Give Arrhenius equation. How will you determine the activation energy of a reaction by graph method?

Open in App

Solution

Arrhenius equation gives the temperature dependence of the rate of a chemical reaction as:
$k = A e^{{- E}_{a} / R T}$
where $A$ is the Arrhenius factor and is constant for a given reaction, $R$ is the gas constant $= 8.314 J K^{- 1} {m o l}^{- 1}$ and $E_{a}$ is the activation energy. It is defined as the threshold energy required for reaction to occur and is measured in $J {m o l}^{- 1}$ . The exponential factor $e^{{- E}_{a} / R T}$ corresponds to the fraction of reactant molecules possessing energy greater than activation energy.
Consider a reaction: $A + B \to C$
Applying log to both sides of the Arrehenius equation we get:
$l n k = l n A - \frac{E_{a}}{R T}$
Thereby, plotting $l n k$ vs $1 / T$ gives a straight line with slope = $\frac{E_{a}}{R}$ and intercept of $l n A$ .
For a given reaction, $k_{1}$ and $k_{2}$ are the rate constants at temperature $T_{1}$ and $T_{2}$ , respectively. Substituting in the equation we get:
$l n k_{1} = l n A - \frac{E_{a}}{R T_{1}} a n d l n k_{2} = l n A - \frac{E_{a}}{R T_{2}}$
Subtracting the two expressions, gives:
$l n \frac{k_{1}}{k_{2}} = \frac{E_{a}}{R T_{2}} - \frac{E_{a}}{R T_{1}} = \frac{E_{a}}{R} (\frac{1}{T_{2}} - \frac{1}{T_{1}})$
Hence $E_{a}$ can be calculated and upon substitution to Arrehenius equation $A$ can be evaluated for the reaction.

Suggest Corrections

Similar questions

k = A e^{- E / R T}

(E_{a})

k = A e^{- E_{a} / R T}

(k)

(E_{a})

k = A e^{- \frac{E_{a}}{R T}}

(k)

k = A e^{- E_{a} / R T}

(E_{a})

E_{a}

10^{13} s^{- 1} and 12.471 k J m o l^{- 1}

10^{- 3} s^{- 1}

Join BYJU'S Learning Program