Two first order reactions proceed at `25^(@)C` at the same rate. The temperature coefficient of the rate of the first reaction is `2` and that of second reaction is `3`. Find the ratio of the rates of these reactions at `75^(@)C`.

Explanation

F or first-order reaction `r_(1)=K[C]^(1)`
`therefore (R_(1))/(R_(2))=k_(1)//k_(2)=` temperature coefficient
Let temperature co-efficient be a
`(R_(35))/(R_(25))=(K_(35))/(K_(25))=a" "(R_(45))/(R_(35))=(K_(45))/(K_(35))=a`
`therefore" "(R_(45))/(R_(25))=axxa=a^(2)`
Similarly, `(R_(75))/(R_(25))=a^(5)`
For I reaction `(R_(75))_(I) =2^(5) xx(R_(25))_(I)`
For II reaction `(R_(75))_(II) =3^(5) xx (R_(25))_(II)`
`therefore" "((R_(75))_(II))/((R_(75))_(I))=(3^(5))/(2^(5))=7.9537" "[therefore (R_(25))_(I) =(R_(25))_(II)]`