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Dalton’s Law

Dalton’s Law. The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. The total pressure is the sum of the partial pressures. P Total = P 1 + P 2 + P 3 + P 4 + P 5 ... For each P = nRT/V. Dalton's Law.

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Dalton’s Law

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  1. Dalton’s Law • The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. • The total pressure is the sum of the partial pressures. • PTotal = P1 + P2 + P3 + P4 + P5 ... • For each P = nRT/V

  2. Dalton's Law • PTotal = n1RT + n2RT + n3RT +... V V V • In the same container R, T and V are the same. • PTotal = (n1+ n2 + n3+...)RT V • PTotal = (nTotal)RT V

  3. The mole fraction • Ratio of moles of the substance to the total moles. • symbol is Greek letter chi c • c1 = n1 = P1 nTotal PTotal

  4. Examples • The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? • What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm?

  5. P1/PT = n1/nT = c1 592 torr /752 torr = .787 = cn .787 = Pn/PT=Pn/5.25 atm= 4.13atm

  6. Examples • When these valves are opened, what is each partial pressure and the total pressure? 4.00 L CH4 1.50 L N2 3.50 L O2 0.752 atm 2.70 atm 4.58 atm

  7. Find the partial pressure of each gas P1V1=P2V2 2.70atm(4.00L) = P(9.00L) = 1.20 atm 4.58atm(1.5L) = P(9.00L) = .76atm .752atm(3.50L) = P(9.00L) = .292atm 1.20atm + .76atm+ .292atm = 2.26atm

  8. Vapor Pressure • Water evaporates! • When that water evaporates, the vapor has a pressure. • Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure to find the pressure of the gas. • It must be given. Table of vapors pressures as different temperatures

  9. Example • N2O can be produced by the following reaction NH4NO3 N2O + 2H2O • what volume of N2O collected over water at a total pressure of 785torr and 22ºC can be produced from 2.6 g of NH4NO3? ( the vapor pressure of water at 22ºC is 21 torr)

  10. 2.6gNH4NO3 1mol NH4NO3 1molN2O = 0.0325mol NO2 80.06g 1mol NH4NO3 PV=nRT V=nRT/P V= 0.0325mol(62.4torr L/mol K)(295K) / (785torr – 21torr) V= .77L

  11. Kinetic Molecular Theory • Theory tells why the things happen. • explains why ideal gases behave the way they do. • Assumptions that simplify the theory, but don’t work in real gases. • The particles are so small we can ignore their volume. • The particles are in constant motion and their collisions cause pressure.

  12. Kinetic Molecular Theory • The particles do not affect each other, neither attracting or repelling. • The average kinetic energy is proportional to the Kelvin temperature.

  13. What it tells us • (KE)avg = 3/2 RT • This the meaning of temperature. • u is the particle velocity. • u is the average particle velocity. • u 2 is the average of the squared particle velocity. • the root mean square velocity is Öu 2 = urms

  14. Combine these two equations • For a mole of gas • NA is Avogadro's number

  15. Combine these two equations • m is kg for one particle, so Nam is kg for a mole of particles. We will call it M • Where M is the molar mass in kg/mole, and R has the units 8.3145 J/Kmol. • The velocity will be in m/s

  16. Example • Calculate the root mean square velocity of carbon dioxide at 25ºC. • Calculate the root mean square velocity of hydrogen gas at 25ºC. • Calculate the root mean square velocity of chlorine gas at 250ºC.

  17. Solutions CO2urms = (3(8.314J/molK)(298)/.04401kg/mol)1/2 = 411 m/s H2Urms = (3(8.314J/molK)(298)/.00202kg/mol)1/2 = 1918m/s Cl2Urms = (3(8.314J/molK)(523)/.0709kg/mol)1/2 = 429m/s

  18. Range of velocities • The average distance a molecule travels before colliding with another is called the mean free path and is small (near 10-7) • Temperature is an average. There are molecules of many speeds in the average. • Shown on a graph called a velocity distribution

  19. 273 K number of particles Molecular Velocity

  20. 273 K 1273 K number of particles Molecular Velocity

  21. Velocity • Average increases as temperature increases. • Spread increases as temperature increases.

  22. Effusion • Passage of gas through a small hole, into a vacuum. • The effusion rate measures how fast this happens. • Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.

  23. Effusion • Passage of gas through a small hole, into a vacuum. • The effusion rate measures how fast this happens. • Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.

  24. Deriving • The rate of effusion should be proportional to urms • Effusion Rate 1 = urms 1 Effusion Rate 2 = urms 2

  25. Deriving • The rate of effusion should be proportional to urms • Effusion Rate 1 = urms 1 Effusion Rate 2 = urms 2

  26. Diffusion • The spreading of a gas through a room. • Slow considering molecules move at 100’s of meters per second. • Collisions with other molecules slow down diffusions. • Best estimate is Graham’s Law.

  27. Helium effuses through a porous cylinder 3.20 times faster than a compound. What is it’s molar mass? √X / √4g = 3.2 √X = 6.4g X = 40.96g/mol

  28. If 0.00251 mol of NH3 effuse through a hole in 2.47 min, how much HCl would effuse in the same time? √MNH3 / √MHCl = √17 / √36.5= .687 times faster 2.51 x 10-3mol (.687) = 1.72 x 10-3 mol HCl

  29. A sample of N2 effuses through a hole in 38 seconds. what must be the molecular weight of gas that effuses in 55 seconds under identical conditions? √MN2 / √X = 55/38 = 1.45 √28 / 1.45 = √X 13.32g/mol = X

  30. Real Gases • Real molecules do take up space and they do interact with each other (especially polar molecules). • Need to add correction factors to the ideal gas law to account for these.

  31. Volume Correction • The actual volume free to move in is less because of particle size. • More molecules will have more effect. • Bigger molecules have more effect • Corrected volume V’ = V - nb • b is a constant that differs for each gas. • P’= nRT (V-nb)

  32. Pressure correction • Because the molecules are attracted to each other, the pressure on the container will be less than ideal gas • Depends on the type of molecule • depends on the number of molecules per liter. • since two molecules interact, the effect must be squared.

  33. Pressure correction • Because the molecules are attracted to each other, the pressure on the container will be less than ideal • depends on the number of molecules per liter. • since two molecules interact, the effect must be squared.

  34. Altogether • Called the Van der Waal’s equation if rearranged • Corrected Corrected Pressure Volume

  35. Where does it come from • a and b are determined by experiment. • Different for each gas. • Look them up • Bigger molecules have larger b. • a depends on both size and polarity. • once given, plug and chug.

  36. Example • Calculate the pressure exerted by 0.5000 mol Cl2 in a 1.000 L container at 25.0ºC • Using the ideal gas law. • Van der Waal’s equation • a = 6.49 atm L2 /mol2 • b = 0.0562 L/mol

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