Question

The rate constant for the first order decomposition
of a certain reaction is described by the equation
log k=9.27 -7.2x10^-3K/T
The activation energy of reaction is
(1) 2 x 10-3 cal (2) 7.2 × 10-3 cal
(3 3.32 * 10-2 cal (4) 1.44 x 10-4 cal​

Answer 1

Answer:

Explanation:

Consider the given equation

log K=$9.27-\frac{7.2*10^{-3}K }{T} ----(1)$

Based on Arrhenius equation

$k=Ae^{-Ea/RT}$

$ln=\frac{k}{A}$

$=-\frac{E_{a} }{RT}$  or

=log k

$=log A-\frac{E_{a} }{2.303RT} ----(2)$

comparing the equations (1) and (2) we get

$\frac{E_{a} }{2.303RT} =\frac{7.2*10^{-3} }{T}$

$E_{a} =7.2*10^{-3} *2.303*R$

$=7.2*10^{-3} *2.303*8.314Jmol^{-1}$

$=1.44*10^{-4} cal$

so the option 4 is correct.

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