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Gases Key Points

Gases Key Points. States of Matter Gas Compressible, variable volume and pressure Expands into available space Rapid mixing No collective structure … except the container Subject to condensation into liquid Liquid Incompressible Flows under pressure Conforms to container

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Gases Key Points

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  1. Gases Key Points • States of Matter • Gas • Compressible, variable volume and pressure • Expands into available space • Rapid mixing • No collective structure … except the container • Subject to condensation into liquid • Liquid • Incompressible • Flows under pressure • Conforms to container • Slow mixing (relative to gases) • Cohesive collective structure • subject to evaporation into gas

  2. Overview • More States of Matter • Solid • Retains shape, not container confined • Subject to cleavage, breakage, bending • More structure, higher degree of order • Crystalline shapes are common • “Lattice Energy” holds things together • No (or slow) mixing, diffusion limited • Plasma … the “4th state of matter” • Not part of everyday experience • Ionized gases, charged particles, subatomic species • Interior of the Sun, “Solar Wind” • Florescent or Neon gas electrical discharge • Arc Welding, “sputtering” of metals in vacuum • Plasma metal cutters, 30K degrees

  3. Gases are unique • Less than 10% of 116 elements are gases • Six of these are non-reactive “noble gases” • He, Ne, Ar, Kr, Xe, Rn • Five remaining gases • H2, N2, O2, Cl2, F2 • All are diatomic, yielding octets of 8 electrons • All are reactive, N2 and O2 in atmosphere • All have some biologic role

  4. The Gaseous Elements

  5. Why a Gas? • Gas molecules have kinetic energy • Energy proportional to Kelvin temperature • Gas molecules have full octets • Gas molecules have little mutual attraction • Energy of collisions keeps molecules apart

  6. Atmospheric Gases • Atmosphere is homogeneous mixture of gases • Nitrogen 76% - “inert” for most uses, but reactive • Numerous oxides “NOX“ components of “smog” • Anesthetics, nitrate fertilizer, nitrite preservatives • Oxygen 21% - essential for animal life • Product of photosynthesis • Oxidizes food for chemical energy, kinetic energy, and heat • Argon 0.93% - most abundant “noble” or inert gas • Used in light bulbs to prevent darkening by evaporating W • Used in gas discharge lamps (blue), lasers, protective package • Carbon Dioxide 0.037% - breathing, fermentation, combustion • Required by plants to provide cellulose, sugars, and Oxygen • Basis of carbonated drinks … soda, beer, champagne • Most life on earth involves both CO2 and O2 • Methane 0.00017% - natural gas, animal waste • Very common natural product • “swamp gas”, land fill decomposition, animal flatulation • Lighter than air, very little stays near the surface

  7. Gas Behavior • Gases • Intertwined relationships • Compressibility relates volume & pressure • Amount of material controls volume of that material • Volume changes with Temperature • Basis of “heat engines” • Subject to phase changes • Water vapor into liquid water or ice • “Liquid Air”, sublimation of “dry ice” • Models needed to explain & predict behavior • Started with simple “2 at a time” relationships • P & V, moles & V, V & Temp, etc • Evolved to “Ideal Gas Law”, PV=nRT • Includes most of the variables in one equation • Other gas laws are special cases with omitted variables

  8. Gases & Gas Laws • Gas Proportions and properties • Gas laws with 2 variables • Boyle’s law, Charles’ law, Avagadro’s Law • Combined gas law with 3 variables • PV/T=constant • Ideal Gas Law with all 4 variables • PV=nRT • Stoichiometry • Applications • Density and Lift • Air Bags, etc.

  9. Gas Pressure • Pressure Units of Measure • Air pressure is familiar concept • High altitude, auto tires, skin diving, sailboats • Pressure defined as force per unit area • Originally 1 Atmosphere = 760 mm Hg (sea level) • 1 Atmosphere = 14.4 psi (Imperial system) • 1 atmosphere ≡ 101,325 Pascal (mks) • MKS units often inconvenient, leading to new units • 100,000 Pa = 1 Bar (not tied to atmosphere) • 1mm Hg = 1 Torr (1/760 = 0.13% of atmospheric pressure)

