Chemical Kinetics - Result Question 64
####64. (i) The rate constant of a reaction is $1.5 \times 10^{7} s^{-1}$ at $50^{\circ} C$ and $4.5 \times 10^{7} s^{-1}$ at $100^{\circ} C$. Evaluate the Arrhenius parameters $A$ and $E _a$.
$(1998,5 M)$
(ii) For the reaction, $N _2 O _5(g) \longrightarrow 2 NO _2(g)+\frac{1}{2} O _2(g)$,
calculate the mole fraction $N _2 O _5(g)$ decomposed at a constant volume and temperature, if the initial pressure is $600 mm Hg$ and the pressure at any time is $960 mm Hg$. Assume ideal gas behaviour.
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Answer:
Correct Answer: 64. $(311.34 K)$
Solution:
- (i) $\ln \frac{k _2}{k _1}=\frac{E _a}{R}\left(\frac{T _2-T _1}{T _1 T _2}\right)$
$$ \begin{array}{ll} \Rightarrow & \ln \left(\frac{4.5 \times 10^{7}}{1.5 \times 10^{7}}\right)=\frac{E _a}{8.314}\left(\frac{50}{323 \times 373}\right) \ \Rightarrow & E _a=22 kJ \end{array} $$
Also
$\ln k=\ln A-\frac{E _a}{R T}$
At $50^{\circ} C: \ln A=\ln \left(1.5 \times 10^{7}\right)-\frac{22 \times 1000}{8.314 \times 323}=8.33$
$$ \Rightarrow \quad A=4.15 \times 10^{3} s^{-1} $$
(ii) $N _2 O _5(g) \longrightarrow 2 NO _2(g)+\frac{1}{2} O _2(g)$
$$ 600-p \quad 2 p \quad p / 2 $$
Total pressure $=960=600+\frac{3}{2} p \Rightarrow p=240 mm$
$\Rightarrow$ Partial pressure of $N _2 O _5(g)$ remaining $=600-240$
$\Rightarrow$ Mole fraction $=\frac{360}{960}=0.375$
$=360 mm$
