Question

The rate constant of a reaction at 700 K and 760 K are $0.011M^{-1}{s}^{-1}$, respectively. The values of Arrhenius parameter is:

• A. $A=2.18\times {10}^{10}{M}^{-1}{s}^{-1}$
• B. $A=2.80\times {10}^{10}{M}^{-1}{s}^{-1}$
• C. $A=2.58\times {10}^{10}{M}^{-1}{s}^{-1}$
• D. $Noneofthese$

Answer 1

Answer: (B)

$A=2.80\times {10}^{10}{M}^{-1}{s}^{-1}$

Substituting the value of K and T in Arrhenius equation:
$k=A{e}^{-Ea/RT}$
log $\frac{k_2}{k_1}=\frac{E_a}{2.3R}\left(\frac{T_2-T_1}{T_1{T}_2}\right)$
log $\left(\frac{0.105M^{-1}{s}^{-1}}{0.011M^{-1}{s}^{-1}}\right)=\frac{E_a}{2.3\times 8.314}\times \left[\frac{760-700}{760\times 700}\right]$
Solve for $E_a$:
$E_a=166.351\times {10}^{3}Jmo{l}^{-1}$
$=166.351kJmo{l}^{-1}$
Value of A can be determined
log k = log A $-\frac{166.35kJmo{l}^{-1}}{2.3\times 8.314}\times \frac{1}{700k}$
Solve for log A and take antilog.
$\therefore A=2.8\times {10}^{10}{M}^{-1}{s}^{-1}$