Liquid propane equilibration between tanks.

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If I have two equal size tanks (150 gallon for example) one with 40% liquid propane the
other with a minimal amount of propane gas, when the tanks are connected would the liquid propane equilibrate, yielding 20% in each tank or would just the gas pressure equilibrate between the head space of the 40% tank and the tank with only gas?
 
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If the tanks hold liquid (and not gas under high pressure) then the pressure inside should be the equilibrium vapor pressure.
At this pressure the evaporation and condensation rates are equal.
This pressure depends only on temperature. Does not depend on how much liquid is in the tank.
When the two tanks are joined, the vapors will have pretty much same pressure and as the evaporation and condensation rate is the same for both tanks, the liquids should keep the same level. If you want to tilt the balance, I suppose you can heat up one tank.