## What is Reaction Kinetics or Chemical Kinetics?

For a chemical reaction, the part of chemistry dealing with the speed as well as the rate of reaction is known as reaction kinetics. Reaction kinetics is also known as chemical kinetics

Reaction kinetics or chemical kinetics are affected by the rate of

- Reactant’s concentration used in the chemical reaction.
- The temperature is given to the kinetics.
- The catalyst used in the chemical reaction.
- Amount of catalysts used in the chemical reaction.

## Catalysis

In chemistry, it is defined as the process due to which there is an increment in the reaction kinetic by adding the catalyst applied to the chemicals in the chemical reaction. Change is directly related to chemistry. Due to the properties of different molecular substances, there occurs conversion for the substance from one form to another.

## Factors Determining a Chemical Reaction

- The possibility of a chemical reaction occurring is determined by the help of thermodynamics (as you know that a reaction with ΔG < 0, at constant temperature and pressure, is feasible).
- Chemical equilibrium is required to know the limits until where the reaction will proceed.
- The reaction speed where the reaction attains equilibrium.

## Rate of Chemical Kinetics and Stoichiometric

In chemistry, the speed is responsible for the change occurring in any chemical composition for a particular time interval. The reaction speed (reaction rate) is the ratio of concentration to the time taken for the change.

It can simultaneously be expressed as:

- The concentration decrement rate for any one chemical.
- The increment rate of concentration for the product chemical.

Let the volume of the system is constant, consider the reaction:

- For 1 mole R, there is 1 mole P i.e., R is the reactant and P is the product.

- If [R]1 and [P]1 are the concentrations of R and P respectively at time t1 and [R]2 and [P]2 are their concentrations at time t2 then,$\Delta t=\text{\hspace{0.33em}}{t}_{2\text{\hspace{0.33em}}}-\text{\hspace{0.33em}}{t}_{1}$

- $\Delta \left[R\right]=\text{\hspace{0.33em}}{\left[R\right]}_{2}-{\left[R\right]}_{1}$

- $\Delta \left[P\right]=\text{\hspace{0.33em}}{\left[P\right]}_{2}-{\left[P\right]}_{1}$

- The molar concentrations are denoted by [ ].

$\begin{array}{l}\text{Reactant}\text{\hspace{0.33em}}\text{rate}\text{\hspace{0.33em}}\text{of}\text{\hspace{0.33em}}\text{disapperance}\text{\hspace{0.33em}}=\text{\hspace{0.33em}}\frac{(Decrease\text{\hspace{0.33em}}in\text{\hspace{0.33em}}R\text{\hspace{0.33em}}concentration)}{Time\text{\hspace{0.33em}}taken\text{\hspace{0.33em}}t}\\ \text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}=\text{\hspace{0.33em}}\frac{R}{t}\text{\hspace{0.33em}}----(1)\end{array}$

$\begin{array}{l}\text{Rate}\text{\hspace{0.33em}}\text{of}\text{\hspace{0.33em}}\text{theappearacneofP}\text{\hspace{0.33em}}=\text{\hspace{0.33em}}\frac{(Increase\text{\hspace{0.33em}}in\text{\hspace{0.33em}}concentration\text{\hspace{0.33em}}of\text{\hspace{0.33em}}p)}{Time\text{\hspace{0.33em}}taken\text{\hspace{0.33em}}t}\\ \text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}\text{\hspace{0.33em}}=\text{\hspace{0.33em}}\frac{P}{t}\text{\hspace{0.33em}}----(2)\end{array}$

Since Δ[R] is a quantity that is negative (as there is a decrement in the concentration of reactants). To make the terms positive multiplication factor of -1 is considered.

The average rate of reactions is defined by the above equations.

The reaction rate is dependent upon parameters like the concentration of one or more involved chemicals or the molecular products formed. The rate law is used to define the rate of reaction in terms of concentration. The change in the reactants or product involves sometimes, this time taken for the change to occur is the average rate.

