Question

The pre-exponential factor in the Arrhenius equation of a second order reaction has the units:
A. \[mol{L^{ - 1}}{s^{ - 1}}\]
B. \[Lmo{l^{ - 1}}{s^{ - 1}}\]
C. \[{s^{ - 1}}\]
D. Dimensionless

Answer 1

Hint: Arrhenius equation gives the relationship between Temperature and Rate constant of a reaction. The Arrhenius equation shows the temperature-dependence of reaction rate. And it highlights the significance of Arrhenius parameter in determining reaction rate.

Complete step by step answer:
Arrhenius equation is given by
 \[K = A.{e^{\dfrac{{ - Ea}}{{RT}}}}\]
Where K is the rate constant of the reaction. Ea is the activation energy. T is the temperature in Kelvin. A is known as the frequency factor or Arrhenius factor. And, it is a Characteristic constant for a particular reaction. R is the universal Gas constant. Ea and A were collectively known as Arrhenius parameters.
In the Arrhenius equation \[e{ - ^{\dfrac{{Ea}}{{RT}}}}\] is a dimensionless quantity.
Thus, \[K = A\]
Unit of A will be equal to Unit of Rate constant. Unit of A=Unit of K
For a general nth order reaction, $Rate = K[A]$
 \[K = {\text{ }}\dfrac{{Rate}}{{{{\left[ A \right]}^n}}}\]
Rate has a unit of mol \[{L^{ - 1}}{s^{ - 1}}\] and concentration has the unit mol \[{L^{ - 1}}\] .
 \[Unit\,of\,K = \dfrac{{mol{L^{ - 1}}{s^{ - 1}}}}{{{{(mol{L^{ - 1}})}^n}}}mol{L^{ - 1}}{s^{ - 1}}\]
  \[Unit\,of\,K = {\left( {mol{L^{ - 1}}} \right)^{1 - n}}{s^{ - 1}}\] . In this equation n is the order of the reaction. So, by putting the value of n in the equation we can find the rate constant of any order reaction
In this question we need to find out the unit of rate constant for a second order reaction. So, put \[n = 2\] .
Unit of Second order Rate constant \[ = {\left( {mol{L^{ - 1}}} \right)^{1 - 2}}{s^{ - 1}}\]
                                                                  \[ = mo{l^{ - 1}}L{s^{ - 1}}\] .
                                                                 \[ = Lmo{l^{ - 1}}{s^{ - 1}}\]
Hence, the correct answer is option (B) i.e \[Lmo{l^{ - 1}}{s^{ - 1}}\]

Note:The frequency factor A in the Arrhenius equation related to the number of binary molecular collisions per second per unit volume. It is a Characteristic constant for a particular reaction. The equation shows the dependence of the reaction rate on the collision frequency. From the equation it is clear that as the frequency collision increases, greater would be the value of K and greater would be the rate of the reaction.