Question

Write Arrhenius equation. Derive an expression for temperature variations.

Answer 1

Arrhenius equation, `"K" ="A" ."e"^(-"E""a"//"RT")` for temperature variation

`"log"_10"k" = "log"_10"A" - "E"_"a"/(2.303  "RT")` at two different temperatures T₁ and T₂ is written as

`"log"_10"k"_1 ="log"_10"A" -"E"_"a"/(2.303  "RT"_1)`  ...(1)

and `"log""k"_2 = "log"_10"A" - "E"_"a"/(2.303  "RT"_2)`  ...(2)

where k1 is the rate constant at T₁ and k₂ at T₂. The subtraction of equation (1) from equation (2)

`"log"_10"k"_2 - "log"_10"k"_1 = - "E"_"a"/(2.303  "RT"_2) + "E"_"a"/(2.303  "RT"_1)`

Or `"log"_10 ("k"_2)/"k"_1  = "E"_"a"/(2.303"R") [1/"T"_1 - 1/"T"_2]`

= `"E"_"a"/(2.303"R") [("T"_2-"T"_1)/("T"_1 "T"_2)]`