The rate constant for two parallel reactions were found to be ${1.0 × 10}^{-2} {dm}^{3} {mol}^{-1} s^{-1} {and 3.0 × 10}^{-2} {dm}^{3} {mol}^{-1} s^{-1}$ . If the corresponding energies of activation of the parallel reactions are ${60. 0 kJ mol}^{-1} {and 70.0kJ mol}^{-1}$ respectively what is the apparent overall energy of activation.

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${130.0 kJ mol}^{-1}$

${65.0 kJ mol}^{-1}$

${67.5 kJ mol}^{-1}$

${100 kJ mol}^{-1}$

answer is C.

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Detailed Solution

$E_{a} = \frac{k_{2} E_{2} {+ k}_{1} E_{1}}{k_{2} {+ k}_{1}}$

$= \frac{{1.0 × 10}^{-2} {× 60 + 3.0 × 10}^{-2} × 70}{{1.0 × 10}^{-2} {+ 3.0 × 10}^{-2}}$

$E_{a} {= 67.5 kJ mol}^{-1}$

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