Question

For a first order reaction, A $\to$ P, the temperature (T) dependent rate constant (k) was found to follow the equation:
$logk=\frac{2000}{T}+6.0$
the pre - exponential factor A and the activation energy $E_{\alpha }$. respectively, are:

• A. $1.0\times {10}^6{s}^{-1}and9.2kJmo{l}^{-1}$
• B. $6.0s^{-1}and16.6kJmo{l}^{-1}$
• C. $1.0\times {10}^6{s}^{-1}and16.6kJmo{l}^{-1}$
• D. $1.0\times {10}^6{s}^{-1}and38.3kJmo{l}^{-1}$

Answer 1

The correct option is D $1.0\times {10}^6{s}^{-1}and38.3kJmo{l}^{-1}$

The logarithmic form of Arrhenius equation is
$logk=logA-\frac{E_{\alpha }}{2.303RT}$
Given: $logk=6-\frac{2000}{T}$
Comparing the above two equations:
$logA=6\Rightarrow A={10}^6$
and $\frac{E_{\alpha }}{2.303R}=2000$
$\Rightarrow E_{\alpha }=2000\times 2.303\times 8.314J$
$=38.3kJmo{l}^{-1}$