A) 140 kJ/mol
B) 240 kJ/mol
C) 370 kJ/mol
D) 30 kJ/mol
Correct Answer: A
Solution :
Idea Problem includes concept of Arrhenius equation for different rate ?constant of a common reaction. To solve this problem student is advised to write the Arrhenius equation for every rate constant. Then, put the value in\[k=\left( \frac{{{k}_{1}}{{k}_{2}}}{{{k}_{3}}} \right)2/3\]to get the value of\[{{E}_{a}}\] Putting\[k=A{{e}^{-{{E}_{a}}IRT}}\] \[{{k}_{1}}=A{{e}^{\frac{-{{E}_{a1}}}{RT}}},{{k}_{2}}=A{{e}^{-\frac{{{E}_{{{a}_{2}}}}}{RT}}}\] \[{{K}_{3}}=A{{e}^{-\frac{{{E}_{{{a}_{3}}}}}{RT}}}\] \[k={{\left( \frac{A{{e}^{-\frac{{{E}_{{{a}_{1}}}}}{RT}}}\cdot A{{e}^{-\frac{{{E}_{a}}_{_{2}}}{RT}}}}{A{{e}^{-{{E}_{{{a}_{3}}}}/RT}}} \right)}^{2/3}}=A{{e}^{-{{E}_{a}}/RT}}\] \[{{E}_{a}}=\frac{2}{3}[{{E}_{{{a}_{1}}}}+{{E}_{{{a}_{2}}}}-{{E}_{{{a}_{3}}}}]\] \[{{E}_{a}}=\frac{2}{3}[200+90-80]=\frac{2}{3}[210]\] = 140 kJ/mol TEST Edge Students are advised to study the concept of Arrhenius equation at different temperatures. Since, these types of questions are also asked.
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