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(a) The decomposition of a hydrocarbon has value of rate constant as $2.5\times 10^{4}s^{-1}$ at $27^{\circ}C$ . At what temperature would rate constant be $7.5\times 10^{4}s^{-1}$ if energy of activation is $19.147\times 10^{3}\; J\; mol^{-1}?$

(b) Write a condition under which a bimolecular reaction is kinetically first order. Give an example of such a reaction.

$\left ( Given : log\; 2=0.3010,log\; 3=0.4771,log\; 5=0.6990 \right )$

Answers (1)

(a) $k=2.418\times 10^{-5}s^{-1}$

$T=546\; K$

$E_{a}=1979.9\; kJ\; mol^{-1}=179.9\times 10^{3}\; J\; mol^{-1}$

$k=Ae^{-Ea/RT}$

$Lnk=LnA-\frac{Ea}{RT}$

$\Rightarrow Log\; k=logA-\frac{Ea}{2.303RT}$

$\Rightarrow Log\; k=log2.418\times 10^{-5}+\frac{179.9\times 10^{3}}{2.303\times 8.314\times 546}$

$=(0.3835-5)+17.2082$

$logA=12.5917$

$A=antilog\; 12.5917=3.9\times 10^{12}s^{-1}$

(b) When one of the reactants is taken in excess so that its concentration hardly changes. In such a condition, the bimolecular reaction will be of 1st order.

for eg. Hydrolysis of ethyl acetate $(0.01\; mol)$ with $10\; mol$ of water.

$\underset{0.01mol}{CH_{3}COOC_{2}H_{5}}+\underset{10mol}{H_{2}O}\rightarrow CH_{3}COOH+C_{2}H_{5}OH$

Posted by

Sumit Saini

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