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Gas Laws and KMT

Gas Laws and KMT. Chapter 5. Pressure. Barometer – first pressure measuring device Torricelli, 1643 A glass tube filled with mercury, inverted into a dish of mercury. At sea level, height of mercury in the tube is 760 mm Why does the Hg stay in the tube, defying gravity?. Air Pressure.

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Gas Laws and KMT

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  1. Gas Laws and KMT Chapter 5

  2. Pressure • Barometer – first pressure measuring device • Torricelli, 1643 • A glass tube filled with mercury, inverted into a dish of mercury. • At sea level, height of mercury in the tube is 760 mm • Why does the Hg stay in the tube, defying gravity?

  3. Air Pressure • Why does a barometer measure lower air pressure when a storm is approaching? • Lower air pressure means the weight of air being pulled toward the earth is lower • Air is being pulled UP, so air is rushing into a low (wind) • Air pressure is also lower at higher elevation • At 9600 ft, air pressure is only 560 mm • Less air pushing down on earth’s surface

  4. Manometer The principle of a manometer measurement depends on the fact that given the same fluid, pressure is the same at equal heights. Pgas= Patm – h OR Pgas= Patm + h Manometer is a substitute for a Barometer and both measure mm Hg Mm Hg =Torr

  5. Pressure • Standard Atmosphere = 760 torr = 760 mm Hg • Pressure = Force/area • SI units of measure • Force = Newtons • Area = m2 • SI unit of measure for pressure is Pascal (Pa) • 1 Standard atmosphere – 101,325 Pa

  6. Gas Laws • Boyles Law • Charles Law • Guy-Lussac’s Law (Not used much) • Avogadro’s Law • Ideal Gas Law • All Lead To: • Gas Stoichiometry

  7. Boyles Law • Boyle studied pressure and volume • PV = k • Temperature constant • Amount of gas constant • Variation: • V=k/P • P=k/V • Boyles Law is also frequently written and used as: • P1V1 = P2V2

  8. Charles Law • Studied relationship between pressure and temperature • Determined that plots of volume vs. temperature are linear • V = bT • Constant pressure • Constant amount of gas • NOTE: gas cannot have a negative volume, so temperature cannot be negative. Thus we MUST use Kelvin scale for temperature at all times. • More on this later • Variations: • V/T=b

  9. Charles Law • Charles Law is also frequently written and used as: • V1/T1 = V2/T2

  10. Avogadro’s Law • Postulated that equal volumes of gases at the same temperature and pressure contain the same number of ‘particles’. • Avogadro’s Law • V = an • a = proportionality constant • N = number of moles of gas • Variations: • V/n = a (constant)

  11. Combined Gas Law • Assumes constant amount of gas • PV/T = k • Or • P1V1/T1 = P2V2/T2

  12. Ideal Gas Law • Boyles Law: V = k/P (constant T & n) • Charles Law: V = bT (constant P & n) • Avogadro’s Law: V=an (constant P & T) • Combined: V = R(Tn/P) • Or PV=nRT • R is universal gas constant (0.08206 L*Atm/mole*K) • MAKE SURE ALL TEMPS ARE IN KELVIN • This is the IDEAL GAS LAW • Real gasses behave somewhat differently

  13. Gas Stoichiometry • Molar volume of a gas = 22.42 L at standard temperature and pressure • STP (standard temperature and pressure) • 0ºC (273K) • 1 atm (760 torr or 760 mm Hg • Using gas density: • Density = mass/volume • PV=nRT  P = nRT/V

  14. Gas Stoichiometry Using Density • Density = mass/volume • PV=nRT  P = nRT/V • n = mass/molar mass =m/molar mass • P = (m/molar mass)RT/V • P = mRT/V(molar mass) • m/V = density (d) • P = dRT/molar mass • Molar mass = dRT/P

  15. Dalton’s Law of Partial Pressures • Applies to Gasses • For a mixture of gasses in a container, the total pressure is the sum of the pressures that each gas will exert if it were alone • PTOTAL = P1 + P2 + P3+….. • PTOTAL = n1RT/V + n2RT/V + n3RT/V…. • Equals (n1 + n2 + n3 + …)RT/V • Equals NtotalRT/V

  16. Collecting Gas Over Water • Whenever you collect gas over water, water vapor is present: • Water molecules escape from surface of water • Pressure due to water, depends on temperature, and is the vapor pressure of water. • Total pressure of gas collected is Pressure of gas + pressure of water vapor