  10. Units of Pressure

  11. Vacuum at top of glass Zero pressure at glass top Mercury rises in tube Air pressure pushes Hg up Mercury height = pressure 760mm Hg ≡ 1 atmosphere 32 feet H2O ≈ 1 atmosphere Blowing versus Sucking Which is stronger? Establishes pump designs Mercury Barometer

  12. Gas Laws • Boyle’s Law • Pressure and Volume are inversely related • Pressure * Volume = constant • assumes constant amount of material & temp • If pressure goes up, volume goes down .. & vice versa • Charles’ Law • Adds temperature as a new variable • Volume proportion al to temperature • Volume / Temperature = constant • Assumes constant amount of material and pressure • If temperature goes up, so does volume • Avagadro’s Law • Adds amount of material as a new variable • Volume of gas depends on moles • Volume / Moles = constant • If moles goes up, so does volume • Each mole of gas occupies approx 22.4 liters

  13. 2-variable Gas Laws • Boyle’s Law • Pressure and Volume are inversely related • Pressure * Volume = constant • assumes constant amount of material & temp • If pressure goes up, volume goes down .. & vice versa • Charles’ Law • Adds temperature as a new variable • Volume proportional to temperature • Volume / Temperature = constant • Assumes constant amount of material and pressure • If temperature goes up, so does volume

  14. Gas Laws, Boyle • Boyle’s Law • Pressure and Volume inversely related • P1V1 = P2V2 • Pressure * Volume = constant • Pressure = constant * 1/Volume • Pressure goes up, volume goes down • NASA graphic shows 4 liters at 1 atmosphere • Converts to 3 liters at 1.33 atmospheres • 4*1 = 4, 3*1.33 = 4 • both P*V products yield same value = a constant

  15. Gas Laws • Boyle’s Law • Pressure and Volume inversely related • Pressure * Volume = constant • Pressure goes up, volume goes down • NASA graphic shows 4 liters at 1 atmosphere • Converts to 3 liters at 1.33 atmospheres • 4*1 = 4, 3*1.33 = 4 • both P*V products yield same value = a constant • Assumes SAME amount of material present • Assumes SAME temperature both cases

  16. Boyle’s LawPressure and Volume inversely relatedsee NASA animation related to this image

  17. Gas Law Animations NASA site for gas law animations http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/gaslab/gastil.html • “stop” prior animation, • lower left red box in the animation itself • Select “New Case”, left-hand column • Freeze 2 of 4 variables • Select one of 2 cases to animate

  18. Alternative Boyle’s Formulas • P1V1 = P2V2 • Generally used relationship, most often quoted • V2 = V1*(P1/P2) solving for Volume • This rearrangement has Volumes directly related V = V*(ratio) • Note that Pressure dimensions cancel (psi, pascal, etc.) • Note that volumes must have same dimensions (liter, quart, mL) • Assumes NO CHANGE in temperature or amount of material • P2 = P1*(V1*/V2) solving for Pressure • Same idea as for volume, cancellation of units • Can use arbitrary units of measure, but must be consistent

  19. Examples • Boyle’s Law: PV = constant • P1V1 = P2V2 (constant temperature & mass) • Can solve for 4th condition when other 3 are known • P1 = P2V2 / V1 • V1 = P2V2 /P1 • P2 = P1V1 / V2 • V2 = P1V1 / P2 • Alternatively, can have ratios of same quantity • P1/P2 = V2/V1 • Important to note DIMENSIONS are UNIMPORTANT • But must be consistent to cancel

  20. Effect of Temperature Change • Charles’ Law • Adds temperature as a variable • Gas volume proportional to temperature • Volume / Temperature = constant • Assumes constant amount of material & pressure • If temperature goes up, so does volume • NASA graphic shows 4 liters at 300 degrees • Also shows 3 liters at 225 degrees • 4 / 300 = 0.013 3 / 225 = 0.013 • Both divisions yield same value = a constant

