Gas Laws
GAS LAWS They’ll save your life! <ul><li>Boyle’s Law </li></ul><ul><li>Charles’s Law </li></ul><ul><li>Avogadro’s Law </li...
BOYLE’S LAW: Pressure & Volume <ul><li>For a given mass of gas at constant temperature the  volume (V)  occupied by the ga...
P i V i  = P f V f High Pressure = Low Volume Low Pressure = High Volume Temperature does not change
CHARLES’S LAW: Volume & Temperature <ul><li>For a given mass of gas at constant pressure, the  volume  occupied by the gas...
V i /T i  = V f /T f Pressure does not change As the temperature increases, the gas expands (volume   ). As Temperature d...
AVOGADRO’S LAW: Equal Volumes <ul><li>At the same temperature and pressure,  equal volumes of gases contain equal numbers ...
V i /n i  = V f /n f Pressure and Temperature remain unchanged Increasing the number of moles of gas causes an increase in...
AVOGADRO’S LAW: Equal Volumes <ul><li>Molar Volume  – it follows from Avogadro’s law that the volume of a mole of any  ide...
4 grams of He gas * 20 grams of Ne gas  * 32 grams of O 2  gas * 46 grams of CO 2  gas * 1 mol of He gas * 1 mol of Ne gas...
COMBINED GAS LAW <ul><li>Boyle’s, Charles’s, & Avogadro’s Laws may be combined algebraically to yield the combined gas law...
IDEAL GAS LAW <ul><li>PV = nRT </li></ul><ul><li>Using the proportionalities in Boyle’s Charles’s, and Avogadro’s Laws: </...
IDEAL GAS CONSTANT <ul><li>PV=nRT </li></ul><ul><li>P (atm,torr,Pa,Kpa) V (mL,L,cm3,dm3)  = nRT (kelvin) </li></ul><ul><li...
<ul><li>Density = mass / volume </li></ul><ul><li>d = m/V </li></ul><ul><li>Substitute into ideal gas law: </li></ul><ul><...
GAS LAWS REVIEW <ul><li>Boyle’s Law P i V i  = P f V f </li></ul><ul><li>Charles’s Law V i /T i  = V f /T f </li></ul><ul>...
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Gas Laws

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Gas Laws

  1. 1. Gas Laws
  2. 2. GAS LAWS They’ll save your life! <ul><li>Boyle’s Law </li></ul><ul><li>Charles’s Law </li></ul><ul><li>Avogadro’s Law </li></ul><ul><ul><li>Molar Volume </li></ul></ul><ul><li>Combined Gas Law </li></ul><ul><li>Ideal Gas Law </li></ul>
  3. 3. BOYLE’S LAW: Pressure & Volume <ul><li>For a given mass of gas at constant temperature the volume (V) occupied by the gas is inversely proportional to the pressure (P) applied to the gas. </li></ul><ul><li>That means that Volume = 1/Pressure </li></ul><ul><li>A more useful expression also describes changes in volume and pressure, given by: </li></ul><ul><li>P i V i = P f V f </li></ul><ul><li>i = initial value of pressure or volume </li></ul><ul><li>f = final value of pressure or volume </li></ul>
  4. 4. P i V i = P f V f High Pressure = Low Volume Low Pressure = High Volume Temperature does not change
  5. 5. CHARLES’S LAW: Volume & Temperature <ul><li>For a given mass of gas at constant pressure, the volume occupied by the gas is directly proportional to its absolute temperature . </li></ul><ul><li>That means that </li></ul><ul><li>Volume = Temperature x Some Constant </li></ul><ul><li>A more useful expression also describes changes in volume and temperature, given by: </li></ul><ul><li>V i /T i = V f /T f </li></ul><ul><li>i = initial value of pressure or volume </li></ul><ul><li>f = final value of pressure or volume </li></ul>
  6. 6. V i /T i = V f /T f Pressure does not change As the temperature increases, the gas expands (volume  ). As Temperature decreases, the gas contracts (volume  ).