  17. Kinetic Molecular Theory • A theory summarizes observed behavior • A model allows you to use theories to predict behavior • Also can be viewed as a way of understanding, a way of thinking, a mental construct • KMT is a model based on gas laws

  18. Kinetic Molecular Theory • Particles are so small compared to distances between the particles that the volume of the particles can be assumed to be negligible (zero). • The particles are in constant motion. Collisions of the particles with the walls of the container are the cause of pressure exerted by the gas. • The particles are assumed to exert no forces on each other; they are assumed to neither attract nor repel each other. • The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

  19. Boyles Law • If volume decreases, pressure increases. • KMT says a decrease in volume means the particles will hit the wall more often

  20. Pressure and Temperature • Ideal Gas Law: Pressure is directly proportional to temperature • KMT: as temperature increases; • Speeds of particles increases • Particles hit wall with greater force • Particles hit walls with greater frequency • Result: increased pressure

  21. Charles Law • Ideal Gas Law: at constant pressure, volume of gas is directly proportional to temperature Kelvin • KMT: When heated; • Speed of molecules increases • Hit walls with greater force • Hit walls with greater frequency • Only way to keep pressure constant is to increase volume

  22. Avogadro’s Law • Ideal Gas Law: Volume is directly proportional to number of particles present • Constant temperature & pressure • KMT: If you add more particles to a container; • Pressure would increase • Only way to maintain pressure is to increase volume

  23. Dalton’s Law • Dalton: Total pressure is the sum of the partial pressures • KMT: Assumes; • all gas particles are independent of each other • Volumes of individual particles are unimportant • Identities of particles do not matter

  24. Deriving Ideal Gas Law • Apply particle physics to assumptions of KMT: • Use definitions of velocity, momentum, force, pressure • See Appendix 2 for details • KE = 1/2 mv2 where v is root mean squared speed. • Total kinetic energy is KE = NA(1/2 mv2) where N is Avogadro's number • Final derivation is: P = 2/3 (n NA(1/2 mv2) / V)

  25. What is Temperature? • KMT bases temperature on Kelvin • Because it is based on average kinetic energy of the particles • Requires an absolute energy scale • Hence: Kelvin

  26. Problem: • Calculate the average kinetic energy of the CH4 particles in a sample of CH4 gas at 273K and at 546K

  27. Thursday • Effusion and Graham’s Law • Diffusion • Real Gases and van der Waal’s equation.

  28. Effusion & Diffusion • Diffusion – the mixing of gases without agitation • Effusion – passage of a gas through a tiny orifice (hole)

  29. √M2 √M1 Rate of Effusion for gas 1 Rate of Effusion for gas 2 = Effusion • Graham’s Law of Effusion M1 and M2 are molar masses for the gases.

  30. Diffusion • Diffusion takes a long time • Even though molecules are travleing 450 and 660 m/s • Why? • Tube is filled with air • Lots of collisions with air that don’t lead to a reaction • Difficult to describe theoretically

  31. Next • Real Gases • Corrections for pressure • Corrections for volume

  32. Real Gases • Ideal gas behavior is best thought of as the behavior approached by real gases under certain conditions. • Ideal gas behavior fails at: • Low temperatures • High pressures • Real gases behave most like ideal gases at: • High temperature • Low pressure

  33. Real Gases • Ideal gas assumption of volume is incorrect: • Molecules always take up some space. • Correct for volume by subtracting volume for the molecules • VREAL = VIDEAL-nb • n is number of moles • b is an empirical correction constant • So: • P’ = nRT/(V-nb)

  34. Real Gases • But we still have to correct for the fact that real gases DO have attraction forces. • Effect is to make observed pressure POBS smaller than it normally would if there were no attractions: • POBS = (P’ – correction factor)(nRT/(V-nb) – correction factor • Size of correction factor depends on concentration of the gas molecules in particles per liter (n/V) • Higher concentration, more likely particles are close enough to attract. Depends on square of number of particles because 2 particles have to get close enough.

  35. Real Gases • So: • POBS = P’ – s(n/V)2 • Inserting correction factors for both volume and attractions gives the equation: • POBS = (nRT/(V-nb)) – a(v/V)2 Pressure correction factor Volume of container Volume correction factor

  36. Van Der Waals Equation • POBS + a(n/V)2 x (V-nB) = nRT

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