Class 11 Chemistry – Chapter 7: Chemical Kinetics (FBISE)
This section provides complete, exam-oriented notes for Class 11 Chemistry Chapter 7 – Chemical Kinetics strictly following the Federal Board (FBISE) syllabus. Concepts are explained in a simple, student-friendly manner for effective understanding and exam preparation.
Key topics covered include rate of reaction, factors affecting reaction rate, order and molecularity of reactions, rate laws, integrated rate equations, activation energy, and collision theory. Detailed examples, solved numericals, and step-by-step explanations are included to help students master the chapter.
Students can also access video lectures, MCQs, numericals, test series, and live classes for this chapter on our official YouTube channel and stay updated through our WhatsApp channel.
Notes: Rates of Reactions
The rate of reaction is defined as the change in concentration of reactants or products per unit time. It describes how fast a chemical reaction occurs.
1. Mathematical Expression
For a general reaction $A \longrightarrow B$, the rate can be expressed in terms of the disappearance of reactant $A$ or the appearance of product $B$:
- $$\text{Rate} = \frac{dx}{dt}$$
- $$\text{Rate} = -\frac{d[A]}{dt} \text{ (Negative sign indicates decrease in concentration)}$$
- $$\text{Rate} = +\frac{d[B]}{dt} \text{ (Positive sign indicates increase in concentration)}$$
Units: Since concentration is measured in $mol/dm^3$ and time in seconds ($s$), the unit for reaction rate is **$mol \cdot dm^{-3} \cdot s^{-1}$**.
2. Graphical Representation
- Reactants: The curve slopes downward as concentration decreases over time.
- Products: The curve slopes upward as concentration increases over time.
- Slope: The slope is steepest at the beginning (high rate) and becomes less steep as the reaction progresses (lower rate), eventually becoming horizontal when the reaction stops.
3. Average Rate of Reaction
The rate measured over a specific time interval is the average rate. It is calculated by dividing the change in concentration by the time elapsed.
Example Calculation:
Between $t = 0.0s$ and $t = 20s$ for product $C$:
$d[C] = 0.38 - 0.0 = 0.38 \text{ mol/dm}^3$
$dt = 20 - 0 = 20s$
$$\text{Rate} = \frac{0.38}{20} = 0.019 \text{ mol} \cdot \text{dm}^{-3} \cdot s^{-1}$$
Questions and Answers
Q1: Why is a negative sign used when expressing the rate in terms of reactants?
A: The negative sign is used because the concentration of reactants decreases over time. Since the rate of reaction must be a positive value, the negative sign mathematically cancels out the negative change in concentration ($d[A] < 0$).
Q2: How does the rate of reaction change as the reaction progresses?
A: The rate of reaction is never constant. It is fastest at the beginning when the concentration of reactants is highest. As reactants are consumed, the rate continuously decreases until it becomes zero (the reaction stops).
Q3: What does a horizontal line on a concentration-time graph indicate?
A: A horizontal line indicates that the concentration is no longer changing, meaning the reaction has reached completion or has stopped.
Q4: Based on the provided data table, calculate the average rate of reaction between 10s and 30s for product C.
A:
1. Change in concentration $d[C] = 0.45 - 0.20 = 0.25 \text{ mol/dm}^3$
2. Change in time $dt = 30s - 10s = 20s$
3. $$\text{Rate} = \frac{0.25}{20} = 0.0125 \text{ mol} \cdot \text{dm}^{-3} \cdot s^{-1}$$
7.2 Rate Law
The rate of reaction is the instantaneous change in concentration of a reactant or product at a specific time. Experimental studies show that the rate is proportional to the molar concentration of reactants, each raised to a specific power determined experimentally.
1. Rate Equation and Rate Constant
For a general reaction $A \rightarrow \text{Product}$, the rate expression is:
- $$\text{Rate} \propto [A]^x$$
- $$\text{Rate} = k[A]^x$$
Where $k$ is the proportionality constant known as the rate constant. If $[A] = 1\text{ M}$, then $\text{Rate} = k$. The rate constant is specific to each reaction and is independent of concentration and time, but it changes with temperature.
