By using partial equation method, balance the equation :
`NaOH+Cl_(2)rarrNaCl+NaClO_(3)+H_(2)O`.

Explanation

This reaction is supposed to take place in the following steps:
(i) Chlorine reacts with water to form hydrochloric acid and hypochlorous acid as intermediate products.
`Cl_(2)+H_(2)Orarr HCl+HClO" …(1)"`
(ii) Sodium hydroxide neutralises the acids formed in step (i) to form the corresponding salts
`NaOH+HClrarr NaCl+H_(2)O" ...(2)"`
`NaOH+HClOrarr NaClO+H_(2)O" ...(3)"`
(iii) Sodium hypochlorite, NaClO, is unstable at higher temperature. It undergoes self oxidation reduction to give a mixture of sodium chloride and sodium chlorate.
`3NaClOrarr 2NaCl+NaClO_(3)" ...(4)"`
(iv) To cancel the intermediate products which do not occur in the final equation, multiply the partial equations (1), (2) and (3) by 3 each and then add all the four equations. We get
`3Cl_(2)+6NaOHrarr 5NaCl+NaClO_(3)+3H_(2)O`
This represents the balanced chemical equation.