Definitions [30]
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.
\[\ce{CH3COOCH3 + H2O - CH3COOH + CH3OH}\]
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 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.
The half-life t1/2 is the time required for the concentration of a reactant to fall to half its initial value.
\[t_{1/2}\propto\frac{1}{[A_0]^{n-1}}\]
A reaction which is actually of higher order but behaves as a first order reaction because one reactant is present in large excess is called pseudo first order reaction.
The rate of reaction measured over a given finite interval of time is called average rate of reaction.
The mathematical expression that relates the rate of reaction with the concentration of reactants is called rate law.
The number of molecular collisions occurring per second per unit volume is called collision frequency.
A collision in which molecules collide with sufficient energy and proper orientation to form products is called effective collision.
The minimum kinetic energy required by colliding molecules for an effective collision is called threshold energy.
The proportionality constant present in the rate equation at a given temperature is called rate constant.
The sum of the powers of the concentration terms in the rate law expression is called order of reaction.
The number of reacting species that collide simultaneously in an elementary reaction is called molecularity.
The rate of reaction at a particular instant of time is called instantaneous rate of reaction.
A reaction whose rate is independent of the concentration of reactants is called zero order reaction.
The constant A in Arrhenius equation which represents the frequency of effective collisions is called frequency factor.
The branch of chemistry which deals with the study of rate of chemical reactions and the factors affecting them is called chemical kinetics.
The change in concentration of a reactant or product per unit time is called rate of reaction.
The minimum amount of energy required by reacting molecules to form products is called activation energy.
The intermediate unstable species formed during a reaction at the top of the energy barrier is called activated complex.
A substance which increases the rate of a reaction without itself undergoing permanent chemical change is called catalyst.
A reaction whose rate is directly proportional to the first power of the concentration of a reactant is called first order reaction.
The time required for the concentration of a reactant to become half of its initial concentration is called half-life of a reaction.
Formulae [9]
\[\mathrm{Rate}=\frac{\text{Decrease in concentration of Reactant}}{\text{Time interval}}\]
\[=-\frac{\Delta[R]}{\Delta T}\]
\[\mathrm{Rate}=\frac{\text{Increase in concentration of Product}}{\text{Time interval}}\]
\[=+\frac{\Delta\left[P\right]}{\Delta T}\]
For a general reaction aA + bB → cC + dD:
\[\frac{dx}{dt}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}\]
\[\mathrm{Rate}=\frac{\text{Concentration}}{\mathrm{Time}}\]
Unit = mol L⁻¹ s⁻¹
Rate = k
Integrated form:
[R] = [R]0 − kt
\[k=\frac{[R]_0-[R]}{t}\]
Units of k = mol L⁻¹ s⁻¹
\[r=-\frac{\Delta[R]}{\Delta t}=\frac{\Delta[P]}{\Delta t}\]
\[r=-\frac{d[R]}{dt}\]
Rate = k[R]
Integrated form:
ln[R] = ln[R]0 − kt
\[k=\frac{2.303}{t}\log\frac{[R]_0}{[R]}\]
Units of k = s⁻¹
For reaction:
Rate = k[A]x[B]y
Order = x + y
Theorems and Laws [6]
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.
Statement:
For a first order reaction, the half-life period is constant and independent of the initial concentration of reactant.
Expression:
\[t_{1/2}=\frac{0.693}{k}\]
Important Points:
- Half-life does not depend on initial concentration.
- Used in radioactive decay and decomposition reactions.
- Helps in determination of rate constant.
Statement:
At a constant temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants, each raised to a power, which may or may not be equal to their stoichiometric coefficients.
Mathematical Expression:
For a reaction
Rate = k[A]x[B]y
Where:
- k = rate constant
- x and y = orders with respect to A and B
- x + y = overall order of reaction
Important Points:
- Order is determined experimentally.
- Order may be zero, whole number, or fractional.
- Order is not necessarily equal to stoichiometric coefficients (except for elementary reactions).
The rate of a chemical reaction at a given temperature is proportional to the product of concentrations of reactants, each raised to a power.
