I have prepared the 1M water solution of magnesium acetate. Then I placed $\ce{Mg}$ and $\ce{Cu}$ electrodes in it. I predict there such reactions take place: $$\ce{Mg-2e^- \rightarrow Mg^{2+}}$$ $$\ce{H_3^+O + e^- \rightarrow\frac12 H_2 + H_2O}$$ The gas bubbles emitting on both electrodes probably confirm my prediction (I did not check is it hydrogen or not). So I expect to obtain the potential difference about 2.3 V. But really I observe something like 1.62 V.
Then I changed the acetate solution to a water (simple water which we drink) and observed almost same value of 1.60 V. Adding there many crystals of $\ce{Mg}$ acetate (I added them till they could not dissolve more) almost did not change the voltage!
When I added much acid to the solution the potential difference became larger - up to 1.9 V.
So, I have two questions: 1) why the real voltage is so different from the expected value? 2) Why changing the $\ce{Mg^{2+}}$ concentration almost does not change the voltage?
You may say I have dirty magnesium electrode etc. But if you search e.g. experiments with potatoes (when one puts $\ce{Mg}$ and $\ce{Cu}$ strips in potato) you can observe that everywhere it is mentioned that such $\ce{Mg-Cu}$ cell gives 1.7 V.
I have several ideas why can it happen: a)some story with overpotentials, b)oxide film on magnesium surface. What is the real reason?