Question

The specific rate constant of a first order reaction depends on-
A) Concentration of reactant
B) Concentration of product
C) Time
D) Temperature

Answer 1

Hint:It is common knowledge that higher temperatures speed up reaction, often doubling the rate for a 10- degree rise. When we combine the concepts of activation energy and Boltzmann distribution law we get the reason behind that.

Complete answer:
A first order reaction depends on the concentration of one reactant. Decaying at an exponential rate, such as radioactivity and some chemical reaction shows first order kinetics. In first order kinetics, the amount of material decaying in a given period of time is directly proportional to the amount of material remaining.

This can be represented as a differential equation- ${\displaystyle \frac{dA}{dt}}=-kt$ .
Here ${\displaystyle \frac{dA}{dt}}$ is rate per unit at which the quantity of material is increasing, t is time, k is rate constant and it expresses the relationship between rate of chemical equation and concentration of the reacting substance.

Here the minus sign indicates that the material remaining will be decreasing with time. The rates of reactions are very sensitive to temperature. Rate constant value increases rapidly with increase in temperature. An increase in 20 degrees can lead to double in the rate constant value. Since the average speed of molecules increases with temperature and for a reaction the participant needs to collide with each other. Therefore as the temperature increases, the relative speed of molecules also increases and hence the collision frequency.

Rate constants vary exponentially with the reciprocal of the absolute temperature. As-
$k=A{e}^{{\displaystyle \frac{-Ea}{RT}}}$ .
Here Ea is activation energy and A is Arrhenius constant. Hence the rate of reaction depends on temperature only.

Hence the correct answer is option ‘D’. temperature.


Note:Heterogeneous catalysis is very important because it enables faster, large scale production and selective product formation. There are two types of adsorption- physisorption which is weakly bonded adsorption, the catalyst and molecules of reactants are bonded through Van der Waals forces. Chemisorptions that are strongly bonded adsorption, the adsorbate reactant molecules and adsorbent catalyst shares electrons and form chemical bonds.