Question

A first order reaction is 50% completed in 20 minutes at ${27}^0$C and in 5 min at ${47}^0$C. The energy of activation of the reaction is :

• A. 43.85 kJ/mol
• B. 55.26 kJ/mol
• C. 11.97 kJ/mol
• D. 6.65 kJ/mol

Answer 1

The correct option is B 55.26 kJ/mol

$t_1{k}_1=t_2{k}_{2}20\ast k_1=5\ast k_2\frac{k_1}{k_2}=4NowArrheniusequationlo{g}_{10}\left(\frac{k_2}{k_1}\right)=\frac{E_a}{2.30\ast R}\left(\frac{T_2-T_1}{T_1.T_2}\right)lo{g}_{10}\left(4\right)=\frac{E_a}{8.314\ast 2.3}\left(\frac{20}{300\ast 320}\right)E_a=55.332kJ/mole$