Definitions [12]
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.
or
The branch of chemistry which deals with the study of reaction rates and their mechanisms is called chemical kinetics.
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"`
Define “zero order reaction”.
Zero order reaction is the reaction whose rate is independent of the reactant concentration and remains constant throughout the course of the reaction.
Define the following term:
Pseudo first-order reaction
The reactions that have higher order true rate law but are found to behave as first order are called pseudo first order reactions.
\[\ce{CH3COOCH3 + H2O - CH3COOH + CH3OH}\]
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)`.
A reaction is zero order if the rate is independent of the concentration of the reactant.
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.
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.
\[t_{1/2}\propto\frac{1}{[A_0]^{n-1}}\]
The Arrhenius equation is a mathematical expression to give a quantitative relationship between the rate constant and temperature.
Define activation energy.
Activation energy is the lowest energy necessary to commence a chemical reaction by disrupting the bonds of reactant molecules and creating the activated complex or transition state. It signifies the energy threshold that must be surmounted for a reaction to transpire. Activation energy is typically represented as Ea.
Activation energy may be defined as the excess energy that the reactant molecules (having energy less than the threshold energy) must acquire in order to cross the energy barrier and to change into the products.
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:
\[\frac{dx}{dt}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}\]
Theorems and Laws [1]
Collision Theory explains why and how temperature increases the rate of reaction.
Microscopic Factors:
Factor 1: Collisional Frequency (Z):
- The number of collisions taking place per second per unit volume of the reaction mixture.
- Effective collision: Only those collisions that actually produce the products.
\[\mathrm{Rate}=\frac{dx}{dt}=Z\times\text{(fraction of effective collisions)}\]
Factor 2: Activation Energy:
- The minimum amount of extra energy required by a reacting molecule to get converted into an activated molecule (transition state).
- Ea = Threshold energy − Average energy of reactant molecules
Conditions for Effective Collision:
- Colliding molecules must possess energy ≥ threshold energy.
- Colliding molecules must have proper orientation at the time of collision.
Drawback of Collision Theory: It considers atoms/molecules to be hard spheres and ignores their structural features.
Key Points
The rate of a reaction depends on:
| Factor | Effect on Rate |
|---|---|
| Concentration of reactants | Higher conc. → more collisions → higher rate |
| Temperature | Higher T → more energetic collisions → higher rate |
| Physical state and surface area | Greater surface area → higher rate |
| Catalyst | Lowers activation energy → higher rate |
| Pressure (gaseous reactions) | Higher pressure → higher rate |
| Light / electromagnetic radiation | Provides energy for photochemical reactions |
Rate Law Expression:
The rate law (or rate expression) gives the experimental relationship between reaction rate and the molar concentration of reactants:
- x and y are the orders with respect to A and B, respectively — they may or may not equal stoichiometric coefficients a and b.
- k is the rate constant (specific reaction rate).
Characteristics of Rate Constant (k):
- Higher value of k → greater rate.
- Depends on temperature and catalyst only.
- Does not depend on initial concentrations, volume, or pressure.
- Its units depend on the overall order of reaction.
Order = the sum of the exponents (powers) to which concentration terms in the rate law are raised to express the observed rate.
- It is an experimentally determined quantity.
- Can be zero, positive, negative, fractional, or greater than three.
- Infinite and imaginary values are not possible.
| 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 |
| Reaction Type | General Units | Units (mol L⁻¹, s) | Units (gaseous, atm) |
|---|---|---|---|
| Order n | conc.¹⁻ⁿ time⁻¹ | mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹ | atm¹⁻ⁿ s⁻¹ |
| First order | time⁻¹ | s⁻¹ | s⁻¹ |
| Second order | conc.⁻¹ time⁻¹ | mol⁻¹ L s⁻¹ | atm⁻¹ s⁻¹ |
| Third order | conc.⁻² time⁻¹ | mol⁻² L² s⁻¹ | atm⁻² s⁻¹ |
| Zero order | conc. time⁻¹ | mol L⁻¹ s⁻¹ | atm s⁻¹ |
| 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.
- \[t_{75\%}=2\times t_{1/2}\]
Temperature Coefficient:
The temperature coefficient μμ is the ratio of rate constants at two temperatures differing by 10°C:
\[\mu=\frac{k_{T+10}}{k_T}=2\mathrm{~to~3}\]
The two reference temperatures are typically 35°C (308 K) and 25°C (298 K).
If R1 = reaction rate at T1 and R2 = reaction rate at T2:
\[\frac{R_1}{R_2}=\frac{\mu T}{10}\]
Arrhenius Equation:
\[k=A\cdot e^{-E_a/RT}\]
where:
- k = rate constant
- A = pre-exponential factor (frequency factor)
- EaEa = activation energy (J mol⁻¹)
- R = gas constant (8.314 J mol⁻¹ K⁻¹)
- T = temperature in Kelvin
The factor \[e^{-E_a/RT}\] is called the Boltzmann factor.
Logarithmic form:
\[\log k=\log A-\frac{E_a}{2.303RT}\]
A plot of log k vs 1/T is a straight line with:
\[\mathrm{Slope}=-\frac{E_a}{2.303R}\]
Intercept = log A
This is of the form y = mx + c.
Two-Temperature Form:
\[\log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1T_2}\right)\]
- 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
A positive catalyst lowers the activation energy and hence increases the rate of reaction.
where:
-
kp = rate constant with catalyst
-
ka = rate constant without catalyst
-
ΔEa = Ewithout catalyst − Ewith catalyst
When a catalyst is used and reaction rate becomes x times:
\[\log x=\frac{\Delta E_a}{2.303RT}\]
If Ea given in kJ: \[\log\frac{k_{p}}{k_{a}}=\frac{52.2\Delta E_{a}}{T}\]
If Ka is given kcal: \[\log\frac{k_p}{k_a}=\frac{218\times\Delta E_a}{T}\]
Concepts [15]
- Concept of Chemical Kinetics
- Rate of Chemical Reaction
- Factors Influencing Rate of a Reaction
- Dependence of Rate on Reactant Concentrations: Rate Law and Rate Constant
- Order of a Reaction
- Molecularity of Reaction
- Units of Rate Constant
- Integrated Rate Equations
- Zero Order Reactions
- First Order Reactions
- Half Life Period of a Reaction
- Pseudo First Order Reaction
- Temperature Dependence of the Rate of a Reaction
- Effect of Catalyst on the Rate of Reaction
- Collision Theory of Chemical Reactions
