Consider the following plots of log of rate constant k (log k) vs 1/T for three different reaction. The correct order of activation energies

Question

Consider the following plots of log of rate constant \(k \ (log \ k) \ vs \ \frac{1}{T}\) for three different reactions. The correct order of activation energies of these reaction is

(1) \(Ea_2 > Ea_1 > Ea_3\)

(2) \(Ea_1 > Ea_3> Ea_2\)

(3) \(Ea_1 > Ea_2 > Ea_3\)

(4) \(Ea_3 > Ea_2 > Ea_1\)

Answer 1

Correct option is:  (1) \(Ea_2 > Ea_1 > Ea_3\)

\(\because \ k = Ae^{-E_a/ RT}\)

\(log \ k = \frac{- E_a}{2.303 \ R} \times \frac{1}{T} + log \ A\)

\(\text{slope} = \frac{-E_a}{2.303 \ R}\)

\(\because \ \text{ slope of } 2<1<3\)

\(\text{Hence : }Ea_2 > Ea_1 > Ea_1\)