The equation
k = (6.5 × 10¹²s⁻¹)e -26000K/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)

Solution

Chemistry ma’am · 3 steps

Match the exponent with -Eₐ/RT: the 26000 K in the exponent is Eₐ/R itself.

1. Compare with Arrhenius. The Arrhenius equation is k = A e^(-Eₐ/RT). Put it next to the given equation and match the exponents term by term.

   Eₐ/RT = (26000 K)/T ⇒ Eₐ/R = 26000 K

2. Solve for Ea. Eₐ = 26000 K × 8.314 J K⁻¹ mol⁻¹ = 216164 J mol⁻¹. The factor 6.5 × 10¹² s⁻¹ is just A and plays no part here.
3. So. Eₐ = 216.164 kJ mol⁻¹, which rounds to 216.

The common slip: 216164. Leaving Eₐ in joules gives 216164, not 216. Divide by 1000 to get kJ.

The idea to keep. When k is written as A e^(-x/T), the number x is Eₐ/R in kelvin. Multiply by R and you have Eₐ; the pre-exponential factor never enters.

Answer from the NTA final answer key. Solution by PrepWiser.