The rate of a reaction quadruples when the temperature changes from \(293 \ K\) to \(313\ K\). Calculate the energy of activation of the reaction assuming that it does not change with temperature.
The rate of a reaction quadruples when the temperature changes from \(293 \ K\) to \(313\ K\). Calculate the energy of activation of the reaction assuming that it does not change with temperature.
Solution and Explanation
\(From\ Arrhenius\ equation,\ we\ obtain\)
\(log \ \frac {k_2}{k_1} = \frac {E_a}{2.303\ R} (\frac {T_2-T_1}{T_1T_2})\)
\(It \ is\ given\ that,\) \(k_2 = 4k_1\)
\(T_1 = 293 \ K\)
\(T_2 = 313\ K\)
\(Therefore,\)
\(log \ \frac {4k_1}{k_1} = \frac {E_a}{2.303 \times 8.314} (\frac {313-293}{293 \times 313})\)
⇒ \(0.6021 = \frac {20\times E_a}{2.303\times8.314\times293\times313}\)
⇒ \(E_a = \frac {0.6021\times 2.303\times 8.314\times293x313}{20}\)
⇒ \(E_a = 52863.33 \ J mol^{-1}\)
⇒ \(E_a = 52.86\ kJ mol^{-1}\)
\(Hence,\ the\ required\ energy\ of\ activation \ is\) \(52.86\ kJ mol^{-1}\).
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Concepts Used:
Rate of a Chemical Reaction
The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit time.
Consider the reaction A → B,
Rate of the reaction is given by,
Rate = −d[A]/ dt=+d[B]/ dt
Where, [A] → concentration of reactant A
[B] → concentration of product B
(-) A negative sign indicates a decrease in the concentration of A with time.
(+) A positive sign indicates an increase in the concentration of B with time.
Factors Determining the Rate of a Reaction:
There are certain factors that determine the rate of a reaction:
- Temperature
- Catalyst
- Reactant Concentration
- Chemical nature of Reactant
- Reactant Subdivision rate