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Ideal Gas Law

Gases

  • Fluid that explains to fill the space that contains it.
  • Free molecules undergoing breif, elastic collisons.
  • Highly compressible,
  • Flows from higher to lower pressure,
  • Generally act “ideally”.

Pressure

Pressure is described as Force Exerted / Area of affected region. Also commonly know as Newtons / m^2

$ Pressure = \frac{(kg)(s^-2)}{m} $

This unit is called the Pascal (Pa)

  • Units
    • IUPAC: Standard Pressure = 100,000 Pa = 1 bar
    • mmHg: millimeters of mercury in a barometer = 1 Torr
    • $ 1 Atm = 760 Torr = 101325 Pa = 101.325 kPa = 1.01325 $

The Gas Laws

  • The properties of gases were elucidated over many tears by several scientists.
    • Pressure-Volume: Robert Boyle and Robert Hooke
    • Volume-Temperature: J.A.C. Charles
    • Volume-Amount: Amedeo Avogadro
    • Pressure-Temperature: Guiaume Amontons
  • $ PV = nRT $ <– Ideal Gas Law

Ideal Gas Law

  • Law applies STRICKLY to ideal, non-interacting gases.
  • Law applies APPROXIMATELY under condictions where gas molecules interact only weakly.
  • Most common gases act like “ideal gases” under typical conditions.

  • PV = nRT
    • n is Number of moles.
    • T is temperature in moles.
    • P is pressure
    • V is Volume
  • Boyles Law:
    • If n and T are constant:
      • $ PV = (nRT) = C $
      • $ P_1V_1 = P_2V_2 $
  • Charles’s Law:
    • Keeping P and n constant:
      • $ V (nR/P)T = CT $
      • $ (V_1/T_1) = (V_2/T_2) $
  • Avogadro’s Law:
    • Keep P and T constant:
      • $(V_1/n_1) = (V_2/N_2)$
      • $V = (RT/P)n = Cn$

Using the Ideal Gas Law

Solve for Volume:

  • $ V = nRT/P $

Solve for pressure:

  • $ P = nRT / V $

Solve for amount:

  • $ n = PV/RT $

Gas Constants

Value Units Pressure Volume
8.31446 m^3 Pa K mol Pa m^3
8.31446x10^-5 m^3 bar K mol bar m^3
8.31446x10^-2 L bar K mol bar L
62.36358 L Torr K mol Torr L
8.205734x10^-2 L atm K mol Atm L