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In the Arrhenius equation, \[{\text{k = A}}{{\text{e}}^{\dfrac{{Ea}}{{RT}}}}\], the rate constant (k) becomes equal to the Arrhenius constant (A), when
A. the temperature becomes infinite
B. the 100 % reactants are converted to product
C. the fraction of molecules crossing over the energy barrier is unity
D. the temperature of the reaction mixture is very low
Answer
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Hint: We must know that the Arrhenius equation is an expression that gives a relationship between the rate constant (‘k’ of a chemical reaction), the absolute temperature (T), and the A factor (also known as the pre-exponential factor. It also provides an insight into the dependence of reaction rates on the absolute temperature.
Complete step by step answer:
The expression of the Arrhenius equation is:
\[{\text{k = A}}{{\text{e}}^{\dfrac{{Ea}}{{RT}}}}\]
Where,
‘\[k\]’ is the rate constant of the reaction
‘\[A\]’ denotes the pre-exponential factor which is related to the collision theory. It is the frequency of correctly oriented collisions between the reacting species
\[e\]is the base of the natural logarithm (Euler’s number)
\[{E_a}\] is the activation energy of the chemical reaction (in terms of energy per mole)
\[R\]denotes the universal gas constant
\[T\]denotes the absolute temperature associated with a chemical reaction (in Kelvin)
In this equation, when the temperature is infinite and the reaction is \[100\% \] complete and all reactants are converted to the product. When all reactant is converted means the molecules crossing over the energy barrier is unity and the reaction is complete when the temperature is very high and constant.
Hence options A, B, and C are correct.
Note:
We must know that the function of a catalyst is to lower the activation energy required by a reaction. Therefore, the lowered activation energy can be substituted into the Arrhenius equation, in order to obtain the rate constant for the catalyzed reaction.
Complete step by step answer:
The expression of the Arrhenius equation is:
\[{\text{k = A}}{{\text{e}}^{\dfrac{{Ea}}{{RT}}}}\]
Where,
‘\[k\]’ is the rate constant of the reaction
‘\[A\]’ denotes the pre-exponential factor which is related to the collision theory. It is the frequency of correctly oriented collisions between the reacting species
\[e\]is the base of the natural logarithm (Euler’s number)
\[{E_a}\] is the activation energy of the chemical reaction (in terms of energy per mole)
\[R\]denotes the universal gas constant
\[T\]denotes the absolute temperature associated with a chemical reaction (in Kelvin)
In this equation, when the temperature is infinite and the reaction is \[100\% \] complete and all reactants are converted to the product. When all reactant is converted means the molecules crossing over the energy barrier is unity and the reaction is complete when the temperature is very high and constant.
Hence options A, B, and C are correct.
Note:
We must know that the function of a catalyst is to lower the activation energy required by a reaction. Therefore, the lowered activation energy can be substituted into the Arrhenius equation, in order to obtain the rate constant for the catalyzed reaction.
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