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# Relation between rate constant and temperature by Arrhenius equation is:A.$lo{{g}_{e}}A=lo{{g}_{e}}k+\dfrac{Ea}{RT}~$B.$\log k+\dfrac{Ea}{RT}~$C.$lo{{g}_{e}}k=lo{{g}_{e}}A+\dfrac{Ea}{RT}~$D.$logA=RT\ln EA-\ln k~$

Last updated date: 23rd Jul 2024
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Hint: We know that the rate constant of a reaction at a particular temperature is defined as the rate of reaction when concentration of reactant is unity. The rate constant depends only on the temperature of the reaction. The relationship between rate constant and temperature can be deduced from the Arrhenius equation.

We know Arrhenius equation is basically a formula which describes the temperature dependence of the reaction rates. The formula of Arrhenius equation is $k=A{{e}^{-~~\dfrac{Ea}{RT}}}.$
Where, k is the rate constant; ${{E}_{a}}$ is the activation energy; T is the temperature; R is the universal gas constant and A is the pre-exponential factor which represents the frequency of collisions that takes place in between reactants at a particular concentration.
Here we have Arrhenius equation is: $k=A{{e}^{-~~\dfrac{Ea}{RT}}}.$
Taking log on both sides we get; $lo{{g}_{e}}k=lo{{g}_{e}}A-\dfrac{Ea}{RT}~~~~~~~~~~~~~\left[ \because \text{ }lo{{g}_{e}}e=1 \right]$