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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.\[logA=RT\ln EA-\ln k~\]

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Last updated date: 23rd Jul 2024
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Answer
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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.

Complete answer:
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 are considering two temperatures, so as we know that the value of rate constant depends on temperature. As we vary the temperature, the value of rate constant will also vary. The rate of a chemical reaction can be affected by one of the parameters that are temperature. We have seen milk boiling on a gas stove. On the stove, the rate of a specific quantity of milk boils depends. The milk boils in less time if the flame e height is maximum, and the milk takes more time to boil if the flame height is minimum. Here the
Here we have Arrhenius equation is: \[k=A{{e}^{-~~\dfrac{Ea}{RT}}}.\]
Taking log on both sides we get; \[lo{{g}_{e}}k=lo{{g}_{e}}A-\dfrac{Ea}{RT}~~~~~~~~~~~~~\left[ \because \text{ }lo{{g}_{e}}e=1 \right]\]
Therefore, the correct answer is option A.

Note:
Remember that it should be noted that in general the rate of a reaction increases for each 10 degrees increase in temperature. Also, the rate constant is a constant and it depends only on the temperature of the reaction. It changes only if the temperature fluctuates.