The oxidation potential of Na is too positive (ie. the reduction
potential of Na+ is too negative); hence Na+ will not be reduced to
Na.
Even in a concentrated solution, it is still a solution, and the
solvent water molecules will be reduced at the cathode to generate
hydrogen gas and hydroxide ions.
Cl2, H2 and NaOH are produced in the molar ratio of 1:1:2.
This industrial process is used to manufacture 3 different
useful products of chlorine, hydrogen and sodium hydroxide.
As to the purpose of the diaphragm :
“In diaphragm cell electrolysis, an asbestos (or polymer-fiber)
diaphragm separates a cathode and an anode, preventing the chlorine
forming at the anode from re-mixing with the sodium hydroxide and
the hydrogen formed at the cathode.”
http://en.wikipedia.org/wiki/Chlorine_productio….28Bipolar.29
You should also be able to write the equations for these
undesirable reactions that would occur, should the diaphragm be
absent, if the question asks for it.