Question

(a) In some cases it is found that a large number of colliding molecules have energy more than threshold value, yet the reaction is slow. Why?
(b) For a reaction ${\text{R}} \to {\text{P}}$, half life is observed to be independent of the initial concentration of reactants.

Answer 1

To solve the first part we must know that the reaction slows down because the colliding molecules are not aligned properly. A chemical reaction in which the rate of the reaction is proportional to the concentration of the reacting substance is known as a first order reaction. To solve the second part we must know the expression for the rate constant of a first order reaction. At half-life period only half of the reactant remains.

Complete solution:
(a) We are given that in some cases it is found that a large number of colliding molecules have energy more than threshold value, yet the reaction is slow. This is because the colliding molecules are not aligned properly. This can be explained by the collision theory.
The assumption of collision theory are:
The rate of a chemical reaction is directly proportional to the number of collisions that the reactant molecules undergo in a given amount of time.
${\text{Rate}} = \dfrac{{{\text{Number of collisions}}}}{{{\text{Time}}}}$
The collision should be in alignment so that a contact is established between the atoms that can bond together to form a product.
The collision must occur with sufficient energy. This energy should be more than the threshold energy so that mutual penetration of the valence shells of the reacting species thus allows the electrons to realign and create new bonds.
According to the collision theory, the rate of reaction increases as concentration increases. As the concentration increases, the number of molecules per unit volume increases and thus, collision increases. And thus, the rate of reaction increases.
But if the molecules are improperly aligned then the rate of reaction decreases and the reaction becomes slow.
(b)We are given a reaction, ${\text{R}} \to {\text{P}}$.
The expression for the rate of reaction is as follows:
${\text{Rate}} \propto - \dfrac{{d[{\text{R}}]}}{{dt}}$
The rate of the reaction is proportional to the concentration of the reactant species. Thus, the given reaction is a first order reaction.
We know the expression for the half-life time of first order reaction is as follows:
${t_{{\text{1/2}}}} = \dfrac{{0.693}}{k}$
Where $k$ is the rate constant of a first order reaction,
${t_{{\text{1/2}}}}$ is half-life time.
The half-life period of the reaction, the concentration of the reactant is equal to the concentration of the product.
The expression for the half-life period of a first order reaction does not contain a concentration term.
Thus, the half-life period for such reactions is independent of the initial concentration of the reactants.

Note: The time taken for the reactant species to reduce to half of its initial concentration is known as the half-life period of the reaction. At the half-life, $50\%$ of the reaction is completed. The unit of half-life time for first order reaction is ${\text{sec}}$ or ${\text{min}}$. The units do not contain concentration terms. Thus, we can say that the half-life time of a first order reaction is independent of the concentration of the reactants.