### Example

Prepare a butyl chloride solution of 0.100M n water and determine the concentration at certain intervals for the given reaction:

$${C}_{4}{H}_{9}Cl(l)\text{\hspace{0.33em}}+\text{\hspace{0.33em}}{H}_{2}O(l)\to {C}_{4}{H}_{9}OH(aq)\text{\hspace{0.33em}}+{H}_{2}O(aq)$$

The average rate is the ratio of decrease in concentration butyl chloride to the time taken for the change.

$$Average\text{\hspace{0.33em}}Rate\text{\hspace{0.33em}}=\frac{\Delta \left[{C}_{4}{H}_{9}Cl\right]}{\Delta t}$$

## Reaction Order

Most of the reactions also defined as the rate law and is expressed as:

Rate=K[reactant1]^{m}[reactant2]^{n}

Where,

- m and n are known to be the reaction orders and the sum of reaction orders is the overall reaction mechanism.
- k denotes rate kinetic constant.

**Consider an example**

$$Rate\text{\hspace{0.33em}}=\text{\hspace{0.33em}}K\left[N{H}_{4}{}^{+}\right]\left[N{O}_{2}{}^{-}\right]$$

Here overall order is second.

The “m” and “n” do not depend upon the coefficient in the balanced reaction but is determined using the concentration or the reaction rate.

## Units of Rate Constant

Consider a general form of reaction.

$$aA+bB\to cC+dD$$

$$Rate\text{\hspace{0.33em}}=\text{\hspace{0.33em}}k\left[A\right]\text{\hspace{0.33em}}\times \left[B\right]y$$

Where $x+y=n\text{\hspace{0.33em}}=order\text{\hspace{0.33em}}of\text{}\text{\hspace{0.33em}}the\text{\hspace{0.33em}}reaction$

$$k=\text{\hspace{0.33em}}\frac{Rate}{{\left[A\right]}^{x}{\left[B\right]}^{y}}\times \frac{1}{Concentratio{n}^{n}}$$

Where,

[A] [B] is time concentration.

Taking SI units of concentration, mol L^{-1}and time, s, the units of k is the kinetic constant as shown in the above equation.

## The Change in Concentration with Time

To know the amount of reactant left after a certain chemical reaction has occurred, mathematical functions like calculus are needed to determine it.

### Zero Order Reaction

$$For\text{\hspace{0.33em}}the\text{\hspace{0.33em}}reaction\text{\hspace{0.33em}}A\to \text{Products}$$

The rate is given as

$$Rate=-k{\left[A\right]}^{0}$$

For a zero-order reaction.

- A zero-order reaction is completed in infinite time.
- Conversion is inversely proportional to the initial concentration of reactant.

### First Order Reaction

$$For\text{\hspace{0.33em}}the\text{\hspace{0.33em}}reaction\text{\hspace{0.33em}}A\to \text{Products}$$

The rate is given as

$$Rate=\text{\hspace{0.33em}}-\frac{\Delta \left[A\right]}{\Delta t}$$

$$=k\left[A\right]$$

Using the method of calculus, the above equation is transformed.

$\left[A\right]$at the start of the reaction $\left[{A}_{0}\right]$$,$to its concentration at any other time t,$\left[{A}_{t}\right]$

$$\mathrm{ln}\left[{A}_{t}\right]-\mathrm{ln}\left[{A}_{0}\right]=-kt\text{\hspace{0.33em}}or\text{\hspace{0.33em}}\mathrm{ln}(\left[{A}_{t}\right]/\left[{A}_{0}\right]=-kt----(1)$$

$$\mathrm{ln}\left[{A}_{t}\right]=-kt+\mathrm{ln}\left[{A}_{0}\right]----(2)$$

It can be seen that it represents the general equation of line $y=mx+g$So, the graph of the above first order will for $\mathrm{ln}\left[{A}_{t}\right]$vs time will be a straight line having a slope of -k and a y-intercept of $\mathrm{ln}\left[{A}_{0}\right]$.

For a first-order reaction

- After the reaction has commenced the concentration at any time.
- Reaction time for a given fraction of the sample.
- The time required for a certain reactant to reach a certain level.

### Second-order Reaction

$$For\text{\hspace{0.33em}}the\text{\hspace{0.33em}}reaction\text{\hspace{0.33em}}A\to \text{Products}$$

The rate is given as

$$Rate=-k{\left[A\right]}^{2}$$

Using the method of calculus, the above equation is transformed.

