Vapor pressure lowering Raoults law

Solutions have two fundamental property changes compared with pure water lowering the vapor pressure and freezing point depression. In cloud microphysics, these changes are crucial for droplet growth and precipitation formation. 

In about 1886, Raoult discovered that substances have lower vapor pressures in solution than in pure form and that the freezing point of an aqueous solution decreases in proportion to the amount of a non-electrolytic substance dissolved. The ratio of the partial vapor pressure of substance i in solution to the vapor pressure of the pure substance (subscript 0 denotes the pure substance) is equal to the mole fraction x of i  

This law is strictly valid only under the assumption that the chemical interaction between the two liquids is equal to the bonding within the liquids the conditions of an ideal solution. In the atmosphere, water is the solvent and dissolved matter is predominantly non-volatile. The vapor pressure of water p in solution is smaller than that of pure water p , whereas the vapor pressure of the solution ps is ps = p + Pi. Because of + x,- = 1 we rewrite Raoulfs law as follows  

Assuming that p°— -0 (the dissolved substance is non-volatile) we find for the relative lowering of vapor pressure of the solution (Apip), i. e. equal to the mole fraction of i  

We can now transform the Kelvin equation (4.223), valid for pure water, by consideration of Raoulfs equation for a droplet with dissolved matter. The total change in vapor pressure consists of the vapor change above the curved surface and the vapor change of the solution  

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