  21. Charles’ LawVolume of gas proportional to absolute temperatureSee NASA animation of slide below

  22. Boyle’s Law Calculation Example • Bag of potato chips San Jose  Tahoe • What is the volume at Tahoe pressure? • P1 = 1.0 atmosphere (14.7psi) in San Jose • V1 = 1.0 liter volume in San Jose • P2 = 0.75 atmosphere at Lake Tahoe (6225 feet) • V2 = ? • P1V1 = P2V2, or V2 = V1*(P1/P2) • V2 = 1 Liter * (1 atmos / 0.75 atmos) • V2 = 1/0.75 = 1.3 liters volume at Tahoe • Note that pressure units vanish, anything consistent is OK (atm, psi, pascals, etc.). Same for volume

  23. Pressure vs Altitude6225 ft at Lake Tahoe, ≈ 0.75 atmosphere

  24. Temperature Change, Charles’ Law • Charles’ Law: V1/T1=V2/T2 • Adds temperature as a new variable • Volume proportional to temperature • Volume / Temperature = constant • Assumes constant amount of material & pressure • If temperature goes up, so does volume • NASA graphic shows 4 liters at 300 degrees • Also shows 3 liters at 225 degrees • 4 / 300 = 0.013 3 / 225 = 0.013 • Both divisions yield same value = a constant

  25. What Temperature Scale to use? • Cannot use arbitrary scales • 2oF is NOT “twice as hot” as 1oF, equally cold • 0oC =melting ice, not absence of temperature • We use ratios in gas law calculations • Temp. Ratio 1oC/0oC =∞… not very useful • What’s needed • A scale with truly proportional temperatures • Where 100o is actually “Twice as Hot” as 50o • A scale which goes to true (absolute) zero • No negative temperatures

  26. Traditional Temperature Scales

  27. Proportional P vs T with scale through zeroProportional scale defined using “Kelvin” degrees

  28. Kelvin Scale is simple idea • Absolute zero is absence of all motion • Cannot go any lower than 0oK • Close to zero is boiling point of helium at 4oK • Kelvin degree “size” same as Centigrade • Zero Kelvin becomes -273oC • Conversion is oK = oC+273 • Going the other way oK-273 = oC • Some die-hards like Fahrenheit degrees • Conversion is “Rankine” scale oR = oF+492 • Could be handy if you have lots of Fahrenheit data

  29. All 4 temperature scales

  30. Charles’ Law Calculation Example • Balloon from ski area into heated lodge • V/T = constant • V1/T1 = V2/T2 = constant • V1 = 1 liter • T1 = -10oC at ski lift (-10+273=263oK) • T2 = 25oC in lodge (25+273 = 298oK) • V2 = V1*(T2/T1) = 1 Liter* (298/263) • V2 = 1.13 Liters (constant pressure)

  31. Gay-Lussac Law Same as Charles’ law, substitute Pressure P = k*T P & T proportional, k=constant P1/T1 = P2/T2 assumes constant volume P2/P1 = T2/T1 P’s and T’s together Useful because easy to see that units cancel P1*T2 = P2*T1 avoids division in formula 34

  32. An example • What is pressure inside a tennis ball going from warm room to winter tennis court • P1/T1 = P2/T2, P2=P1*(T2/T1) • P1 = 2 atmospheres inside ball (assumed) • no change to tennis ball volume • T1 = 298oK (25oC) , T2 = 263oK (-10oC) • P2=P1*(T2/T1) • P2 = 2atm*(263/298) = 2*0.88 atm • P2 = 1.76 atmospheres (less bounce)

  33. Combination 3-Variable Gas Law • Can combine Charles’ and Boyle’s Laws • Boyle’s Law • P1V1 = P2V2 (constant temperature & mass) • Charle’s Law • V / T = constant • Algebraic substitution & simplification yields • P*V = constant, also V/T = constant • Both are related to same variables, so • P1V1 / T1= P2V2 / T2 • Can calculate any quantity if other 5 are known

  34. Formula Variations P1V1 / T1= P2V2 / T2 • P2 = P1 (V1 /V2)*(T2 / T1) • Pressure change given by ∆T and inverse of ∆V • V2 = V1 (P1 /P2)*(T2 / T1) • Volume change given by ∆T and inverse of ∆P • T2 = T1 (P2 /P1)*(V2 /V1) • Temperature change given by ∆P and ∆V

  35. Combined Law Calculation • Automobile driven to Death Valley • Temperature changed 70oF  120oF • 70oF  21oC  294oK • 120oF  49oC  322oK • Tire volume changed 20 21 liters • Tire pressure 30psi in S.Jose ? In Death V. • P2 = P1 (V1 /V2)*(T2 / T1) • P2 = 30( 20/21)*(322/ 294) • P2 = 31.3 psi