$\left[A\right]$at the start of the reaction $\left[{A}_{0}\right]$$,$to its concentration at any other time t,$\left[{A}_{t}\right]$

$$\frac{1}{\left[A\right]}-\frac{1}{{\left[A\right]}_{0}}=kt$$

The above rate equation is the relationship between concentration and rate constant with time.

## Half-Life

The half-life of a reaction (t_{1/2}) is the amount of time required for the chemical

reactant concentration to drop to one-half its initial value$\left[{A}_{t1/2}\right]=\frac{1}{2}{\left[A\right]}_{0}$ The half-life of a first-order reaction is determined by substituting [At1/2] into equation (1).

$\mathrm{ln}1/2\left[{A}_{0}\right]/\left[{A}_{0}\right]=-k{t}_{1/2}\mathrm{ln}1/2=-k{t}_{1/2}{t}_{1/2}=-(\mathrm{ln}1/2/k)=0.693/k$

Half-life is not dependent upon the initial concentration. For example, pick any point in a reaction. For a first-order reaction, the reactant concentration decreases by half of the regularly spaced interval.

## Temperature and Rate

### Collision Model

Molecules must collide to react as per the collision model. The reaction rate is directly proportional to the number of collisions. The collision increases due to an increase in temperature as well as concentration.

### Activation Energy

The minimum energy possessed by the molecules to react is due to the kinetic energy. Hence this minimum energy is termed as activation energy.

### Catalyst

A catalyst is responsible for increasing the reaction rate of chemicals but is not present in the reaction. The catalyst provides a lower level of activation energy. Hence, ΔH remains the same.

### Reaction Mechanisms

The trajectory for a chemical reaction occurring shows the mechanism of the reaction. A single-step reaction mechanism:

The reaction between CO and NO_{2} at high temperatures (above 600 K)

$$CO(g)+N{O}_{2}(g)\to NO(g)+C{O}_{2}(g)$$

Research shows that at low temperatures, this reaction occurs in two steps:

$$\begin{array}{l}Steps1:N{O}_{2}(g)+N{O}_{2}(g)\to N{O}_{3}(g)+NO(g)\\ Steps2:\\ N{O}_{3}(g)+CO(g)\to N{O}_{2}(g)+C{O}_{2}(g)\\ \_\_\_\_\_\_\_\_\_\_\_CO(g)+N{O}_{2}(g)\to NO(g)+C{O}_{2}(g)\end{array}$$

## Rate Laws in Reaction Mechanisms

The reaction mechanism cannot be derived as it involves more steps. The overall rate law will be determined using the rate law and the relative speed. The overall rate law is smaller than the rate of elementary steps.

The molecularity of the following step is determined by the total molecules participating in the step of the reaction.

### Unimolecular

Consider the given equation.

$$\text{\hspace{0.33em}}A\to \text{Products}$$

$$Rate=\frac{k}{\left[A\right]}$$

### Bimolecular

The elementary step involves the collision of two reactant molecules.

### Termolecular

The elementary step involves the simultaneous collision of three molecules.

These are rarely encountered.

$$\begin{array}{l}{H}_{2}+B{r}_{2}\to 2HBr(g)\text{\hspace{0.33em}}or\text{\hspace{0.33em}}N{O}_{2}+N{O}_{2}\to NO+N{O}_{3}\\ Rate=k\left[A\right]\left[B\right]=K{\left[A\right]}^{2}\end{array}$$

$$A+A+A\to \text{Products}\text{\hspace{0.33em}}or\text{\hspace{0.33em}}A+A+B\to \text{Products}\text{\hspace{0.33em}}A+B+C\to \text{Products}$$

$$Rate=k{\left[A\right]}^{3}\text{\hspace{0.33em}}or\text{\hspace{0.33em}}Rate=k{\left[A\right]}^{2}\left[B\right]\text{\hspace{0.33em}}or\text{\hspace{0.33em}}Rate=k\left[A\right]\left[B\right]\left[C\right]$$

## Context and Application

This topic is significant in the professional exams for undergraduate and postgraduate courses, especially for Chemistry.

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