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Ideal Gas Law

Ideal Gas Law. 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.

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Ideal Gas Law

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  1. Ideal Gas Law

  2. 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.

  3. Adding atoms increases the volume of a gas. Twice the air in a balloon doubles the volume Constant pressure and temperature Try a relationship: Counting Atoms + =

  4. Mass Independent • Density is mass divided by volume. • Mass in an equation can be converted to density • PV=amT becomes P = arT • Experimentally a would vary for each type of gas • Constant is the same if the number of molecules N is counted instead of the mass m.

  5. 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.

  6. 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

  7. 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

  8. 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

  9. 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 next

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