looking at this another way. If as you mention delta T = 0 then delta H = 0. Therefore, delta G = (-1)* T * delta S, subsequently if concentration increases delta S is negative. Negative times negative is positive therefore delta G is positive! I hope that simplifies the concept and brings...
You need to go back to the fundamentals. Entropy tends to increase unless energy is expended to reduce it within a closed system. Therefore, the more concentrated a solution is (be it solid liquid or gas) the less entropy it has. COncentrating and purifying takes enormous energy (heat...