Definitions [7]
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.
Rate of Reaction = `"Change in concentration of a reactant or a prodect"/"Time taken for the change"`
The number of reacting species which must collide simultaneously in order to bring about a chemical reaction is called the molecularity of a reaction.
or
The number of atoms, ions or molecules taking part in an elementary reaction, which must collide with one another simultaneously to bring about a chemical reaction is called as molecularity.
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)`.
Define first-order reaction.
A chemical reaction in which the rate of reaction depends solely linearly on the concentration of one ingredient is referred to as a first-order reaction.
A first-order reaction is a reaction whose rate depends upon the first power of the concentration of reactants, i.e., the rate is directly proportional to the concentration of reactants.
A reaction is zero order if the rate is independent of the concentration of the reactant.
Define half life of a reaction.
Half life of a reaction is defined as the time required for the reactant concentration to reach one half of its initial value.
The half-life t1/2 is the time required for the concentration of a reactant to fall to half its initial value.
\[t_{1/2}\propto\frac{1}{[A_0]^{n-1}}\]
Formulae [3]
\[\mathrm{Rate}=\frac{\text{Decrease in concentration of Reactant}}{\text{Time interval}}\]
\[=-\frac{\Delta[R]}{\Delta T}\]
\[\mathrm{Rate}=\frac{\text{Increase in concentration of Product}}{\text{Time interval}}\]
\[=+\frac{\Delta\left[P\right]}{\Delta T}\]
For a general reaction aA + bB → cC + dD:
\[\frac{dx}{dt}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}\]
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 |
A reaction is first order if the rate depends on the first power of concentration of one reactant.
For A → Products:
| Time | Concentration |
|---|---|
| t = 0 | a |
| t = t | a − x |
\[k=\frac{2.303}{t}\log\frac{a}{a-x}\quad\mathrm{or}\quad k=\frac{2.303}{t}\log\frac{[A]_0}{[A]}\]
Also: \[[A]=[A]_0\cdot e^{-kt}\]
Half-life:
\[t_{1/2}=\frac{0.693}{k}\]
- Half-life is independent of initial concentration — a defining feature of first order reactions.
- \[t_{75\%}=2\times t_{1/2}\]
