carter tomlenovich

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Mixtures of Gases

Ideal Gas Mixtures

  • Ideal mixtures of gases are comprised of molecules that do not interact.

  • Their contrubutions simply add together.

  • Consider a mixture of ideal gases in a volume V aty temperature T. For any ideal gas “X” in the mixture, we have:

    • $PV = nRT -> P_x = \frac{n_xRT}{V} $

Partial Pressure

  • The total pressure of an ideal gas mixture is related to the total number of gas molecules:
    • $P_{total} = \frac{n_{total}RT}{V} $
  • The total number of moles is the sum of the moles for each componenet gas:
    • $ n_{total} = n_a + n_b … $
  • Therefore the total pressure is:
    • $ P_{total} = \frac{n_aRT}{V} + \frac{n_bRT}{V} + \frac{n_cRT}{V} … $
  • Each of these statements of the total pressure due to one gas mixture componenet as if it were alone in the vessel.
  • These are called the “partial pressure” pf the component gas, $P_x$

Dalton’s Law of Partial Pressures

  • ” The total Pressure of a gas mixture is the sum of the partial pressures of the componenets of the mixture.
  • $P_{total} = P_a + P_b + P_c + …$

Mole Fractions

  • The “Mole fraction” of gas A is the fraction of moles in a mixture that are of type A:
    • $x_a = \frac{moles of a_a}{total moles in a mixture} = \frac{n_a}{n_{total}}$
  • As a result we can easily determine partial pressure from mole fractions:
    • $P_A = x_aP_{total}$