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

For first oder reaction, `r_(1)=k[A]^(1)`
`:. R_(1)//r_(2)//=k_(1)//k_(2)` = temperature coefficient
Let the rate or reaction for Ist at `25^(@C)` be `R_(1)` and the rate of reaction for Iind at `25^(@)C ` be `R_(2)`
Also, `" " R_(1)=R_(2)`
`" "` Rates of reactions
`{:( :.,At, 25^(@)C,R_(1),R_(2)),(,,35^(@)C,2R_(1),3R_(1)),(,,45^(@)C,(2)^(2)R_(1),(3)^(2)R_(2)),(,,55^(@)C,(2)^(3)R_(1),(3)^(3)R_(2)),(,,65^(@)C,(2)^(4)R_(1),(3)^(4)R_(2)),(,,75^(@)C,(2)^(5)R_(1),(3)^(5)R_(2)):}`
`:.` Tempeature coefficient for 1st reaction `=(k_(35)/(k)(25))=(R_(35))/(R_(25))=2`
i.e., for each `10^(@)C` rise in temperature, rate becomes 2 times.
Similarly, for 2nd reactin becomes 3 times
`:. At 75^(@)C`
`("rate of reaction for 2nd")/("rate of reaction for 1st")=((3)^(2))/((2)^(5)R_(1))=7.5937( :. R_(1)=R_(2))`