Vapor Pressure, Raoult's law, conc of gases in the vapor phase

[Zellmer, Robert]

I got a couple of questions about vapor pressure of two volatile substances, Raoult's law
and mole fraction of the substances in the vapor phase.  I did an example for a mixture
of two volatile substances like this in lecture in the section on vapor pressure in
colligative properties.  EOCE 13.69 and 13.70 are additional examples.

For any gas in a mixture of gases the partial pressure of the gas is given by,

P_gas = X_gas * P_total,

where X_gas is the mole fraction of the gas in the gas phase.

The total P and the partial pressures of the solvent and solute above the solution are
given below.  The P_gas can be obtained from Raoult's law as well as the eqn above
but Raoult's law uses the mole fractions in the liquid phase.

P_total = P_solvent + P_solute          (Dalton's Law of Partial Pressures)


P_solvent = X_solvent in liq phase * P_pure solvent             (Raoult's Law)

P_solute = X_solute in liq phase * P_pure solute                  (Raoult's Law)

so, to get the mole fraction of solute in the vapor phase,

P_solute, the vapor pressure of solute in the vapor phase is given above by
Raoult's Law.

P_solute is also given by,

P_solute = X_solute in the vapor (gas) phase * P_total

X_solute in vapor phase = P_solute/P_total

Dr. Zellmer

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