Does addition of solute affect the rate of condensation?

I know that addition of a non-volatile solute in a pure solvent effects the rate of evaporation as the number of molecules leaving the liquid bulk per unit time decreases. However when the rate of evaporation decreases immediately , rate of condensation should automatically increase , this is because, if we consider a liquid 'X' in equilibrium as:


$$\ce{X(l) <=> X(g)}$$


Now when some amount of solute is added in the pure $\ce{X}$ , this dynamic equilibrium is obviously disturbed. $\mathrm{(Rate)\_{evap}} \downarrow$ so to attain equilibrium $\mathrm{(Rate)\_{cond}} \uparrow$ as reaction shifts backward.
also when equilibrium is attained the number of molecules entering a liquid has decreased , so at equilibrium rate of condensation has decreased. So, overall it has been affected.


But when it browsed various sites , all agreed that it is unchanged by solute.
So, where's the problem? Isn't my logic correct?




When a solvent is at isobaric conditions in equilibrium with its gaseous phase, the rate of evaporation and condensation are equal.


If we add a solute to the solvent, the activity, chemical potential, saturated vapor pressure and rate of evaporation decreases. As the rate of condensation remains the same, the **net** condensation increases from its equilibrium zero value.


If the system is isolated, then while there is ongoing condensation, temperature raises, saturated vapor pressure increases (due both increasing temperature and diluting by the condensate), while pressure of vapor decreases, until there is reached the new equilibrium with higher temperature but lower gas(vapor) pressure. This presure is now equal to saturated vapor pressure for the final solution and temperature.


If the system is also isothermic, then the heat from ongoing condensation is dissipated. The saturated vapor pressure and the gas (vapor) pressure at the new equilibrium are lower, compared to pure solvent, according to the Raoult law and eventual its deviations.


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