Chapter 4 Chemical Kinetics

Case Study 1: Rate of Reaction and Factors Affecting It

Case: The rate of a chemical reaction is defined as the change in the concentration of reactants or products per unit time. It is influenced by several factors including temperature, concentration of reactants, and the presence of a catalyst. According to the Arrhenius equation, the rate constant $k$ depends on temperature and activation energy ($E_a$ ):

$$k = A e^{-E_a/RT}$$

where $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin.

As the temperature increases, the number of particles with sufficient energy to react also increases, which leads to an increase in the rate of reaction. Catalysts lower the activation energy, thereby increasing the rate of reaction without being consumed in the process.

Questions:

1. Which of the following factors does NOT affect the rate of a chemical reaction?

   • A) Temperature
   • B) Concentration of reactants
   • C) Volume of the container
   • D) Presence of a catalyst
   • Answer: C) Volume of the container

2. According to the Arrhenius equation, if the temperature of a reaction is increased, the rate constant ($k$ ) will:

   • A) Decrease
   • B) Remain constant
   • C) Increase
   • D) Become zero
   • Answer: C) Increase

3. A catalyst increases the rate of reaction by:

   • A) Increasing the concentration of reactants
   • B) Decreasing the activation energy
   • C) Increasing the energy of reactants
   • D) Decreasing the number of reactant molecules
   • Answer: B) Decreasing the activation energy

4. The effect of temperature on the rate of a reaction is explained by the:

   • A) Le Chatelier's Principle
   • B) Arrhenius Equation
   • C) Van't Hoff's factor
   • D) Rate Law
   • Answer: B) Arrhenius Equation

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Case Study 2: Order of Reaction and Rate Law

Case: The order of a reaction is the sum of the powers of the concentration terms in the rate law equation. For a reaction:

$$aA + bB \rightarrow products$$

the rate law is expressed as:

$$\text{Rate} = k[A]^m[B]^n$$

where $m$ and $n$ are the orders of reaction with respect to reactants A and B, respectively. The overall order of the reaction is $m + n$ . The rate constant $k$ depends on temperature and the nature of the reaction.

For a first-order reaction, the rate is directly proportional to the concentration of only one reactant. For a second-order reaction, the rate is proportional to the square of the concentration of one reactant, or to the product of the concentrations of two reactants.

Questions:

1. The rate law for a reaction can be determined experimentally by:

   • A) Using the balanced chemical equation
   • B) Measuring the concentration of products over time
   • C) Applying the Le Chatelier's principle
   • D) Using the atomic number of reactants
   • Answer: B) Measuring the concentration of products over time

2. The unit of the rate constant $k$ for a second-order reaction with respect to one reactant is:

   • A) mol/L·s
   • B) L/mol·s
   • C) s⁻¹
   • D) mol/s
   • Answer: B) L/mol·s

3. If the rate of a reaction is directly proportional to the concentration of a single reactant, the reaction is said to be:

   • A) Zero-order
   • B) First-order
   • C) Second-order
   • D) Third-order
   • Answer: B) First-order

4. In a reaction $A + B \rightarrow C$ , if the rate law is $\text{Rate} = k[A]^1[B]^2$ , the overall order of the reaction is:

   • A) 1
   • B) 2
   • C) 3
   • D) 4
   • Answer: C) 3

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Case Study 3: Half-Life of Reactions

Case: The half-life ($t_{1/2}$ ) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. The half-life is different for reactions of different orders. For a first-order reaction, the half-life is constant and independent of the initial concentration of the reactant. For a second-order reaction, the half-life is inversely proportional to the initial concentration of the reactant.

For a first-order reaction, the half-life is given by:

$$t_{1/2} = \frac{0.693}{k}$$

For a second-order reaction, the half-life is given by:

$$t_{1/2} = \frac{1}{k[A]_0}$$

where $[A]_0$ is the initial concentration of reactant A.

