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, $N _2 O _5(g) \longrightarrow 2 NO _2(g)+\dfrac{1}{2} O _2(g)$,
calculate the mole fraction of $N _2 O _5(g)$ 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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Solution:
- (i) $\ln \dfrac{k _2}{k _1}=\dfrac{E _a}{R}\left(\dfrac{1}{T _1}-\dfrac{1}{T _2}\right)$
$ \begin{array}{ll} \Rightarrow & \ln \left(\dfrac{4.5 \times 10^{7}}{1.5 \times 10^{7}}\right)=\dfrac{E _a}{8.314}\left(\dfrac{50}{323 \times 373}\right) \\ \Rightarrow \ E_a=22\ \text{kJ} \end{array} $
Also
$\ln k=\ln A-\dfrac{E _a}{R T}$
At $50^{\circ} C: \ln A=\ln \left(1.5 \times 10^{7}\right)-\dfrac{22 \times 1000}{8.314 \times 323}=10.33$
$ \Rightarrow \quad A=4.15 \times 10^{3} s^{-1} $
(ii) $N _2 O _5(g) \longrightarrow 2 NO _2(g)+\dfrac{1}{2} O _2(g)$
$ 600-p \quad \quad \quad\quad 2 p \quad \quad \quad\quad\quad p / 2 $
Total pressure $=960=600+\dfrac{3}{2} p \Rightarrow p=240$ $ mm$
$\Rightarrow$ Partial pressure of $N_2O_5(g)$ remaining $=600-240$
$$=360 mm$$
$\Rightarrow$ Mole fraction $=\dfrac{360}{960}=0.375$
BETA