2. Order of Reaction
The order of reaction is defined as the sum of all exponents to which the molar concentration terms in the rate equation are raised.
- For a reaction $aA + bB \rightarrow cC + dD$, the rate equation is $\text{Rate} = k[A]^x[B]^y$.
- The exponents $x$ and $y$ (the orders with respect to $A$ and $B$) may or may not be the same as the stoichiometric coefficients $a$ and $b$.
- The overall order is $x + y$.
- Order of reaction can be a whole number, zero, or a fraction. It must be determined experimentally.
3. Types of Order of Reactions
| Type | Definition | Example |
|---|---|---|
| Zero Order | Rate is independent of reactant concentration. | Decomposition of $NH_3$ on heated tungsten; $\text{Rate} = k[NH_3]^0$. |
| First Order | Rate is proportional to the first power of a single reactant. | Thermal decomposition of $N_2O_5$; $\text{Rate} = k[N_2O_5]$. |
| Second Order | Sum of exponents in the rate equation is two. | $NO + O_3 \rightarrow NO_2 + O_2$; $\text{Rate} = k[NO][O_3]$. |
| Third Order | Sum of exponents in the rate equation is three. | $2NO + O_2 \rightarrow 2NO_2$; $\text{Rate} = k[NO]^2[O_2]$. |
| Fractional Order | Sum of exponents is a fraction. | $H_2 + Br_2 \rightarrow 2HBr$; $\text{Rate} = k[H_2][Br_2]^{0.5}$ (Order = 1.5). |
| Pseudo First Order | A bimolecular reaction where one reactant (solvent) is in large excess, keeping its concentration constant. | Hydrolysis of tertiary butyl bromide: $(CH_3)_3C-Br + H_2O \rightarrow (CH_3)_3C-OH + HBr$. |
Questions and Answers
Q1: Can the order of a reaction be determined by looking at a balanced chemical equation?
A: No. The order of a reaction for a particular species cannot be predicted by looking at the balanced equation. It can only be determined by experiment. For example, in the reaction $2NO_2 + O_3 \rightarrow N_2O_5 + O_2$, the coefficient of $NO_2$ is 2, but the experimental order with respect to $NO_2$ is 1.
Q2: Define the "Rate Constant" ($k$).
A: The rate constant is the rate of reaction when the molar concentration of each reactant is unity (1 M). It provides the relationship between concentration and reaction rate and is specific to a given reaction at a specific temperature.
Q3: What characterizes a "Pseudo First Order" reaction?
A: It is a bimolecular reaction where one reactant is present in such large excess (often the solvent) that its concentration remains effectively constant throughout the reaction. Consequently, the rate depends only on the concentration of the other reactant, making it behave like a first-order reaction.
Q4: Calculate the overall order of the reaction between $CHCl_3$ and $Cl_2$ given the rate law: $\text{Rate} = k[CHCl_3][Cl_2]^{0.5}$.
A: The order with respect to $CHCl_3$ is 1, and the order with respect to $Cl_2$ is 0.5. The overall order is the sum of these exponents: $1 + 0.5 = 1.5$.
7.2 Rate Law and Order of Reaction
The rate of reaction is defined as the instantaneous change in concentration of a reactant or product at a given time. Experimental studies show that the reaction rate is proportional to the molar concentrations of reactants, each raised to a specific power.
1. The Rate Equation
For a general reaction $aA + bB \rightarrow cC + dD$, the relationship is expressed as:
- $$\text{Rate} \propto [A]^x [B]^y$$
- $$\text{Rate} = k [A]^x [B]^y$$
Where $k$ is the proportionality constant known as the rate constant. The expression itself is called the rate law or rate equation.
- The rate constant $k$ is equal to the reaction rate when the molar concentration of each reactant is unity (1 M).
- $k$ is independent of concentration and time but changes with temperature.
2. Order of Reaction
The order of reaction is the sum of all exponents to which the molar concentration terms in the rate equation are raised.
