Question

Answer the following in brief.

How will you determine activation energy from rate constants at two different temperatures?

Answer 1

Determination of activation energy from rate constants at two different temperatures.

Arrhenius equation is k = `"Ae"^((-"E"_"a")/("RT"))`

From two different temperatures T₁ and T₂

log₁₀k₁ = log₁₀A - `"E"_"a"/(2.303"RT"_1)`   ....(1)

log₁₀k₂ = log₁₀A - `"E"_"a"/(2.303"RT"_2)`   ....(2)

where k₁ and k₂ are the rate constants at temperatures T₁ and T₂ respectively. Subtracting Eq.(1) from Eq.(2),

log₁₀k₂ - log₁₀k₁ = `-"E"_"a"/(2.303"R") 1/"T"_2 + "E"_"a"/(2.303"R") 1/"T"_1`

Hence, `"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))`