760 mmHg = 14.7 psi • 1 atm = 101,325 Pa (use kPa) • Temperature • 25 ºC = 298 Kelvin  USE KELVIN! ALL THE TIME! Kelvin = Celsius + 273  REMEMBER ME!

  6. Gas Laws • There are three gas laws discovered independently that tell us how gases behave when certain variables are changed. • Boyle’s • Charles’ • Avogadro’s

  7. Boyles Law PV=k (constant) V = 1/P x k Pressure and Volume are Inversely Proportional

  8. Charles’ Law Volume and Temperature are directly proportional V = bT The temperature that Volume = zero is Absolute zero

  9. Avogadro’s Law • Volume of a gas is directly proportional to the number of molecules • V = na • V = volume in liters • n = number of moles • a = proportionality constant • Avogadro did not invent Avogadro’s number! It was named after him 50 years after his death

  10. Ideal Gas Law • If PV = k • And V = bT • And V = an • Then PV = nT x constant • PV = nRT

  11. Ideal Gas Law • Ideal Gas Law is an Equation of State • Given any three, you can determine the fourth • It is empirically derived • It expresses what REAL gases approach • At low pressure • High temperature • Using KMT : • Why is low pressure and high temp conditions required for a gas to approach ideal conditions?

  12. Gas Law Problems • Use the equation for all problems. • R = PV nT • What is constant in the problem? • Derive the equation and solve.

  13. A 125.01 L balloon is at 250.0K It is heated to 350.0K. What is the volume? • R = PV nT • What is constant? • Moles and pressure. • R = V1= V2 T1 T2 • 175.0 L

  14. Gas Stoichiometry • One mole of any gas at STP (273K, 1 atm) is 22.4 liters. • True for Ideal Gases. • R = PV nT • P = 1 atm, V = 22.4L, T = 273.15K, and moles (n) = 1.0, then R = 0.0821 L atm / mol K

  15. Units of R • There are two common “R”’s • Besides the pirates “rrrrrr” • 0.0821 L atm /mol k • Used in gas problems And • 8.3145 L Kpa / mol K • used in thermo problems, whenever the answer is in joules

  16. 15.0 TL (teraliter) of hydrogen gas at 450 K and 1488 torr was reacted with 273 Tg (teragram) of iron (III) oxide. • What is the reaction? • What is the limiting reactant? • How much iron will be formed? • What is the pressure of the water assuming the reaction tank is at the same conditions (temperature and volume) as the reactants?

  17. Gas and Molar Mass • Whenever moles are used in a relationship • Like the ideal gas law • It can be thought of as “grams divided by molar mass” • Or • g molar mass (M)

  18. Molar Mass of Gas • PV = nRT • P = nRT = (m/M) R T V V • P = (m)(RT) = d R T V M M m = mass, d = density (units = g/L)

  19. Rearrange the Equation • P = d R T M • Molar mass = d R T P • m = mass, d = density (units g/L)

  20. Dalton’s Law The total pressure of a gas mixture is the sum of the partial pressures of the gases if they were alone. Ptotal = P1 + P2 + P3 +…..

  21. Dalton’s Law • The pressure is a combination of all partial pressures • It assumes gases have no influence on each other • Under what conditions do gases act ideally?

  22. Mole Fraction • Mole Fraction is the fraction of the moles of one substance in a mixture compared to the total number of moles • Mole fraction • X1 = n1 = n1 ntotal n1+ n2+ n3+ …… • If V and T are constant X1 = P1 or P1 = X1 • Ptotal Ptotal

  23. Gas Collected Over Water Gases collected over water always have some water vapor included due to evaporation. (Vapor pressure) If the water level in the flask is equal to the surrounding water, than the inside pressure is equal to the outside pressure. Pin = PO2 + PH2O = P atmospheric

  24. Vapor Pressure • Explaining Vapor Pressure on a Molecular Level • Some of the molecules on the surface of a liquid have enough energy to escape the attraction of the bulk liquid. • These molecules move into the gas phase. • As the number of molecules in the gas phase increases, some of the gas phase molecules strike the surface and return to the liquid. • After some time the pressure of the gas will be constant at the vapor pressure.

  25. Vapor Pressure Explaining Vapor Pressure on the Molecular Level • Dynamic Equilibrium: the point when as many molecules escape the surface as strike the surface. • Vapor pressureis the pressure exerted when the liquid and vapor are in dynamic equilibrium.

