JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Chemical Kinetics

The equation

k = (6.5 \times 1 0^{12} s^{- 1}) e^{- 26000 K / T}

is followed for the decomposition of compound A .
The activation energy for the reaction is ____ kJ

mol^{- 1}

. [nearest integer]
(Given:

R = 8.314 J K^{- 1} mol^{- 1}

)

Answer: 216

Solution

The Arrhenius equation is:

k = A e^{- E_{a} / R T}

Comparing with the given equation:

k = (6.5 \times 1 0^{12} s^{- 1}) e^{- 26000 K / T}

We can write:

e^{- E_{a} / R T} = e^{- 26000/ T}

Therefore:

\frac{E _{a}}{R} = 26000

E_{a} = 26000 \times R = 26000 \times 8.314 J mol^{- 1}

E_{a} = 216164 J mol^{- 1} = 216.164 kJ mol^{- 1}

Rounding to the nearest integer: **216 kJ mol

^{- 1}

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Integer answer