J.R. S. answered 11/19/19
Ph.D. University Professor with 10+ years Tutoring Experience
You have the reaction written backwards, and also the moles of H2O produced from the reaction of NaOH + Cl2 gas will depend on the concentration of NaOH AND THE TEMPERATURE. So, the following are the possible reactions, and we can't really answer the question without knowing which is occurring.
2NaOH(aq) + Cl2(g) ==> NaCl(aq) + NaOCl(aq) + H2O(l) if NaOH is dilute and cold
6NaOH(aq) + 3Cl2(g) ==> 5NaCl(aq) + NaClO3(aq) + 3H2O(l)
If we assume that 0.4 M NaOH is dilute and the reaction is run under cold temperature conditions, then we proceed as follows:
NaOH(aq) + Cl2(g) ==> NaCl(aq) + NaOCl(aq) + H2O(l) ... balanced equation
3.0 moles H2O x 1 mole NaOH / mol H2O = 3.0 moles NaOH needed
Volume of NaOH needed:
(x L)(0.4 mol/L) = 3.0 moles
x = 7.5 liters of 0.4 M NaOH