- The exponents $x$ and $y$ represent the order with respect to species $A$ and $B$ respectively.
- The sum $x + y$ is the overall order of the reaction.
- Order of reaction cannot be predicted from a balanced equation; it must be determined experimentally.
- It can be a whole number, zero, or a fraction.
3. Types of Reaction Orders
| Type | Description | Example / Rate Law |
|---|---|---|
| Zero Order | Rate is independent of reactant concentration. | Decomposition of $NH_3$ on heated tungsten: $\text{Rate} = k[NH_3]^0$. |
| First Order | Rate is proportional to the first power of concentration. | Thermal decomposition of $N_2O_5$: $\text{Rate} = k[N_2O_5]^1$. |
| Second Order | The sum of exponents is two. | $NO + O_3 \rightarrow NO_2 + O_2$: $\text{Rate} = k[NO][O_3]$. |
| Third Order | The sum of exponents is three. | Oxidation of $NO$ by $O_2$: $\text{Rate} = k[NO]^2[O_2]$. |
| Fractional Order | The sum of exponents is a fraction. | $H_2 + Br_2 \rightarrow 2HBr$: $\text{Rate} = k[H_2][Br_2]^{1/2}$ (Order = 1.5). |
| Pseudo First Order | A bimolecular reaction where one reactant (solvent) is in excess, so its concentration remains constant. | Hydrolysis of tertiary butyl bromide: $\text{Rate} = k[(CH_3)_3C-Br]$. |
Questions and Answers
Q1: Why is the order of reaction considered an experimental quantity?
A: The order of reaction for a particular species cannot be predicted by looking at the stoichiometric coefficients in a balanced chemical equation. For example, in the reaction $2NO_2 + O_3 \rightarrow N_2O_5 + O_2$, the coefficient for $NO_2$ is 2, but experimental studies show the order with respect to $NO_2$ is actually 1.
Q2: Define the Rate Constant ($k$) based on reactant concentration.
A: The rate constant $k$ is defined as the rate of reaction when the molar concentration of each reactant is unity (1 M).
Q3: Based on Example 7.2, if the concentration of $NO$ is doubled while $O_3$ is constant, what happens to the rate?
A: According to the experimental data, doubling the concentration of $NO$ (from $1.00 \times 10^{-6}$ M to $2.00 \times 10^{-6}$ M) causes the initial rate to double (from $1.98 \times 10^{-4}$ to $3.96 \times 10^{-4}$), indicating the reaction is first order with respect to $NO$.
Q4: What is a Pseudo First order reaction? Give an example.
A: A Pseudo First order reaction is a bimolecular reaction in which the solvent is in such large excess that its concentration remains effectively constant and does not affect the rate determining step. An example is the hydrolysis of tertiary butyl bromide: $(CH_3)_3C-Br + H_2O_{(excess)} \rightarrow (CH_3)_3C-OH + HBr$.
Q5: Calculate the overall order for the reaction $CO_{(g)} + Cl_{2(g)} \rightarrow COCl_{2(g)}$ using the data from Concept Assessment Exercise 7.1.
A:
1. Comparing experiments 2 and 3: $[CO]$ is constant, $[Cl_2]$ increases 10x, but the rate remains $1.30 \times 10^{-30}$. Thus, order with respect to $Cl_2$ is 0.
2. Comparing experiments 1 and 2: $[Cl_2]$ is constant, $[CO]$ decreases 10x, and the rate decreases 10x (from $1.29 \times 10^{-29}$ to $1.30 \times 10^{-30}$). Thus, order with respect to $CO$ is 1.
3. Overall Order = $1 + 0 = 1$.
7.2 Rate Law and Order of Reaction
The rate of reaction is the instantaneous change in concentration of a reactant or product at a specific time. Experimental studies show that the rate is proportional to the molar concentration of reactants, each raised to a power determined experimentally.
