If you can recover the acid after the electrolysis has taken place, then yes, it is a catalyst. A catalyst is defined as a substance which speeds up the rate of a reaction without being consumed in the overall reaction itself.
I do not fully agree with the acid being a catalyst. A real catalyst has a uniform effect, with net zero-consumption
locally at any location in the reaction mix.
With electrolysis this is not the case. Suppose we have electrolysis of water with dilute HNO3. At the anode we have the reaction:
2H2O - 4e --> 4H(+) + O2
At the cathode we have the reaction:
4H2O + 4e --> 4OH(-) + 2H2
So, the net reaction indeed is decomposition of water to H2 and O2, the acid (or even more generally, the inert electrolyte) being the compound, which assures that the reaction proceeds at acceptable rate.
However, locally, there is definite change of the liquid. Near the anode, the liquid becomes more acidic and near the cathode, the liquid becomes less acidic. This effect can be demonstrated nicely if a solution of NaNO3 is used for electrolysis with an indicator in solution, which is colorless at pH near 7, red at pH above 11 and blue at pH below 3 (a mix of phenolphtalein and bromothymolblue is suitable for this). Graphite rods need to be used as electrode. At the anode, the liquid becomes acidic and turns blue and at the cathode the liquid becomes pink/red. When the liquid is shaken again, the liquid becomes colorless again, because of precise neutralization of the OH(-) and H(+) ions. With suitable membranes between anode and cathode area, the liquids start to differ more and more in the different compartments.
So, you see that the electrolysis really changes the properties of the liquid and electrolyte. Only if they are mixed well these changes counterbalance precisely. Jdurg, would you really call this a catalyst?
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Yet another thing:
User 3.3.141592653 mentioned that without catalyst more energy is needed than with a catalyst. A catalyst does NOT change the amount of energy, released or taken by a reaction, it only changes the pathway of the reaction. Sometimes, the use of a catalyst makes a reaction appear more energetically, but this only is apparent.
As an analogy I use a fully charged battery. You can discharge it slowly, using a LED, you can also discharge it quickly, using a heavy bulb. With the heavy bulb, it looks more energetic, but the time that this energy can be released is shorter than the time that the LED can glow from the same battery. The peak
power was larger, but the
total energy was the same.