Consider a case I where I have a container halfway filled with a pure volatile solvent. Now we know that liquid molecules will start getting converted into vapour phase, and then dynamic equilibrium will be reached. The equilibrium constant here is given by $K= [P_0]$, where $P_0$ is the partial pressure of the vapours. ($[P]$ due to pure liquids is considered as 1, so denominator is 1 and hence $K = [P_0]$).
Now we know $K$ only depends on temperature and is independent of any impurities being added, right?
Now, consider the case if I add some impurities to the pure solvent. We know there will be a lowering of vapour pressure and now if I write the equilibrium constant equation, $K = [P_1]$ , where $P_1$ denotes the new vapour pressure when impurities are present, and also $P_1 < P_0$.
So the problem is: $K$ has changed ! I mean previously $K$ was $P_0$ and now $K$ is $P_1$.
So $K$ value has changed by adding impurities. But my book says impurities has no effect on equilibrium constant. Where am I wrong?