For a chemical reaction, $$X \to Y,$$  the rate of reaction increases by a factor of 1.837 when the concentration of $$X$$ is increased by 1.5 times, the order of the reaction with respect to $$X$$ is

Solution :
$$\eqalign{ & {\text{Initially rate }}\left( {{r_1}} \right) = k{\left[ X \right]^n}...\left( {\text{i}} \right) \cr & {\text{(let }}n{\text{ be the order of reaction)}} \cr & {\text{then,}}\,{r_1} \times 1.837 = k{\left( {1.5X} \right)^n}...\left( {{\text{ii}}} \right) \cr & {\text{dividing (ii) by (i)}} \cr & 1.837 = {\left( {1.5} \right)^n};\,\,\,\,\therefore \,\,n = 1.5 \cr & {\text{Thus, order of reaction is 1}}{\text{.5}}{\text{.}} \cr} $$