Question

For a chemical reaction A $\to$products, the rate of disappearance of A is given by: $\dfrac{-\partial {{C}_{A}}}{\partial t}=\dfrac{{{K}_{1}}{{C}_{A}}}{1+{{K}_{2}}{{C}_{A}}}$ at low ${{C}_{A}}$ the reaction is of the __ order with rate constant. (Assume ${{K}_{1}},{{K}_{2}}$ are lesser than $1$ )

Answer 1

Chemical kinetics basically deals with the different aspects of a chemical reaction. It deals with the rate of change of the reaction. It helps us to understand the rate of reaction and how it changes with certain conditions. It helps to analyse the mechanism of the reaction.

Complete step-by-step answer: During a chemical reaction, when a reaction starts, it decreases the amount of the reactant and increases the amount product in the reaction. Rate of disappearance of reaction tells us about how an amount of reactant decreases with time.
Order of the reaction is defined as power of the concentration of the reactant in a chemical reaction. For example, the rate of first order reaction depends only on one concentration of the reactant.
In this question, the rate of disappearance of A is given by:
$\dfrac{-\partial {{C}_{A}}}{\partial t}=\dfrac{{{K}_{1}}{{C}_{A}}}{1+{{K}_{2}}{{C}_{A}}}$
This is equation $1$
We also know that $\dfrac{-\partial {{C}_{A}}}{\partial t}=K{{\left[ A \right]}^{n}}$
This is equation $2$
Where, ${{C}_{A}}$ is the concentration of A
$K$ is the rate constant
$n$ is the order of the reaction
Now we will equate equation $1$ and $2$, we get
$\dfrac{-\partial {{C}_{A}}}{\partial t}=\dfrac{{{K}_{1}}{{C}_{A}}}{1+{{K}_{2}}{{C}_{A}}}=K{{\left[ A \right]}^{n}}$
Now, it is given that ${{K}_{1}},{{K}_{2}}<1$
Hence we can say that ${{K}_{2}}{{C}_{A}}<<1$
Therefore, $1+{{K}_{2}}{{C}_{A}}\approx 1$
We can also write equation $2$ like this:
$\dfrac{-\partial {{C}_{A}}}{\partial t}=\dfrac{{{K}_{1}}{{C}_{A}}}{1}$
Now, we will equate both the values of disappearance of A, we get
${{K}_{1}}{{C}_{A}}=K{{\left[ A \right]}^{n}}$
Hence, we can see that the value of $n$ will be $1$
Therefore, this proves that this reaction is first order.

Note: There are many factors that affect rate of reaction:
Concentration of the reactant: the increase in the concentration of the reactant will increase the colliding particle which further increases the rate of the reaction.
Temperature: if we increase the temperature then the collision between the reactant molecules per second increases which further increases the rate of reaction.
Solvent: the nature of the solvent affects the rate of reaction of the solute particles.