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Ideal Gas

Ideal Gas. Gas Expansion. For small changes in volume, gas acts like a liquid. Air (1 atm) b = 3400 x 10 -6  C -1 For a 40  C change this would be a 14% volume change. Not a small fraction of the total. Boyle’s Law.

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Ideal Gas

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  1. Ideal Gas

  2. Gas Expansion • For small changes in volume, gas acts like a liquid. • Air (1 atm) b = 3400 x 10-6C-1 • For a 40 C change this would be a 14% volume change. • Not a small fraction of the total

  3. Boyle’s Law • Experimental observations show that the volume of gas is inversely proportional to the pressure. • Fixed temperature • Use absolute pressure, not gauge pressure • Named after Robert Boyle who observed it in the 17th century.

  4. Charles’ Law • Pressure and mass can be kept constant for a gas. • The gas then does behave in a very linear way • Volume and temperature • Named after Jacques Charles who observed it in the 18th century.

  5. Gay-Lussac’s Law • Pressure is also related to the temperature. • The effect is linear if the volume is kept the same. • Named after Joseph Gay-Lussac who observed it in the early 19th century. hot high P cold low P

  6. Combining Relationships • Science often relies on a controlled experiment. • Hold all variables fixed except one • Measure change in another property • Gas laws were each made with all but two properties constant. • Combine those three laws into a single relationship.

  7. Adding atoms increases the volume of a gas. Twice the air in a balloon doubles the volume Number of atoms N Constant pressure and temperature This describes the state of the system, and is called an equation of state. Counting Atoms + =

  8. Ideal Gas Law I • The equation of state links pressure, volume, temperature, and amount of gas. • This is an ideal gas law, since real gases may vary slightly.

  9. Boltzmann’s Constant • The constant k applies to all gases. • It’s called Boltzmann’s constant. • k = 1.38 x 10-23 J/K • Dimension links temperature and energy

  10. The Mole • Boltzmann’s constant has a very small value. • There are a vast number of atoms in a macroscopic system • Define a fundamental unit to count large numbers • The mole (mol) is a unit of amount. • Number of carbon-12 atoms in 12.00 g • Amount of molecules equal to Avogadro’s number • NA = 6.022 x 1023

  11. Ideal Gas Law II • The amount of gas can be measured in moles. • n = N / NA • R is the universal gas constant • R = NA k • R = 8.314 J / mol-K

  12. Standard temperature and pressure (STP) is 0 C and 1 atm = 1.013 x 105 Pa. What is volume of one mole? Convert temperature to K. T = 0 + 273.15 = 273.15 K Use the molar form of the ideal gas law. V = nRT/P Substitute values: V = (1.000 mol)(8.314 J/mol-K)(273.15 K) / (1.013 x 105 Pa) V = 2.242 x 10-2 m3 = 22.42 L Mole Size

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