the question is gas M is formed as a by-product during the manufacture of NaOH. The gas M reacts with
dry slaked lime to give a compound N which is used to make drinking water free from
germs. Identify M and N giving chemical equations of the reactions involved. marks (3)

Dear Student,

Sodium chloride is used for manufacture of sodium hydroxide which is called chloralkali process. 
In this process, chlorine and hydrogen gas are formed as byproducts along with sodium hydroxide. 
Chlorine gas gives bleaching power when reacts with lime water and used as bleaching agent in chemical industries. 
2NaCl(aq)+2H₂O(l)→ 2NaOH(aq)+Cl₂(g)+H₂(g) Ca(OH)₂+Cl2⟶ CaOCl₂+H₂O 
Therefore, the gas M is chlorine (Cl₂).
Compound N is calcium oxychloride (CaOCl2) which is commonly known as bleaching powder and used to make drinking water free from germs.

Regards

Here-

Dear Student,
NaOH is prepared by electrolysis of aqueous solution of NaCl.

Cathode: H₂O + 2e →→H₂ + 2OH^-
Anode: 2Cl^- →→ Cl₂ + 2e

Here the gas M is Cl₂
Because Cl₂ reacts with slaked lime (Ca(OH)₂) to produce CaOCl₂ (N) which is used to make drinking water germ free
Ca(OH)₂ + Cl₂ →→ CaOCl₂ + H₂O
M is Cl₂
N is CaOCl₂

Regards

Hope this helps