| Consider the following reactions at 300 K. |
| \[A\to B\](uncatalysed reaction) |
| \[A\xrightarrow{\text{catalyst}}B\](catalyst reaction) |
| The activation energy is lowered by \[8.314\,\,KJ\,\,mo{{l}^{-1}}\] for the catalysed reaction. How many times the rate of this catalysed reaction greater than that of uncatalysed reaction? \[(Given\,\,{{e}^{3.33}}=28)\] |
A) 15 times
B) 38 times
C) 22 times
D) 28 times
Correct Answer: D
Solution :
| \[A\to B\] (uncatalysed reaction) |
| \[A\xrightarrow{\text{catalyst}}B\] (catalyst reaction) |
| \[K=A{{e}^{-{{E}_{a}}/RT}}\] |
| \[{{K}_{\text{cat}\text{.}}}=A{{e}^{-{{E}_{a(cat.)}}/RT}}\] |
| \[\frac{{{K}_{\text{cat}\text{.}}}}{K}={{e}^{({{E}_{a}}-E{{'}_{a}})\,\,\times \,\,\frac{1}{RT}}}\] |
| \[\frac{{{K}_{\text{cat}\text{.}}}}{K}={{e}^{\frac{8.314\times {{10}^{3}}}{8.314\times 300}}}={{e}^{3.33}}=28\,\,\text{time}\] |
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