The vapor pressure of water at $\pu{70 ^\circ C}$ is $\pu{233.7torr}$.
If I were to put a temperature probe directly above the liquid water, what would it read?

In other words, does a water molecule need to have $\frac32kT$ (where $T=\pu{373 K}=\pu{100 ^\circ C}$) to escape the liquid?

  • 1
    $\begingroup$ While it's a liquid water can escape what contains it due to the difference of chemical potential and it will escape until the thermodynamic equilibrum has not been reached. This is due to phenomenas of diffusion. You'll find some explaination there $\endgroup$
    – ParaH2
    Apr 3 '17 at 23:01

No, the average thermal energy doesn't need to be the one corresponding to 100C. Solo water molecules can exist in vacuum or in a gas phase with whatever kinetic energy. Liquid water condensation starts when the concentration of the water molecules is enough high (there is a tipping point), i.e. when the partial pressure of water reaches the vapor pressure for the given temperature.

From the classical thermodynamic point of view (similar argument to Hexacoordinate-C's comment), there is a chemical potential of water in the gas phase which is dependent on the partial pressure of water, and there is a chemical potential of condensed water for a given temperature. When the partial pressure is low, the gas phase chemical potential is lower than it would in the condensed phase -> it is stable in gas phase. When the partial pressure reaches the vapor pressure, the chemical potential is equal to the gas phase and condensed phase.

  • $\begingroup$ I'm sorry, this answer doesn't make much sense to me. Is there a resource that discusses the relationship between chemical potential and partial pressure that you recommend? $\endgroup$
    – Nova
    Apr 4 '17 at 21:03
  • $\begingroup$ Any thermodynamics textbook which discusses chemical topics (concentration, pressure etc dependence of chemical potential, generally around concepts like fugacity) $\endgroup$
    – Greg
    Apr 5 '17 at 8:12

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