  7. 7. AVOGADRO’S LAW: Equal Volumes <ul><li>At the same temperature and pressure, equal volumes of gases contain equal numbers of molecules (or atoms for the Noble Gases). </li></ul><ul><li>That means that if temperature and pressure remain constant, </li></ul><ul><li>V i /n i = V f /n f </li></ul><ul><li>V = volume n = number of molecules </li></ul><ul><li>One of any gas contains 6.02x10 23 gas particles (Avogadro’s number) </li></ul>
  8. 8. V i /n i = V f /n f Pressure and Temperature remain unchanged Increasing the number of moles of gas causes an increase in the volume needed to keep constant pressure and temperature.
  9. 9. AVOGADRO’S LAW: Equal Volumes <ul><li>Molar Volume – it follows from Avogadro’s law that the volume of a mole of any ideal gas at STP occupies the same volume as a mole of any other ideal gas at STP. </li></ul><ul><li>For ideal gases, this molar volume is 22.4 L @ STP (1 atm & 273K). </li></ul>
  10. 10. 4 grams of He gas * 20 grams of Ne gas * 32 grams of O 2 gas * 46 grams of CO 2 gas * 1 mol of He gas * 1 mol of Ne gas * 1 mol of O 2 gas * 1mol of CO 2 gas *
  11. 11. COMBINED GAS LAW <ul><li>Boyle’s, Charles’s, & Avogadro’s Laws may be combined algebraically to yield the combined gas law: </li></ul>Temperature must be in Kelvin Pressure must be in atm, torr, Pa, or Kpa (but same for 1 & 2) Volume must be in mL, L, cm 3 , or dm 3 (but same for 1 & 2) n = the number of moles
  12. 12. IDEAL GAS LAW <ul><li>PV = nRT </li></ul><ul><li>Using the proportionalities in Boyle’s Charles’s, and Avogadro’s Laws: </li></ul><ul><li>V = constant x 1/Pressure (fixed mass & temperature) </li></ul><ul><li>V = constant x Temperature (fixed mass & pressure) </li></ul><ul><li>V = constant x moles (fixed pressure *temperature) </li></ul><ul><li>V = constant x 1/P x T x n </li></ul><ul><li>R is the ideal gas constant. </li></ul>
  13. 13. IDEAL GAS CONSTANT <ul><li>PV=nRT </li></ul><ul><li>P (atm,torr,Pa,Kpa) V (mL,L,cm3,dm3) = nRT (kelvin) </li></ul><ul><li>* Depending on the units you use, will choose an R to cancel the units* </li></ul><ul><li>R = 0.0821 L atm/K mol </li></ul><ul><li>R = 8.31 dm 3 kPa / K mol </li></ul><ul><li>R = 8.314 J/mol K </li></ul><ul><li>R = 62.36 L torr / mol K </li></ul>
  14. 14. <ul><li>Density = mass / volume </li></ul><ul><li>d = m/V </li></ul><ul><li>Substitute into ideal gas law: </li></ul><ul><li>PV=nRT </li></ul><ul><li>Molecular Weight = mass / moles </li></ul><ul><li>M = m/n </li></ul><ul><li>Substitute into ideal gas law: </li></ul><ul><li>PV=nRT </li></ul>IDEAL GAS LAW to solve for Gas Density & Molecular Weight
  15. 15. GAS LAWS REVIEW <ul><li>Boyle’s Law P i V i = P f V f </li></ul><ul><li>Charles’s Law V i /T i = V f /T f </li></ul><ul><li>Avogadro’s Law V i /n i = V f /n f </li></ul><ul><ul><li>Molar Volume 22.4 L @ 1atm and 273 K </li></ul></ul><ul><li>Combined Gas Law </li></ul><ul><li>Ideal Gas Law PV = nRT </li></ul>
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