1. The Rate Equation and Rate Constant
For a general reaction $A \rightarrow \text{Product}$, the rate expression is:
- $$\text{Rate} = k[A]^x$$
Where $k$ is the rate constant. It is defined as the rate of reaction when the molar concentration of each reactant is unity ($1\text{ M}$). While $k$ is independent of concentration and time, its value changes with temperature.
2. Order of Reaction
The order of reaction is the sum of all exponents to which the molar concentration terms in the rate equation are raised.
- For $aA + bB \rightarrow cC + dD$, the rate law is $\text{Rate} = k[A]^x[B]^y$.
- The overall order is $x + y$.
- Order of reaction cannot be predicted from a balanced equation; it must be determined experimentally.
- It can be a whole number, zero, or a fraction.
3. Half-Life ($t_{1/2}$)
The half-life is the time required for the concentration of a reactant to be reduced to half of its initial value. The relationship between half-life and the rate constant depends on the reaction order:
- Zero Order ($n=0$): $$t_{1/2} = \frac{[A_0]}{2k}$$
- First Order ($n=1$): $$t_{1/2} = \frac{0.693}{k}$$
- Second Order ($n=2$): $$t_{1/2} = \frac{1}{k[A_0]}$$
4. Effect of Temperature and Arrhenius Equation
Reaction rates generally increase with temperature because higher temperatures increase the average kinetic energy and collision frequency of molecules. However, only effective collisions (those with sufficient activation energy and correct orientation) result in a reaction.
The Arrhenius Equation relates the rate constant $k$ to temperature: $$\mathbf{k = Ae^{-E_a/RT}}$$
- $A$: Arrhenius constant (frequency factor).
- $E_a$: Activation energy.
- $R$: Gas constant ($8.3143\text{ J}\cdot\text{K}^{-1}\cdot\text{mole}^{-1}$).
- $T$: Absolute temperature.
Questions and Answers
Q1: Why does a $10\text{ K}$ increase in temperature often double or triple the reaction rate?
A: According to the Maxwell-Boltzmann distribution, an increase in temperature increases the kinetic energy of molecules. This significantly increases the proportion of molecules that possess energy equal to or greater than the activation energy ($E_a$), leading to more effective collisions per unit time.
Q2: Define a Pseudo First order reaction with an example.
A: A bimolecular reaction where one reactant (usually a solvent) is in large excess, so its concentration remains effectively constant, is called a Pseudo First order reaction.
Example: Hydrolysis of tertiary butyl bromide:
$$\text{Rate} = k[(CH_3)_3C-Br]$$
Q3: A reaction has a half-life of $30\text{ s}$ and follows first-order kinetics. Calculate its rate constant.
A: For a first-order reaction: $$k = \frac{0.693}{t_{1/2}}$$ $$k = \frac{0.693}{30\text{ s}} = 0.0231\text{ s}^{-1}$$
Q4: Can the order of reaction be zero? Give an example.
A: Yes, a zero-order reaction is independent of the concentration of reactants. An example is the decomposition of ammonia on heated tungsten or reactions catalyzed by enzymes.
Q5: What information is required to determine the rate law of a reaction experimentally?
A: The method of initial rates is used, where the concentration of one reactant is varied while others are kept constant, and the resulting change in the initial reaction rate is measured.
7.4 The Mechanism of a Chemical Reaction
The sequence of steps that reactants take to form products in a chemical reaction is called the mechanism. While some reactions occur in a single step, many proceed through several elementary steps.
1. Rate-Determining Step
- In a multi-step reaction, one step is typically much slower than the others.
- This slowest step is known as the rate-determining step because it limits the overall rate at which the reaction can proceed.
- The experimental rate law provides information about the number of molecules involved in this specific step.
2. Reaction Intermediates
Species that are produced in one step of a mechanism and consumed in a subsequent step, and therefore do not appear in the overall balanced equation, are called reaction intermediates.
3. Potential Energy Diagrams
- The number of peaks in a potential energy diagram indicates the number of elementary steps in the mechanism.
- The step with the highest activation energy ($E_a$) peak is the slow, rate-determining step.
- The "valleys" or local minima between peaks represent the formation of reaction intermediates.
