You could do it like this:
At the cathode, water molecules are reduced:
Hydrogen gas is evolved and
If the solution is sufficiently concentrated then chlorine is evolved at the anode:
The charge on 1 mole of electrons
Now this is a very low concentration so I would predict the pH to be very slightly above 7.
It is actually less than the concentration of
I have explained how to calculate the pH more precisely in a similar answer here:
In reality it is important that the products at each electrode are kept separate as they will react with each other.
This process forms the basis of the chlor - alkali industry where hydrogen, chlorine and sodium hydroxide are manufactured from the electrolysis of brine.