Which of the following compounds will be the most soluble in a basic solution? So here we're wanting to take a look at the cations. When they dissolve, we're going to create this positive amine. Remember, positive amines are acidic. Since it's an acidic ion, its solubility will increase within a basic solution. So this would be an answer.
Next we have cobalt one. Remember, transition metals need to be 2 or higher in order to be acidic. This one does not meet that minimum requirement, so it is neutral. Next we have barium ion. Barium's a group on main group metal. They have to be 3 or higher in order to be acidic. Here it doesn't meet that minimum requirement, so it's neutral.
Next we have lead 2 ion. Same thing. Lead two is a main group metal. It has to be at least 3 or higher to be acidic. Then finally here we have potassium which is only plus one as a main group metal. So here the only cation that is acidic in nature would be the first one we produced a positively charged amine. Since it is an acidic ion, its solubility would increase within a basic solution. So here our answer is option A.