4. Temperature and Reaction Rate
Reaction rates generally increase with temperature because a higher percentage of molecules possess kinetic energy equal to or greater than the activation energy ($E_a$). This relationship is quantified by the Arrhenius Equation:
$$k = Ae^{-E_a/RT}$$
- $k$: Rate constant.
- $A$: Arrhenius constant (frequency factor).
- $E_a$: Activation energy.
- $R$: Gas constant ($8.3143 \text{ J} \cdot \text{K}^{-1} \cdot \text{mol}^{-1}$).
- $T$: Absolute temperature in Kelvin.
Questions and Answers
Q1: Given the reaction $2NO_2 + CO \rightarrow NO + CO_2$ with experimental rate $= k[NO_2]^2$, what can be inferred about the mechanism?
A: The rate law indicates that the reaction is second order with respect to $NO_2$ and zero order with respect to $CO$. This means two molecules of $NO_2$ are involved in the rate-determining step, while $CO$ is not involved in that step. Because the rate law does not match the stoichiometry of the overall reaction, the reaction must proceed in more than one step.
Q2: How do you identify the rate-determining step from a potential energy diagram?
A: The rate-determining step is identified by finding the elementary step with the largest activation energy peak. In a potential energy diagram like Figure 7.3, if the first peak is higher than the second, Step 1 is the slow, rate-determining step.
Q3: What is the relationship between temperature and the rate constant according to Arrhenius?
A: The rate constant $k$ increases exponentially with temperature. Generally, for every $10 \text{ K}$ increase in temperature, the reaction rate increases two to three times because more molecules have enough energy to overcome the activation energy barrier.
Q4: In the decomposition of hypochlorite ion ($3ClO^- \rightarrow ClO_3^- + 2Cl^-$), the rate law is $Rate = k[ClO^-]^2$. If Step I is $ClO^- + ClO^- \rightarrow ClO_2^- + Cl^-$, why is this the rate-determining step?
A: The experimental rate law shows that two $ClO^-$ ions participate in the rate-determining step. Since Step I involves exactly two $ClO^-$ ions, it is consistent with the experimental rate law and is therefore the slow, rate-determining step.
Q5: Define half-life and provide the formula for a first-order reaction.
A: The half-life ($t_{1/2}$) of a reaction is the time required for the concentration of a reactant to be reduced to half its initial value. For a first-order reaction, the relationship is constant regardless of initial concentration: $$t_{1/2} = \frac{0.693}{k}$$
7.4 The Mechanism of a Chemical Reaction
The mechanism of a reaction is the series of elementary steps that reactants undergo to form products. While some reactions happen in a single step, others proceed through multiple stages.
1. Rate-Determining Step
- In multi-step reactions, one step is significantly slower than the others.
- This slowest step is called the rate-determining step because it limits the overall speed of the reaction.
- The experimental rate law identifies the number of molecules involved in this specific step.
2. Reaction Intermediates
A reaction intermediate is a species that is produced in one step of a mechanism and consumed in a later step. Because they are consumed, they do not appear in the overall balanced chemical equation.
3. Potential Energy Diagrams and Mechanism
- The number of peaks in a potential energy diagram corresponds to the number of elementary steps in the reaction mechanism.
- The step with the highest activation energy ($E_a$) peak is the slow, rate-determining step.
- Local minima (valleys) between peaks represent the formation of reaction intermediates.
4. Temperature and the Arrhenius Equation
Reaction rates generally increase with temperature because a higher fraction of molecules gain kinetic energy equal to or greater than the activation energy ($E_a$). This relationship is defined by the Arrhenius Equation:
$$k = Ae^{-E_a/RT}$$
- $k$: Rate constant.
- $A$: Arrhenius constant (frequency factor related to collision frequency and orientation).
- $E_a$: Activation energy.
- $R$: Gas constant ($8.3143 \text{ J} \cdot \text{K}^{-1} \cdot \text{mole}^{-1}$).
- $T$: Absolute temperature.