Questions:

1. For a first-order reaction, the half-life is:

   • A) Dependent on the concentration of the reactant
   • B) Independent of the concentration of the reactant
   • C) Directly proportional to the rate constant
   • D) Always increasing with time
   • Answer: B) Independent of the concentration of the reactant

2. For a second-order reaction, the half-life:

   • A) Is constant for all concentrations
   • B) Decreases with increasing initial concentration
   • C) Increases with increasing initial concentration
   • D) Is unaffected by the initial concentration
   • Answer: C) Increases with increasing initial concentration

3. The half-life for a first-order reaction is:

   • A) Proportional to the concentration of the reactant
   • B) Inversely proportional to the concentration of the reactant
   • C) Constant for all initial concentrations
   • D) Dependent on temperature
   • Answer: C) Constant for all initial concentrations

4. The formula for the half-life of a second-order reaction is:

   • A) $t_{1/2} = \frac{0.693}{k}$
   • B) $t_{1/2} = \frac{1}{k[A]_0}$
   • C) $t_{1/2} = k[A]^2$
   • D) $t_{1/2} = k[A]$
   • Answer: B) $t_{1/2} = \frac{1}{k[A]_0}$

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Case Study 4: Activation Energy and Temperature Dependence

Case: The activation energy ($E_a$ ) of a reaction is the minimum energy required for reactants to transform into products. The higher the activation energy, the slower the reaction rate, as fewer molecules have the required energy to react. The rate constant $k$ increases with temperature, and this temperature dependence can be described by the Arrhenius equation.

The rate constant $k$ is related to the activation energy and temperature by:

$$k = A e^{-E_a/RT}$$

where $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin.

Questions:

1. The activation energy of a reaction is the energy:

   • A) Needed to break bonds in the reactants
   • B) Released when products are formed
   • C) Required for reactants to reach the transition state
   • D) Released when reactants collide
   • Answer: C) Required for reactants to reach the transition state

2. According to the Arrhenius equation, if the activation energy increases, the rate constant $k$ will:

   • A) Increase
   • B) Decrease
   • C) Remain the same
   • D) Become negative
   • Answer: B) Decrease

3. The rate constant $k$ increases with temperature because:

   • A) The collision frequency increases
   • B) The activation energy decreases
   • C) The number of molecules with energy greater than the activation energy increases
   • D) The concentration of reactants increases
   • Answer: C) The number of molecules with energy greater than the activation energy increases

4. The frequency factor $A$ in the Arrhenius equation represents:

   • A) The probability that reactants will collide
   • B) The activation energy of the reaction
   • C) The temperature dependence of the rate constant
   • D) The concentration of reactants
   • Answer: A) The probability that reactants will collide

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Case Study 5: Collision Theory

Case: The collision theory of chemical reactions states that for a reaction to occur, reacting molecules must collide with sufficient energy and proper orientation. The rate of reaction depends on the number of effective collisions per unit time. The frequency of collisions increases with an increase in the concentration of reactants, temperature, and the presence of a catalyst. According to the collision theory, only those collisions that have energy equal to or greater than the activation energy of the reaction lead to the formation of products.

Questions:

1. According to the collision theory, a higher concentration of reactants leads to:

   • A) A decrease in the number of collisions
   • B) An increase in the number of collisions
   • C) No change in the number of collisions
   • D) Decrease in the activation energy
   • Answer: B) An increase in the number of collisions

2. For a reaction to occur, the molecules must collide with:

   • A) High speed
   • B) Sufficient energy and proper orientation
   • C) No energy
   • D) Maximum pressure
   • Answer: B) Sufficient energy and proper orientation

3. The effectiveness of collisions in a chemical reaction is influenced by:

   • A) Temperature
   • B) Activation energy
   • C) Molecular orientation
   • D) All of the above
   • Answer: D) All of the above

4. The role of a catalyst in a chemical reaction is to:

   • A) Increase the energy of reactants
   • B) Increase the number of collisions
   • C) Lower the activation energy of the reaction
   • D) Decrease the concentration of reactants
   • Answer: C) Lower the activation energy of the reaction