Calculate the rate constant of a first-order | vedclass

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Question

(D) The Arrhenius equation is given by $k = A \cdot e^{-E_a / RT}$.Taking the logarithm on both sides,we get $\log k = \log A - \frac{E_a}{2.303 RT}$.

Vedclass · Accepted Answer

$1.6 	imes 10^{-8} \ s^{-1}$

Vedclass · Answer

(D) The Arrhenius equation is given by $k = A \cdot e^{-E_a / RT}$.Taking the logarithm on both sides,we get $\log k = \log A - \frac{E_a}{2.303 RT}$.Given values are $A = 1.6 	imes 10^{13} \ s^{-1}$ and $\frac{E_a}{2.303 RT} = 21$.Substituting these values into the equation: $\log k = \log(1.6 	imes 10^{13}) - 21$.$\log k = \log(1.6) + \log(10^{13}) - 21$.$\log k = 0.204 + 13 - 21$.$\log k = 13.204 - 21 = -7.796$.$k = 	ext{antilog}(-7.796) = 	ext{antilog}(-8 + 0.204) = 1.6 	imes 10^{-8} \ s^{-1}$.

Calculate the rate constant of a first-order reaction having a pre-exponential factor $A = 1.6 \times 10^{13} \ s^{-1}$ and $\frac{E_a}{2.303 RT} = 21$.

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