  36. What about mass change? • Avogadro’s Law • Adds amount of material as a new variable • Intuitive that volume related to material amount • Volume of gas depends on moles • Volume / Moles = constant • If moles goes up, so does volume • Each mole of gas occupies approx 22.4 liters

  37. Gas Law Summary • Four variables involved for Gases • Pressure, can be “atmospheres” or Pascals • For ratios involving 2 pressures, dimensions cancel • Volume, can be liters or cubic meters • For ratios involving 2 volumes, dimensions cancel • Temperature, always in Kelvin, oC+273=oK • Kelvin is linear, “0” is really zero (not so for oC, oF) • Mass, usually in moles • For ratios involving 2 masses, dimensions cancel

  38. Gases & Gas Law Summary • Avagadro’s Gas Law • Addition of mass as a variable • Ideal Gas Law with all 4 variables • PV=nRT • Gas Density & Volume • Stoichiometry, STP • Applications • Auto air Bags, dirigibles, hot-air balloons

  39. Avagadro’s Gas LawChange of mass is added variable, see animation more material  more pressure and/or more volume

  40. Total of 4 Gas Law Variables • Variables involved for Gases • Pressure, can be “atmospheres” or Pascals • For ratios involving 2 pressures, dimensions cancel • Volume, can be liters or cubic meters • For ratios involving 2 volumes, dimensions cancel • Temperature, always in Kelvin, oC+273=oK • Kelvin is linear, “0” is really zero (not so for oC, oF) • Mass, usually in moles • For ratios involving 2 masses, dimensions cancel

  41. Gas Law Summary • Boyle’s Law: PV = constant • P1V1=constant=P2V2 • no changes in temperature or mass • Only 2 variables to consider • Charles’ Law: V/T = constant • Volume inversely related to absolute temperature • V = constant * T (no change in pressure or mass) • says rising temperature increases volume • Assumes constant amount of material & pressure • Only 2 variables involved

  42. Gas Law Summary • Avagadro’s law: V/n = constant • Volume inversely related to amount of material • V = constant * moles • no changes in pressure or Temperature • More moles provides larger volume • Assumes constant Temperature and Pressure • Only 2 variables involved • Combined Gas Law P1V1/T1 = P2V2/T2 • Handles 3 variables • Mass not included

  43. Gas Law Summary • Why have 4 laws? • Bad News • 4 different relationships to remember • PV=c, V/T=c, V/n=constant, combo P1V1 / T1= P2V2 / T2 • Three People’s names, which one goes where? • Good News • Simple formulas, fewer variables required • Dimensions tend to cancel • Not forced into MKS or self-consistent unit system • Can mix any units where dimensions cancel • PSI1/PSI2 = Pascal1/Pascals2 = Atmosph1/Atmosph2 • OK to choose the SIMPLEST formula to solve a problem

  44. Ideal Gas LawBringing it all together Combination of P, V, n, and T • Pressure = Pascals (MKS definition, or atmos) • Volume = Liters, or cubic meters • n = moles of material • Temperature = degrees Kelvin (Centigrade + 273) • Constant = R (depends on dimensions used) • R = 8.314 Joules/(mole-degree K) • R = 0.082 Liter-Atmospheres/(mole-degree K) PV = nRT

  45. Ideal Gas Law • PV=nRT is extremely useful • Handles all 4 variables (plus a constant) • Can determine 4th variable if other 3 are known • Moles of methane in tank of known P, V, T • Pressure on piston if V, n, and T are known • Temperature of a system if P, V, and n are known • Volume of gas if P, n, and T are known • Lots of examples in text and homework • These are linear relationships, no square laws

  46. Ideal Gas • Ideal Gas Law PV=nRT • Simplifies to Boyle’s Law when n and T are constant • PV = nRT = constant “k” • Simplifies to Charles’ Law when n and P are constant • V/T = nR/P = constant “k” • Simplifies to Avagadro’s Law when T and P are constant • V/n = RT/P = constant “k” • PV=nRT Very useful • handles many gas calculations

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