A) \[2.303\times 10\text{ }R\text{ }kJ.mo{{l}^{-1}}\]
B) \[2.303\times 5\text{ }R\text{ }kJ.mo{{l}^{-1}}\]
C) \[2.303\times 3\text{ }R\text{ }kJ.mo{{l}^{-1}}\]
D) \[2.303\times 2.7\text{ }R\text{ }kJ.mo{{l}^{-1}}\]
Correct Answer: D
Solution :
: Rate of souring of milk at \[{{27}^{o}}C\]is 10 times faster than at \[-{{3}^{o}}C\]. hence, \[\frac{{{k}_{300}}}{{{k}_{270}}}=10,\,\,{{T}_{1}}=270K,\,\,{{T}_{2}}=300K\] \[{{E}_{a}}=2.303R\left( \frac{{{T}_{1}}{{T}_{2}}}{{{T}_{2}}-{{T}_{1}}} \right)\log \frac{{{k}_{300}}}{{{k}_{270}}}\] \[{{E}_{a}}=2.303R\left( \frac{270\times 300}{300-270} \right)\log 10\] \[{{E}_{a}}=2.303R(2.7\times {{10}^{3}})Jmo{{l}^{-1}}\] \[{{E}_{a}}=2.303\times 2.7R\,kJ\,mo{{l}^{-1}}\]
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