Write the Arrhenius equation representing the relationship between the rate constants $k_1$ and $k_2$ at two different temperatures $T_1$ and $T_2$.
(N/A) The Arrhenius equation at two different temperatures is given by: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} [\frac{T_2 - T_1}{T_1 T_2}]$
Where:
$k_1$ and $k_2$ are the rate constants at temperatures $T_1$ and $T_2$ respectively.
$E_a$ is the activation energy.
$R$ is the universal gas constant.
Where:
$k_1$ and $k_2$ are the rate constants at temperatures $T_1$ and $T_2$ respectively.
$E_a$ is the activation energy.
$R$ is the universal gas constant.
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For a reaction where the activation energies of the forward and reverse directions are equal in value,then:
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$A$ reaction takes place in three steps with individual rate constant and activation energy as follows: $Step$ $Rate \ constant$ $Activation \ energy$ $Step-1$ $k_1$ $E_{a1} = 180 \ kJ/mol$ $Step-2$ $k_2$ $E_{a2} = 80 \ kJ/mol$ $Step-3$ $k_3$ $E_{a3} = 50 \ kJ/mol$
If overall rate constant,$k = (\frac{k_1 k_2}{k_3})^{2/3}$,then overall activation energy of the reaction will be .......... $kJ/mol$.
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| $Step-1$ | $k_1$ | $E_{a1} = 180 \ kJ/mol$ |
| $Step-2$ | $k_2$ | $E_{a2} = 80 \ kJ/mol$ |
| $Step-3$ | $k_3$ | $E_{a3} = 50 \ kJ/mol$ |
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