The rate constant for two parallel reactions were found to be $1.0 \times 10^{- 2} {dm}^{3} {mol}^{- 1} s^{- 1}$ and $3.0 \times 10^{- 2} {dm}^{3} {mol}^{- 1} s^{- 1}$ If the corresponding energies of activation of the parallel reactions are $60.0 kJ {mol}^{- 1}$ and $70.0 kJ {mol}^{- 1}$ respectively, what is the apparent overall energy of activation?

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

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

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

$100.0 kJ {mol}^{- 1}$

answer is D.

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Detailed Solution

Apparent overall energy of activation

$E_{overall} = \frac{k_{1} E_{1} + k_{2} E_{2}}{k_{1} + k_{2}}$

$k_{1} = 1.0 \times 10^{- 2} {dm}^{3}$

$k_{2} = 3.0 \times 10^{- 2} {dm}^{3}$

$E_{1} = 60.0 kJ$

$E_{2} = 70.0 kJ$

$E_{o v e r a l l} = 65.0 kJ {mol}^{- 1}$

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