Two `I^(st)` order reactions have same reactant concentrations 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 reaction at `75^(@)C`.

Answer

8

Explanation

For I order reaction `r_(1) =K[C]^(1)`
`therefore (R_(1))/(R_(2)) = K_(1)//K_(2)` = temperature coefficient, `" "` Let temperature coefficient 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)) = a xx = a^(2)`
Similarly, `(R_(75))/(R_(25)) = a^(5)`
For I reaction `(R_(75)) = 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 " "[because (R_(25))_(I) = (R_(25))_(II)]`