Question

The temperature coefficient of a reaction is:
(A) Ratio of rate constants at two temperatures differing by ${1^ \circ }C$ .
(B) Ratio of rate constants at temperature ${35^ \circ }C$ and ${25^ \circ }C$ .
(C) Ratio of rate constants at temperature ${30^ \circ }C$ and ${25^ \circ }C$ .
(D) Specific reaction rate at ${25^ \circ }C$

Answer 1

Rate of reaction: It is defined as the rate of disappearance of reactant and the rate of appearance of the product.
Rate constant: It is proportionality constant between the rate of reaction and the concentration terms.

Complete step by step solution
To understand this question first we will discuss the various terms like frequency factor, Arrhenius equation and activation energy.
Activation energy: It is defined as the least required energy for a chemical reaction to happen. It is represented by ${E_a}$ .
Frequency factor is defined as the rate of molecular collisions that occur during the chemical reaction. It is also known as pre-exponential factor and is represented as A.
Rate of reaction: The rate of a reaction is the speed at which a chemical reaction happens.
Rate law: Rate law is the mathematical relation between the rate of reaction and concentration of each reactant.
For example: the reaction is as $A \to B$ i.e. the reactant $A$ is converting to the product $B$ .
Then the expression for rate law will be as: $rate = - \dfrac{{\Delta [A]}}{{\Delta t}}$ . And we know that the rate of disappearance of reactant is equal to the concentration of reactant (by the definition of rate of reaction). So the equation for rate law will become: $rate\alpha [A]$ . To remove the proportionality sign let us take a constant $k$ which is known as rate constant. So the final equation will be as $rate = k[A]$ .
Rate constant: It is proportionality constant between the rate of reaction and the concentration terms.
Arrhenius equation: It is the equation which relates frequency factor, activation energy and temperature. The equation of Arrhenius equation is as:
$k = A{e^{\dfrac{{ - {E_a}}}{{RT}}}}$ , where $k$ is rate of the reaction, $A$ is as frequency factor, ${E_a}$ is the activation energy.
Temperature coefficient is defined as the factor by which the rate of reaction gets increased on increasing the temperature by ${10^ \circ }C$ . Hence, the temperature coefficient of a reaction is the ratio of rate constants at temperature ${35^ \circ }C$ and ${25^ \circ }C$ .
So option B is correct.

Note
Order of reaction is defined as the power relation of the rate on the concentration of the reactants. For example: If the reaction is of one order then rate of the reaction is directly proportional to the single power of the concentration of that reactant.