Mathematically,
Rate = k[A]x[B]y
Where:
- k = rate constant
- x, y = orders with respect to reactants
- x + y = overall order
Note: Order is determined experimentally.
Statement:
The rate constant of a reaction increases exponentially with increase in temperature and is given by the Arrhenius equation.
Mathematical Expression:
\[k=Ae^{-E_a/RT}\]
Taking logarithm:
\[\ln k=-\frac{E_a}{RT}+\ln A\]
Where:
- A = frequency factor
- Ea = activation energy
- R = gas constant
- T = temperature
Important Results:
- A plot of ln k vs 1/T is a straight line.
- Slope = −Ea/R
- Intercept = ln A
- Increase in temperature increases rate constant.
Statement:
According to collision theory, a chemical reaction occurs only when reacting molecules collide with sufficient energy and proper orientation.
Expression for Rate:
\[\mathrm{Rate}=Z_{AB}e^{-E_a/RT}\]
Including orientation factor:
\[\mathrm{Rate}=PZ_{AB}e^{-E_a/RT}\]
Where:
- ZAB = collision frequency
- Ea = activation energy
- P = steric factor
Important Points:
- Not all collisions are effective.
- Effective collisions require:
- Energy ≥ activation energy
- Proper orientation
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 |
| 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: \[\log\frac{k_p}{k_a}=\frac{218\times\Delta E_a}{T}\]
Important Questions [58]
- Assertion (A): Order of reaction is applicable to elementary as well as complex reactions. Reason (R): For a complex reaction, molecularity has no meaning.
- Define the following term: Pseudo first-order reaction
- Write the Principle Behind the Following Methods of Refining: Hydraulic Washing
- A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is doubled?
- The conversion of molecules A to B follow second order kinetics. If concentration of A is increased to three times, how will it affect the rate of formation of B?
- Identify the order of reaction from the following unit for its rate constant: L mol–1 s–1
- A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is reduced to half?
- For a Reaction R ---> P, Half-life (T1/2) is Observed to Be Independent of the Initial Concentration of Reactants. What is the Order of Reaction?
- Define the Following Terms: Half-life Period of Reaction (T1/2).
- For a reaction Rate = k (i) Write the order and molecularity of this reaction. (ii) Write the unit of k.
- For the first order thermal decomposition reaction, the following data were obtained
- Write two factors that affect the rate of reaction.
- For a reaction A + B ⟶ P, the rate is given by Rate = k [A] [B]2. How is the rate of reaction affected if the concentration of B is doubled?
- For a reaction A + B ⟶ P, the rate is given by Rate = k [A] [B]2. What is the overall order of reaction if A is present in large excess?
- For a reaction (i) Write the order and molecularity of this reaction. (ii) Write the unit of k.
- Read the following passage and answer the questions that follow: The rate of reaction is concerned with decrease in the concentration of reactants or increase in the concentration of products
- For the Hydrolysis of Methyl Acetate in Aqueous Solution, the Following Results Were Obtained
- A Reaction is Second Order in a and First Order in B
- For a chemical reaction R → P, the variation in the concentration (R) vs. time (t) plot is given as: (i) Predict the order of the reaction. (ii) What is the slope of the curve?
- The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume : SO2Cl2 (g) → SO2 (g) + Cl2 (g) Calculate the rate constant.
- Assertion (A): For a zero-order reaction, the unit of rate constant and rate of reaction are same. Reason (R): Rate of reaction for zero order reaction is independent of concentration of reactant.
- The decomposition of NH3 on platinum surface is zero order reaction. What are the rates of production of N2 and H2 if k = 2.5 × 10^−4 mol−1 L s−1?
- The slope in the plot of [R] Vs. time for a zero-order reaction is ______.
- The decomposition of NH3 on a platinum surface is a zero-order reaction. If the rate constant (k) is 4 ×10-3 ms-1 , how long will it take to reduce the initial concentration of NH3 from 0.1 M to 0.
- The following experimental rate data were obtained for a reaction carried out at 25°C: A(g)+B(g)⟶C(g)+A(g) What are the orders with respect to A(g) and B(g)?
- Write the expression of integrated rate equation for zero order reaction.
