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Chapter 9b-2

Chapter 9b-2. Gases. Dalton’s Law of Partial Pressures. The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. In other words, P total = P 1 + P 2 + P 3 + …. n 1. P 1 = n 1 RT/V. =. n 2. P 2 = n 2 RT/V.

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Chapter 9b-2

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  1. Chapter 9b-2 Gases

  2. Dalton’s Law of Partial Pressures • The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. • In other words, Ptotal = P1 + P2 + P3 + …

  3. n1 P1 = n1RT/V = n2 P2 = n2RT/V Partial Pressures and Mole Fraction Since P1 = n1RT/V Then = X (mole fraction)

  4. Partial Pressures and Mole Fraction • So, when one collects a gas over water, there is water vapour mixed in with the gas. • To find only the pressure of the desired gas, one must subtract the vapour pressure of water from the total pressure. Figure 9.13

  5. Kinetic-Molecular Theory • Gases consist of large numbers of molecules that are in continuous, random motion. • The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. • Attractive and repulsive forces between gas molecules are negligible. (See note*)

  6. N2 =28g/M Maxwell-Boltzmann Distribution

  7. Maxwell-Boltzmann Distribution

  8. Kinetic-Molecular Theory • Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. • The average kinetic energy of the molecules is proportional to the absolute temperature.

  9. Molecular Effusion and Diffusion Gas Molecules spread uniformly Effusion The escape of gas molecules through a tiny hole into an evacuated space. Diffusion The spread of one substance throughout a space or throughout a second substance. You cannae hide a fert! Figure 9.17

  10. Oh what a sleekit horrible beastieLurks in yer belly efter the feastieJust as ye set doon among yer kinThere sterts to stir an enormous wind. The neeps and tatties and mushy peasStert workin like a gentle breezeBut soon the puddin wi the sauncie faceWill have ye blawin’ all ower the place. Nae matter whit the hell ye daeA’bodys gonnae have tae payEven if ye try to stifle,It’s like a bullet oot a rifle. Hawd yer bum tight tae the chairTae try and stop the leakin airShift yersel frae cheek tae cheekPrae tae God it disnae reek. But aw yer efforts go assunderOot it comes like a clap o’ thunderRicochets aroon the roomMichty me, a sonic boom! God almighty it fairly reeks;Hope I huvnae shit ma breeksTae the bog I better scurryAw whit the hell, its no ma worry. A’body roon aboot me chokin,Wan or two are nearly bokinI’ll feel better for a whileCannae help but raise a smile. Wis him! I shout with accusin glower,Alas too late, he’s just keeled owerYe dirty bugger they shout and stareI dinnae feel welcome any mair. Where ere ye go, let yer wind gan freeSoonds like just the job fur meWhit a fuss at Rabbie's pertyOwer the sake o won wee ferty. Tae a Fert, Roy Williamson

  11. Graham’s Law of Effusion & Diffusion • The ratio of the rates of effusion of two gases is equal to the square root of the inverse ratio of their molecular masses or densities. • The effusion rate of a gas is inversely proportional to the square root of its molecular mass. • Mathematically, this can be represented as: • Rate1 / Rate2 = square root of (Mass2 / Mass 1)

  12. Graham’s Law of Effusion & Diffusion • For the 2 common gases in air: the rate off effusion of Nitrogen and Oxygen. • N2, Nitrogen, has a molecular mass of 28.0 g. O2, Oxygen, has a molecular mass of 32.0 g. Therefore, to find the ratio, the equation would be: • RateN2/RateO2 = square root of 32.0 g / 28.0 g. • This works out to: RateN2/RateO2 = 1.069

  13. Applying Graham’s Law of Effusion • Gas X2 effuses at 0.355 times that of O2 • rx2 = 0.355 rO2 • rx2 / rO2 = 0.355 = SQRT [(32.0 g/Mol)/Mx2] • (32.0 g/Mol)/ Mx2) = (0.355)2 = 0.126 • Mx2 = (32.0 g/Mol)/0.126 = 254 g/Mol • X g/Mol = 254/2 = 127 g/Mol • Iodine is 126.9 so the gas was I2 • Since WWII we have separated 2 Uranium isotopes 235 from 238 as UF6 gas • r235 / r238 = sqrt (352.04/349.03) = 1.0043

  14. The mean free path.

  15. Real Gases Figure 9.21 For n=1, for H2 (blue) and heavier gases (red, green). Note that heavy gases are attractive at low pressure & all are repulsive at high pressure. Why? In the real world, the behaviour of gases only conforms to the ideal-gas equation at: relatively high temperature and low pressure, low gas concentrations, low molecular weights and simple symmetric molecules or atoms.

  16. Deviations from Ideal Behaviour The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature. Figure 9.22 Figure 9.23

  17. Corrections for Non-ideal Behaviour • The ideal-gas equation can be adjusted to take these deviations from ideal behaviour into account. • The corrected ideal-gas equation is known as the van der Waals equation. • nRT n2a • P = --------- - -------- • V – nb V2

  18. (P + ) (V−nb) = nRT n2a V2 The van der Waals Equation Table 9.2

  19. Examples of Gas Chemistry& Physics in the Real World • Atmospheric pollution: industry, engines, cows • O3 generating & destroying reactions • Volcanic aerosols • Warfare: Cl2, Sarin, Mustard Gas, Phosgene • Photosynthesis, O2 and the Carbon cycle • Rocket & Jet Propulsion • Gas Shocks, Combustion Engines • Perfume and pheromones • Clathrates and Gas Hydrates • Explosives

  20. End of Part 9b2: Real Gas Applications

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