Does increasing concentration of copper sulfate decrease or increase its conductivity? I am a high school student and for my chemistry lab, I did an electrolyis experiment on how the changing concentration of electrolyte (copper sulfate) will change the rate at which the copper is deposited on the cathode.

My hypothesis was that as the concentration is increased, so will the rate of electrolysis. However, my results are completely opposite. When I use 0.1 M solution, loads of copper is deposited on the cathode but as I increase the concentration, the amount of copper deposited becomes progressively less and less. With 1 M solution, there was almost no copper being deposited.

This makes no sense to me. Could somebody explain what is going on? Am I doing something wrong?

I used both copper electrodes. I did not use distilled water, just normal tap water. I used 12 V power supply.

EDIT:

I tried adding a little sulfuric acid (making the pH around 3) to the copper sulfate but it did not make any difference on electrolysis.

I tried to observe the electrolysis very closely today and noticed that there was some sort of oily liquid falling off from the anode. Also, I noticed that initially some flaky brown/black substance fell off from the anode (which may or may not be copper)and soon there was a silvery layer formed on the anode.

Also, I checked using Hanna checker that the overall pH of the solution was around 3 but the pH near the anode read between 9 and 14.

Also, I noticed that when I used a higher concentration, the copper deposition on the cathode was brown and clearly copper. But when I used lower concentration, even though the amount of deposit was a lot more, the substance was probably not pure copper as I had assumed earlier. It was black and flaky. It was certainly different to the deposit I observed when I used higher concentration of copper sulfate.

Does anybody know now what is happening? Is there anything that I can do to fix the problem?
I'm thinking maybe at the higher concentrations your tap water is making a film of $\ce{Cu(OH)2}$ on the surface of your electrode, and that is what's shutting down your electroplating. Your tap water might be mildly alkaline (tap water pH's can range from about $6.5$ to as high as $9.5$).

Try adding a little sulfuric acid to your solutions. If alkaline films are the problem, that will fix it. 

It will also increase the conductivity of your solutions tremendously, because hydrogen ions are extremely mobile. 

The solubility of copper sulfate decreases with increasing sulfuric acid concentration, so don't add too much acid.