- Observe the graph shown in figure and answer the following questions: (a) What is the order of the reaction? (b) What is the slope of the curve? (c) Write the relationship between k and t1/2 (half
- Following Data Are Obtained for Reaction :N2o5 → 2no2 + 1/2o2 Show that It Follows First Order Reaction. Calculate the Half-life
- A First Order Reaction Takes 20 Minutes for 25% Decomposition. Calculate the Time When 75% of the Reaction Will Be Completed. (Given : Log = 2 = 0·3010, Log 3 = 0·4771, Log 4 = 0·6021)
- Define Order of Reaction. How Does Order of a Reaction Differ from Molecularity for a Complex Reaction?
- A First Order Reaction is 50% Complete in 25 Minutes. Calculate the Time for 80% Completion of the Reaction.
- The slope in the plot of ln[R] vs. time for a first order reaction is ______.
- The slope in the plot of RRlog [R]0[R] Vs. time for a first-order reaction is ______.
- What is the rate constant?
- Assertion (A): The half-life of a reaction is the time in which the concentration of the reactant is reduced to one-half of its initial concentration.
- The Decomposition of a Hydrocarbon Has Value of Rate Constant as 2.5×104s-1 at 27° What Temperature Would Rate
- Write a Condition Under Which a Bimolecular Reaction is Kinetically First Order. Give an Example of Such a Reaction. (Given : Log2 = 0.3010,Log 3 = 0.4771, Log5 = 0.6990).
- Predict the Main Product of the Following Reactions:
- A First-order Reaction is 50% Completed in 40 Minutes at 300 K and in 20 Minutes at 320 K. Calculate the Activation Energy of the Reaction.
- Explain the Following Terms : Half Life Period of a Reaction (T1/2)
- What happens to the rate constant k and activation energy Ea as the temperature of a chemical reaction is increased? Justify.
- What is the Effect of Adding a Catalyst on Activation Energy (Ea)
- Define activation energy.
- The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.
- Sum: The rate constant of a first order reaction increases from 2 × 10−2 to 4 × 10−2 when the temperature changes
- A First Order Reaction Takes 30 Minutes for 50% Completion. Calculate the Time Required for 90% Completion of this Reaction.
- The Rate Constant for the First-order Decomposition of H2O2 is Given by the Following Equation
- Rate Constant ‘K’ of a Reaction Varies with Temperature ‘T’ According to the Equation
- A first-order reaction is 50% complete in 30 minutes at 300 K and in 10 minutes at 320 K. Calculate activation energy (Ea) for the reaction. [R = 8.314 J K−1 mol−1] [Given: log 2 = 0.3010,
- A first order reaction takes 23.1 minutes for 50% completion. Calculate the time required for 75% completion of this reaction.
- For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
- The rate constant of a first order reaction increases from 4 × 10−2 to 8 × 10−2 when the temperature changes from 27°C to 37°C. Calculate the energy of activation
- A First Order Reaction Takes 40 Minutes for 30% Decomposition. Calculate t1/2 for this Reaction.
- Show that the Time Required for 99% Completion is Double of the Time Required for the Completion of 90% Reaction.
- A First Order Reaction Takes 10 Minutes for 25% Decomposition. Calculate T1/2 for the Reaction. (Given : Log 2 = 0.3010, Log 3 = 0.4771, Log 4 = 0.6021)
- For a Reaction (I) Write the Rate Law for the Reaction. (Ii)Write the Overall Order of a Reaction. (Iii) Out of Steps(1) and (2), Which One is the Rate-determining Step?
- For the reaction 3A⟶2B, rate of reaction dAdt-d[A]dt is equal to ______.
- For the reaction 3A → 2B, rate of reaction +d[B]dt is equal to ______.
Concepts [11]
- Concept of Chemical Kinetics
- Rate of Chemical Reaction
- Factors Influencing Rate of a Reaction
- Integrated Rate Equations
- Zero Order Reactions
- First Order Reactions
- Half Life Period of a Reaction
- Temperature Dependence of the Rate of a Reaction
- Effect of Catalyst on the Rate of Reaction
- Collision Theory of Chemical Reactions
- Overview of Chemical Kinetics