Questions and Answers
Q1: What information does the experimental rate law provide about a reaction's mechanism?
A: The rate law provides information about the number of molecules participating in the rate-determining step. If the exponents in the rate law do not match the coefficients of the balanced equation, the reaction must proceed through more than one step.
Q2: In the reaction $2NO_2 + CO \rightarrow NO + CO_2$, the rate law is $Rate = k[NO_2]^2$. What is the rate-determining step?
A: The rate law indicates that two molecules of $NO_2$ are involved in the rate-determining step, while $CO$ is not involved in that step. A proposed mechanism consistent with this is Step I (Slow): $NO_2 + NO_2 \rightarrow NO_3 + NO$.
Q3: Define the term "Half-life" and provide the formula for a first-order reaction.
A: Half-life ($t_{1/2}$) is the time it takes for the concentration of a reactant to be reduced to half of its initial value. For a first-order reaction ($n=1$), the formula is: $$t_{1/2} = \frac{0.693}{k}$$
Q4: How does a catalyst affect a reaction based on a potential energy diagram?
A: Although not explicitly detailed in the text, a catalyst provides an alternative mechanism with a lower activation energy ($E_a$). On a diagram, this would be shown as a lower peak, allowing more molecules to have enough energy to react at a given temperature.
Q5: According to the collision theory, what two conditions must be met for a collision to be "effective"?
A: For a collision to result in a reaction, the colliding molecules must possess sufficient activation energy and must be correctly oriented.
7.4 The Mechanism of a Chemical Reaction
The mechanism of a reaction is the path or sequence of elementary steps that reactants take to form products. While some reactions occur in a single step, many proceed through several steps.
1. Rate-Determining Step
- In a multi-step reaction, the overall reaction rate is limited by the slowest step in the sequence.
- This slowest step is known as the rate-determining step.
- The experimental rate law provides information about the number of molecules participating in this specific step.
2. Reaction Intermediates
Species that are produced in one step of a mechanism and consumed in a subsequent step are called reaction intermediates. These species do not appear in the overall balanced chemical equation.
3. Potential Energy Diagrams
- The number of peaks in a potential energy diagram indicates the number of elementary steps in the reaction mechanism.
- The step with the highest activation energy peak is the slow, rate-determining step.
- The local minima (valleys) between peaks represent the formation of reaction intermediates.
4. Temperature and the Arrhenius Equation
Reaction rates generally increase with temperature because a higher proportion of molecules possess kinetic energy equal to or greater than the activation energy ($E_a$). This relationship is expressed by the Arrhenius Equation:
$$k = Ae^{-E_a/RT}$$
- $k$: Rate constant.
- $A$: Arrhenius constant or frequency factor.
- $E_a$: Activation energy.
- $R$: Gas constant ($8.3143 \text{ J} \cdot \text{K}^{-1} \cdot \text{mol}^{-1}$).
- $T$: Absolute temperature.
Relevant Questions and Answers
Q1: What is the significance of the rate-determining step in a multi-step reaction?
A: The rate-determining step is the slowest step in a reaction mechanism. It acts as a bottleneck, determining the overall rate at which the reaction can proceed.
Q2: How can a potential energy diagram help identify the rate-determining step?
A: By examining the activation energy ($E_a$) of each step; the step with the largest $E_a$ (the highest peak relative to its reactants) is the rate-determining step.
Q3: Based on Example 7.5, if a reaction is second order in $ClO^-$ ion, what does this imply about the rate-determining step?
A: It implies that two $ClO^-$ ions must participate in the rate-determining step of the mechanism.
Q4: Why does a reaction rate typically double or triple for every $10\text{ K}$ increase in temperature?
A: An increase in temperature shifts the Maxwell-Boltzmann distribution, significantly increasing the number of molecules with energy equal to or greater than the activation energy ($E_a$), leading to more effective collisions.
Q5: Define a Pseudo First order reaction.
A: It is a bimolecular reaction where one reactant (often the solvent) is in large excess, causing its concentration to remain effectively constant. This makes the reaction behave as if it were first order.