Question

The first-order reaction, $2 N _{2} O (g) \rightarrow 2 N _{2}(g)+ O _{2}(g)$ has a rate constant of $1.3 \times 10^{-11} s ^{-1}$ at $270^{\circ} C$ and $4.5 \times 10^{-10} \,s ^{-1}$ at $350^{\circ} C$. 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}}{2.303 \,R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] $
$\log \frac{4.5 \times 10^{-10}}{1.3 \times 10^{-11}}=\frac{E_{a}}{2.303 \times 8.314} $
${\left[\frac{1}{(270+273)}-\frac{1}{(350+273)}\right]} $
$\log 34.62=\frac{E_{a}}{2.303 \times 8.314}\left[\frac{1}{543}-\frac{1}{623}\right] $
$1.539=\frac{E_{a}}{2.303 \times 8.314}\left[\frac{80}{543 \times 623}\right] $
$E_{a}=\frac{1.539 \times 2.303 \times 8.314 \times 543 \times 623}{80} $
$=\frac{9.968 \times 10^{6}}{80} $
$=1.246 \times 10^{5}\, J $
$=124 \,k \,J \approx 120\, k\, J$