Question

Rate constant k varies with temperature by equation
$\log k({\min ^{ - 1}}) = 5 - \dfrac{{2000K}}{T}$. We can conclude
A. Pre exponential factor A is 5
B. ${E_a}$is 2000 kcal
C. Pre exponential factor A is ${10^5}$
D. ${E_a}$is 9.212 kcal

Answer 1

Hint: Rate constant is defined as the proportionality constant which helps us in understanding the relationship between molar concentration of the reactants and the reaction rate of the chemical reaction. We can calculate the rate constant by using the concentration of the reactants or using the Arrhenius equation. The unit for rate constant is dependent on the reaction order.

Complete step by step answer:
Arrhenius equation is a mathematical expression which shows us the effect of temperature on the velocity of a chemical reaction. This is the basis of all expressions which are predicted and used for calculating the reaction-rate constants.
The Arrhenius equation is:
$k = Ae^{\dfrac {- {E_a}}{RT}}$
K is rate constant
The rate constant is also called the specific rate constant. It is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.
A is a pre exponential factor.
Pre-exponential factor which is also calledA factor is the pre-exponential constant in the Arrhenius equation.
${E_a}$ is activation energy.
Activation energy is known as the minimum amount of extra energy required for a reacting molecule that is a reactant to get converted into a product.
T is temperature.
$k = Ae^{\dfrac {- {E_a}}{RT}}$
By taking log on both sides, we get
$\log k = \log A - \dfrac{{{E_a}}}{{2.303RT}}$
The equation in the question is:
$\log k({\min ^{ - 1}}) = 5 - \dfrac{{2000K}}{T}$
On comparing both the equations we can conclude that:
logA is 5
So A i.e. pre exponential factor is ${10^5}$
Also, $\dfrac{{{E_a}}}{{2.303RT}} = \dfrac{{2000K}}{T}$
Hence ${E_a} = 2.303 \times 8.314 \times 2000 = 38.2kcal$
Hence only option C is correct. Pre exponential factor A is ${10^5}$

So, the correct answer is Option C.

Note: The rate law is defined as the rate equation which helps in expressing the relationship between the reaction rate and the concentration of the species of reactant participating. The order of reaction is the addition of the partial order of the species of reactant in the rate law expression. The order of reaction changes the rate of reaction by changing the concentrations.