Would you expect the solubility of PbCl2 in water to change dramatically if it were to be dissolved into a solution of 3.091×10−4 M KCl?

Yes, the solubility of PbCl2 would decrease dramatically.
Yes, the solubility of PbCl2 would increase dramatically.
No, the solubility of PbCl2 would remain roughly unchanged.

I wonder what is meant by dramatically.

To determine whether the solubility of PbCl2 in water would change dramatically when dissolved into a solution of KCl, we need to consider the common ion effect.

The common ion effect states that the solubility of a salt decreases when a common ion is added to the solution. In this case, both PbCl2 and KCl contain the chloride ion (Cl-), so the addition of KCl introduces a common ion into the solution.

When PbCl2 dissolves in water, it dissociates into Pb2+ and 2Cl- ions. The solubility of PbCl2 is dependent on the concentration of Pb2+ and Cl- ions in the solution. If we add KCl, it will increase the concentration of Cl- ions in the solution due to the dissociation of KCl into K+ and Cl- ions.

According to Le Chatelier's principle, the increase in concentration of Cl- ions will shift the equilibrium of PbCl2 dissolution to the left, reducing the solubility of PbCl2. Therefore, the solubility of PbCl2 would decrease dramatically if it were to be dissolved into a solution of KCl.

So, the correct answer is: Yes, the solubility of PbCl2 would decrease dramatically.