Definitions [11]
Chemical kinetics is the branch of chemistry which deals with the study of chemical reactions with respect to the reaction rates, the effect of various arrangements of atoms and the formation of intermediates. It also describes the conditions in which rates can be altered.
Define the rate of a reaction.
The rate of chemical reaction is defined as the change in concentration of reactant or product per unit time.
The rate of a chemical reaction may be defined as the change in concentration of any of the reactants or any of the products per unit time. Thus,
`"Rate of reaction" = "(Change in concentration of a reactant or a product)"/"Time taken for the change"`
The rate of change of concentration of either products or reactants per unit time is termed the rate of reaction.
Reactants ⟶ Products
It is the ratio of the total change in concentration of a reactant or product to the total time taken by the reaction.
\[r_{\mathrm{av}}=-\frac{\Delta[R]}{\Delta t}=+\frac{\Delta[P]}{\Delta t}\]
The rate of a reaction at any instant of time is called the instantaneous rate of reaction. It is equivalent to the small change in concentration (dx) in a small interval of time (dt).
Instantaneous rate of reaction,
\[r_{\mathrm{inst}}=\frac{-dx}{dt}\]
Rate law is the expression in which the reaction rate is given in terms of molar concentration of reactants, with each term raised to some power, which may or may not be the same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.
The sum of the coefficients (or powers) of the reacting species that are involved in the rate law expression for the reaction represents the order of the reaction.
The number of reacting species which must collide simultaneously in order to bring about a chemical reaction is called the molecularity of a reaction.
Define molecularity of reaction.
The molecularity of a chemical reaction is the number of molecules or ions involved in an elementary process. The integer value represents the number of entities involved in a reaction.
Define molecularity.
The molecularity of an elementary reaction refers to how many reactant molecules are involved in reactions.
Define the half-life of a first-order reaction.
The time in which concentration of reactant becomes half of its initial concentration is called half Life. It is denoted by `t_(1/2)`.
Formulae [1]
\[\mathrm{Rate}=k[A]^a[B]^b\]
Where:
k = Rate constant
[A], [B] = Concentrations of reactants
a = Order with respect to A
b = Order with respect to B
Overall Order of Reaction:
Order = a + b
Theorems and Laws [1]
According to this theory, the reactant molecule is assumed to be a hard sphere, and the reaction is postulated to occur when molecules collide with each other. It is related to the rate as,
\[\mathrm{rate}=PZ_{AB}e^{-E_{a}/RT}\]
where,
Zₐᵦ = collision frequency of reactants A and B.
P = steric factor.
Key Points
| Type of Reaction | Description | Example |
|---|---|---|
| Elementary reaction | Occurs in a single step | O₃ → O₂ + O |
| Unimolecular reaction | One reactant involved | C₂H₅I → C₂H₄ + HI |
| Bimolecular reaction | Two reactants involved | O₂ + O → O₃ |
| Complex reaction | Occurs in multiple steps | NO₂Cl → NO₂ + Cl \[\frac{\mathrm{NO}_2\mathrm{Cl}+\mathrm{Cl}\longrightarrow\mathrm{NO}_2+\mathrm{Cl}_2}{2\mathrm{NO}_2\mathrm{Cl}\longrightarrow2\mathrm{NO}_2+\mathrm{Cl}_2}\] |
Difference between Order and Molecularity:
| Order | Molecularity |
|---|---|
| Determined experimentally | Theoretical concept |
| Sum of powers in the rate law | Number of reacting molecules |
| Can be 0, a fraction or an integer | Always Integer |
| Not based on a balanced equation | Based on a balanced chemical equation |
| Concept | Zero Order Reaction | First Order Reaction |
|---|---|---|
| Rate law | Rate = k | Rate = k[A] |
| Differential form | \[-\frac{\mathrm{d[A]}}{[\mathrm{dt]}}=\mathrm{k}[\mathrm{A}]^{0}=\mathrm{k}\] | \[-\frac{\mathrm{d[A]}}{[\mathrm{dt]}}=\mathrm{k[A]}\] |
| Integrated form | \[\mathrm{k}=\frac{\left[\mathrm{A}\right]_{0}-\left[\mathrm{A}\right]_{t}}{\mathrm{t}}\] | \[\mathrm{k=\frac{2.303}{t}\log_{10}\frac{\left[A\right]_{0}}{\left[A\right]_{t}}}\] |
| Unit of k | mol L⁻¹ s⁻¹ | s⁻¹ |
| Half-life (t₁/₂) | \[\mathrm{t}_{1/2}=\frac{[\mathrm{A}]_0}{2\mathrm{k}}\] | t₁/₂ = 0.693 / k |
| Dependence | Independent of concentration | Depends on concentration |
- The rate constant (k) depends on temperature
- \[k=Ae^{-E_{a}/RT}\]
A = frequency factor
Ea = activation energy
T = temperature - \[e^{-E_a/RT}\] represents fraction of molecules having energy ≥ Ea
- Increase in temperature → fraction of molecules with energy ≥ Ea increases → rate increases
- A catalyst increases the rate of reaction
- Works by lowering the activation energy (energy barrier)
- Helps reaction reach equilibrium faster
- Does not change the equilibrium position
