First slide

Kinetics of chemical reactions

Question

A first order chemical reaction. A ®P is occurring at 500 K. If the same reaction is to be carried out in presence of a catalyst, temperature of 400 K is required to be maintained in order to maintain the same rate of reaction. If the catalyst lowers the activation energy by 30 kJ, then what would be the value of activation energy of the original pathway (uncatalysed reaction)/25.

Moderate

Solution

$\log_{unncatalysed} = \log A - \frac{E a_{c}}{500 RT}$
${logk}_{cat} = logA - \frac{{Ea}_{uc}}{400 RT}$
$\frac{E a_{u c}}{5} = \frac{E a_{c}}{4}$
$4 E a_{u c} = 5 E a_{c}$
${Ea}_{uc} - {Ea}_{c} = 30$
$\frac{5}{4} E a_{c} - E a_{c} = 30$
${Ea}_{c} = 120 kJ$
${Ea}_{uc} = 150 kJ$
$150 \div 25 = 6$

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