Question

The first-order reaction, $2N_{2}O(g)→2N_2(g)+O_2(g)$ has a rate constant of $1.3×10^{−11}{s}^{−1}$ at $270^{∘}C$ and $4.5×10^{−10}{s}^{−1}$ at $350^{∘}C$. What is the activation energy for this reaction?

• A. 15kJ
• B. 30kJ
• C. 68 kJ
• D. 120 kJ

Answer 1

Answer: (D)

From Arrhenius equation,
$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{1}{T_1}−\frac{1}{T_2}\right]$
$\log \frac{4.5×10^{−10}}{1.3×10^{−11}}=\frac{E_a}{2.303×8.314}$
$\left[\frac{1}{(270+273)}−\frac{1}{(350+273)}\right]$
$\log 34.62=\frac{E_a}{2.303×8.314}\left[\frac{1}{543}−\frac{1}{623}\right]$
$1.539=\frac{E_a}{2.303×8.314}\left[\frac{80}{543×623}\right]$
$E_a=\frac{1.539×2.303×8.314×543×623}{80}$
$=\frac{9.968×10^6}{80}$
$=1.246×10^{5}J$
$=124kJ≈120kJ$