  26. Kinetic-Molecular Theory Theory of moving molecules developed to explain gas behavior. Assumptions: • Gases consist of a large number of molecules in constant random motion. • Volume of individual molecules negligible compared to volume of container. • Intermolecular forces (forces between gas molecules) negligible. • Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. • Average kinetic energy of molecules is proportional to temperature.

  27. Kinetic-Molecular Theory • Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level. • Pressure of a gas results from the number of collisions per unit time on the walls of container.

  28. Kinetic-Molecular Theory • Magnitude of pressure given by how often and how hard the molecules strike. • Since the mass is small, the momentum of the atom is really small, however there are a lot of atom • What ever increases the number of collisions will increase the pressure (more atoms in the same space) • What ever increases the kinetic energy of the particle will increase the pressure (Temperature increase) • Gas molecules have an average kinetic energy but each molecule has a different energy within a certain range. • As the temperature increases, the average kinetic energy of the gas molecules increases.

  29. Kinetic-Molecular Theory Boltzman Distribution Colder gas Warmer gas

  30. Kinetic Molecular Theory

  31. Kinetic Molecular Theory

  32. Kinetic-Molecular Theory • As kinetic energy increases, the velocity of the gas molecules increases. • Root mean square speed, u, is the speed of a gas molecule having average kinetic energy. It is calculated by taking the square root of the average of the squared speeds of the gas molecules in a gas sample. • Average kinetic energy, KE, is related to root mean square speed and the molar mass of the gas: KE = 1/2mu2

  33. Kinetic-Molecular Theory Application to the Gas Laws • Asvolume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases. • If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.

  34. Molecular Effusion and Diffusion • If one particle has more mass than the other, it must be moving slower since they have the same KEavg! • Different gases at the same temperature have different average speeds. The bigger particles are moving slower. • Mathematically: The lower the molar mass, M, the higher the rms, u, for that gas at a constant temperature.

  35. Using Equation • Velocity of a gas particle can be calculated • In AP exam, you will be given the equation: • urms= (3RT)1/2 M • R is 8.3145 J/k •mol (from KE) • M is in Kg/mol ( molar mass x 10-3) • Derivation on Pg 216

  36. Molecular Effusion and Diffusion

  37. Molecular Effusion and Diffusion Graham’s Law of Effusion

  38. Molecular Effusion and Diffusion • Graham’s Law of Effusion • Only those molecules that hit the small hole will escape through it. • Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole. • We can show

  39. Molecular Effusion and Diffusion • Diffusion and Mean Free Path • Diffusion of a gas is the spread of the gas through space. • Diffusion is faster for light gas molecules. • Diffusion is significantly slower than rms speed (consider someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr). • Diffusion is slowed by gas molecules colliding with each other. • Average distance of a gas molecule between collisions is called mean free path.

  40. Molecular Effusion and Diffusion • Diffusion and Mean Free Path • At sea level, mean free path is about 6  10-6 cm.

  41. Size of atom doesn’t count Molecules do not interact Kinetic energy (velocity) is directly proportional to temperature Size of atom does Molecules do interact Even non-polar molecules interact! Velocity is not directly proportional (close but no cigar) Ideal vs Real Gases

  42. Real Gases: Deviations from Ideal Behavior • From the ideal gas equation, we have • For 1 mol of gas, PV/RT = 1 for all pressures. • In a real gas, PV/RT varies from 1 significantly. • The higher the pressure the more the deviation from ideal behavior.

  43. Real Gases • P= nRT V • Pobs = P’ - factor = P’ – a(n/V)2 • P = nRT V – nb • The molecules actually take up space • P = nRT – a(n/V)2 V – nb • Molecules attract

  44. Van der Waals Equation • Corrected version of the ideal gas law. • Uses two constants: a and b – which are experimentally determined and will be given for real gas calculations. • These constants “correct” the pressure and volume from ideal to real.

  45. an2 V2 ( ) P + (V - nb) = nRT Van der Waals equation This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume. Correction for Molecular volume Correction for attractive forces between molecules

  46. Clearly, not all gases behave ideal.

  47. Even the same gas acts differently at different temperatures.

  48. Real Gases • The assumptions of the kinetic-molecular theory break down at low temperature and high pressure. • Increased collisions between particles change the ideal behavior.

  49. Values for a,b

  50. Van der Waals Equation • If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0 ºC, it would exert a pressure of 1.000 atm. Use the van der Waals equation and the values of a and b for Cl2 to estimate the pressure exerted by 1.000 mol of Cl2 in 22.41 L at 0.0 ºC. • a = 6.49 L2-atm/mol2 • b = 0.0562 L/mol

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