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Ideal Gas Law

Learn about the ideal gas law and the four variables that describe a sample of gas, including temperature, pressure, volume, and amount. Explore the equations of state, solve gas law problems, and understand extensions of the ideal gas law. Discover Dalton's Law of Partial Pressures, collect gases by water displacement, and explore effusion and diffusion processes.

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Ideal Gas Law

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  1. Ideal Gas Law

  2. Describing a sample of a gas • 4 variables are needed to completely describe a sample of a gas: • Temperature • Pressure • Volume • Amount (number of moles) of gas

  3. Equation of State • An equation relating the macroscopic variables that describe some type of matter. • The ideal gas law is an equation of state for gases.

  4. Boyle’s Law Graphs PV = k Volume vs. 1/Pressure Pressure vs. Volume P = kV-1 V = kP-1

  5. Charles’ Law Graph V = mT (in Kelvins)

  6. Gay-Lussac’s Law Graph P = m’T

  7. Avogadro’s Law V = nK

  8. Recall So V  1/P X n X T or V  nT/P

  9. Ideal Gas Law • To turn a proportionality into an equation, insert a constant: V = RnT/P • Or multiply both sides by P: • PV = nRT where R is the ideal gas law constant. If three of the variables are known, the 4th can be determined. • The units of R depend on the units used for P, T, and V.

  10. Units of R • Two common values of R: • 0.08206 LiterAtm • 8.314 Joules or 8.314 LiterKPa MoleK MoleK MoleK

  11. Problem-Solving • Most commonly used value of R in the US: • 0.08206 LiterAtm • Note: • Pressure must be in atm • Volume must be in liters • Temperature must be in Kelvins MoleK

  12. Ideal Gas Law Problems • What pressure is exerted by 0.75 moles of a gas at 25C in a container with a volume of 1.5 L? • Find the volume of 0.85 moles of gas at a pressure of 520 torr and a temperature of 15C. • How many moles of gas are present in a sample at 700 torr, 333C, and occupying a volume of 452 mL?

  13. Extensions of Ideal Gas Law Problems • PV = nRT • n = mass • Density = mass formula mass volume

  14. Memorize the three fundamental equations. • Substitute and rearrange as problem demands. • PV = nRT or PV = massRT • Rearrange to solve for mass or density • (Pformula mass) = mass/volume = density formula mass volume RT

  15. Formula mass (Identity) of gas • Formula mass = massRT • Or formula mass = densityRT PV P

  16. Density of a gas • At STP, density of a gas = molar mass/22.4 L • This is an easy relationship but it is only true at STP!!!

  17. Dalton’s Law of Partial Pressures

  18. Dalton’s Law of Partial Pressures • For a mixture of gases: • Ptot = P1 + P2 + P3 + … • The total pressure of a gas mixture is the sum of the partial pressures of the component gases. The pressure exerted by each gas in an unreactive mixture is independent of the other gases in the mixture.

  19. Addition or Subtraction Problems • Three gases, He, N2, and Ar are present in a gas mixture. The partial pressure of He is 360 torr, of N2 is 400 torr, and of Ar is 250 torr. Find the total pressure. • Ar is added to the above mixture until the total pressure is 1200 torr. Find the new pressure of the Argon.

  20. Collecting Gas by Water Displacement When the water levels inside and outside the inverted container are the same, the total pressure inside the container above the water is equal to the atomspheric pressure.

  21. Sometimes gases are collected by water displacement C2H2(g) + H2O(g)

  22. Line up the water levels!

  23. Ptot = Pgas + Pwater • The volume of gas collects above the water, but some of the water molecules evaporate and go into the gas phase as well. • The vapor pressure of water depends only on the temperature. Look it up in a reference table and then subtract it from the total pressure.

  24. Extension of Dalton’s Law • Since PV = nRT then • Ptot = ntotRT & for each component, Pi = niRT Pi = niRT/V Which reduces to Pi / Ptot = ni / ntot V V Ptot ntotRT/V

  25. Mole Fraction • ni / ntot is called the mole fraction = i • Pi = (ni / ntot)Ptot

  26. Effusion gas vacuum

  27. Effusion • Process where molecules of a gas confined in a container randomly pass through a tiny opening in the container. • Rates of effusion can be used to determine the molar mass of a gas. • Kinetic energy of molecules in a gas depends only on temperature and equals ½ mv2.

  28. Effusion Two gases at the same T have the same average KE: ½ M1V12 = ½ M2V22 Note: This V is the velocity of the molecules, NOT the volume of the container. V12 = M2 V22 M1

  29. Effusion Two gases at the same T have the same average KE: ½ M1V12 = ½ M2V22

  30. Graham’s Law of Effusion • The rates of effusion of gases at the same pressure and temperature are inversely proportional to the square roots of their molar masses. • The heavier gases move more slowly.

  31. Effusion • Recall: the faster you are going, the less time it takes you to get somewhere.

  32. Diffusion • Gradual mixing of two or more molecules due to their spontaneous, random motion. Gases are in constant, random motion and tend to move from regions of higher concentration to regions of lower concentration.

  33. Diffusion

  34. Molecular speed and Temperature

  35. Molecular speed and mass

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