For the elementary reaction $$M → N,$$  the rate of disappearance of $$M$$ increases by a factor of 8 upon doubling the concentration of $$M.$$ The order of the reaction with respect to $$M$$ is

Solution :
$$\eqalign{ & M \to N \cr & r = k{\left[ M \right]^x} \cr & {\text{when}}\,M = 2M;\,r = 8r,\,{\text{thus}} \cr & 8r = k{\left[ {2M} \right]^x} \cr & 8 = {\left( 2 \right)^x} \cr & x = 3 \cr} $$