Chemical Kinetics

Imagine the reaction between hydrogen gas (H₂) and oxygen gas (O₂) to form water vapour (H₂O). This reaction produces energy and is crucial for various processes, including combustion and respiration.

The chemical equation for this reaction is:

$2{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2\to 2{\mathrm{H}}_2\mathrm{O}$

Chemical kinetics would involve studying how quickly this reaction occurs and what factors impact its speed. Factors like temperature, concentration of the gases, and the presence of a catalyst influence the rate at which hydrogen and oxygen combine to form water.

1.0Definition of Chemical Kinetics

Chemical kinetics, or reaction kinetics, helps us understand how fast reactions occur and what factors affect their speed. It also assists in gathering data about how reactions happen and what defines their characteristics.

In a chemical reaction, substances change into different ones by breaking and forming chemical bonds, causing shifts in how atoms are arranged in molecules and changes in electron arrangements. 

A description of a reaction mechanism focuses on how atoms and electrons move and their speeds. The specific process by which a chemical change happens is called the reaction pathway.

2.0Rate of Reaction

The rate of a reaction measures how quickly products are made and reactants are used up. In chemical systems, we often use substance concentrations, which show the amount of a substance in a given volume. 

The rate can then be described as the change in concentration of a substance over time. Sometimes, it's easier to express rates as the number of molecules formed or used up per unit time.                                   

$\text{ Rate of reaction }=\frac{\text{ Change in Concentration of reactant or Product }}{\text{ Time taken in change }}or\mathbf{r}=\pm \frac{\Delta C}{\Delta t}$

Where, ΔC = change in concentration in a small interval Δt

[+] sign is used when we refer for product concentration.

[–] sign is used when we refer for reactant concentration

3.0Types of Rate of Reaction

There are mainly two types of rate of reaction we are going to discuss, which involves average and instantaneous rate

Types of Rates of reactions-

1. Average Rate of Reaction                               
2. Instantaneous Rate of Reaction
3. Average Rate of Reaction-

The rate of reaction over a certain measurable period of time during the course of reaction is called average rate of reaction. It is denoted by r_average .

For a reaction   A → B

${\mathrm{r}}_{\text{average}}=\left(\frac{[\mathrm{A}{]}_2-[\mathrm{A}{]}_1}{{\mathrm{t}}_2-{\mathrm{t}}_1}\right)=\frac{\Delta [\mathrm{A}]}{\Delta \mathrm{t}}$

Where, [A]₁ = Concentration of reactant A at time t₁,

[A]₂ = Concentration of reactant A at time t₂.

2. Instantaneous Rate of Reaction-

The rate of reaction at any particular instant during the course of reaction is called instantaneous rate of reaction.

For a reaction,                                     A→ B

Mathematically ;   

$\text{ Instantaneous rate }={\lim }_{\Delta t\to 0}\text{ (Average rate) }$

${\mathbf{r}}_{\text{inst }}={\lim }_{\Delta t\to 0}\left(\frac{\Delta [A]}{\Delta t}\right)={\lim }_{t\to 0}\left(\frac{\Delta [B]}{\Delta t}\right)$

or

${\mathbf{r}}_{\text{inst }}=(-)\frac{d[A]}{dt}=(-)\frac{d[B]}{dt}$

Hence, Slope of the tangent at time t in the plot of concentration with time gives an instantaneous rate of reaction.

Instantaneous rate of reaction 

${\lim }_{\Delta t\to 0}\left(土\frac{\Delta C}{\Delta t}\right)=\pm \frac{dC}{dt}$

4.0Rate Law

The experimental expression of rate of reaction in terms of concentration of reactants is known as rate law. In this expression the rate of a reaction is proportional to the product of molar concentration of reactants with each term raised to the power or exponent that has to be found experimentally.

In a chemical reaction: aA + bB → Product

The rate law is:  

$\text{ Rate }\propto [A{]}^x[B{]}^{y\mid }$

The values of exponents x and y are found experimentally which may or may not be the same as stoichiometric coefficients.

Above relationship can be written as :- 

$\text{ Rate }=k[A{]}^x[B{]}^y$

 Where, k is a proportionality constant known as rate constant.

Rate constant :

In a chemical reaction –    

n₁A + n₂B   →   m₁C + m₂D                               

according to law of mass action -

Rate = k [A]ⁿ¹[B]ⁿ²               

but according to rate law (experimental concept)

Rate = k [A]^x [B]^y

if [A] = [B] = 1 mol/L

then, Rate = k

• Rate of reaction at unit concentration of reactants is called rate constant or specific reaction rate. 
• Rate constant does not depend on concentration of reactant but it depends on temperature and catalyst.

5.0Order of Reaction

The sum of powers of concentration of reactants in rate law expression is known as order of reaction.

For the reaction aA + bB → Product

Rate law is,     Rate = k [A]^x [B]^y

Here, x = order of reaction with respect to A

y = order of reaction with respect to B

x + y = n (overall order of reaction)

• Order of reaction may be zero, positive, negative or fractional.
• Order of reaction is an experimental quantity, Which will help us to solve numerical problems on Chemical Kinetics. 

Units of Rate Constant (k)

Rate = k[A]ⁿ

$\begin{array}{rl}& \mathrm{k}=\frac{\mathrm{r}}{[\mathrm{A}{]}^{\mathrm{n}}}=\frac{\text{ unit of rate }}{[\text{ unit of concentration }{]}^{\mathrm{n}}}=\frac{\frac{\mathrm{mol}}{\mathrm{L}}\times {\mathrm{time}}^{-1}}{{\left[\frac{\mathrm{mol}}{\mathrm{L}}\right]}^{\mathrm{n}}}\\ & \mathrm{k}={\left[\frac{\mathrm{mol}}{\mathrm{L}}\right]}^{1-\mathrm{n}}\times {\mathrm{time}}^{-1}\end{array}$

For gaseous reaction unit of k may be = (atm)^1–n × time^–1