5.1.A.1 Kinetics of a Chemical Reaction: Rate of Reactant Conversion: 

1. Reaction Rate: The reaction rate is the speed at which a chemical reaction takes place. It is defined as the change in concentration of reactants or products over a specific time period. The reaction rate can be calculated using the formula:

$$\text{Reaction Rate}=\frac{\text{Change in Concentration}}{\text{Change in Time}}$$

This rate is typically measured in units such as moles per liter per second (mol/L·s).

i. Factors Influencing Reaction Rate:

a. Temperature: Generally, increasing the temperature boosts the reaction rate. This happens because higher temperatures give more energy to the reacting molecules, which raises the frequency and energy of their collisions. Consequently, there’s a higher chance of successful collisions that result in a reaction.
– For many reactions, the rate roughly doubles with every 10°C increase in temperature, a concept known as the Arrhenius equation.

b. Concentration of Reactants: A higher concentration of reactants leads to a faster reaction rate, as there are more molecules or ions present in a given volume. This increases the chances of collisions between reactant particles, resulting in more successful reactions.
– This factor is especially significant for reactions involving gases or solutions, where the concentration of molecules or ions can be adjusted.

c. Pressure (for Gaseous Reactions): Raising the pressure of gases enhances the concentration of gas molecules, which in turn increases the frequency of collisions and the reaction rate.
– In reactions involving gases, higher pressure results in a greater concentration of reactant molecules within the same volume, thereby accelerating the reaction.

d. Catalysts: A catalyst is a substance that speeds up a reaction without being consumed in the process. It achieves this by offering an alternative pathway for the reaction that has a lower activation energy.

2. Rate Laws and Order of Reaction: A rate law defines how the rate of a chemical reaction relates to the concentrations of the reactants. The order of reaction shows how the rate is influenced by the concentration of these reactants.

i. Form of Rate Laws:

The general expression for a rate law involving reactants (A) and (B) is:

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

Where:
– (k) represents the rate constant, which varies with temperature and the presence of a catalyst.
– [A] and [B] denote the concentrations of reactants A and B.
– m and n are the orders of reaction for A and B, respectively. These values are determined through experiments, not derived from the coefficients in the balanced chemical equation.

– The overall order of the reaction is the total of the exponents (m + n).

ii. Determining Reaction Order:

The order of a reaction indicates how the rate varies with changes in the concentrations of the reactants. There are three primary types of reaction orders: zero, first, and second.

a. Zero-Order Reaction (m = 0)
In a zero-order reaction, the rate remains constant regardless of the concentration of the reactant.

– Rate Law: (Rate = k)
– Rate vs. [A]: The rate remains unchanged as the concentration of (A) varies.
– Integrated Rate Law: For a zero-order reaction, the concentration of the reactant decreases linearly over time:

$$[A] = [A]_0 – kt$$

where $[A]_0$​ is the initial concentration of A,

$k$ is the rate constant, and

$t$ is time.

b. First-Order Reaction (m = 1)
In a first-order reaction, the rate is directly proportional to the concentration of one reactant.

Rate vs. [A]: The rate is directly proportional to the concentration of $A$.If the concentration of $A$ is doubled, the rate also doubles.

Integrated Rate Law: For a first-order reaction, the natural logarithm of the concentration of $A$ decreases linearly over time:

$$\ln [A]=\ln [A{]}_0-kt$$

Units of k: The units of the rate constant for a first-order reaction are s⁻¹

c. Second-Order Reaction ( $m = 2$m=2)

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

Rate Law:

$\text{Rate} = k[A]^2$ (for a single reactant) or

$\text{Rate} = k[A][B]$Rate=k[A][B] (for two reactants).

Rate vs. [A]: The rate is proportional to the square of the concentration of A. If the concentration of A is doubled, the rate increases by a factor of four.

Integrated Rate Law: For a second-order reaction:

$$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$$

d. How to Determine the Order of a Reaction:

To experimentally determine the order of a reaction, we typically follow these steps:

1. Measure the rate of the reaction at various concentrations of reactants.

2. Plot data: Depending on the suspected order of the reaction, you can plot concentration vs. time or use integrated rate laws to determine which gives a straight-line relationship.

3. For a zero-order reaction, plot $[A]$  vs. time.

4. For a first-order reaction, plot $\ln[A]$ vs. time.

5. For a second-order reaction, plot $\frac{1}{[A]}$ vs. time.

6. Examine the graph: The plot that gives a straight line will correspond to the correct order of the reaction.

3. Activation Energy and Collision Theory:

i. Activation Energy (Ea):

Activation energy is the lowest energy that the reactant molecules must have so that a chemical reaction occurs. It is the energy barrier which must be crossed so that reactants are transformed into products.

– Definition: Activation energy is the energy required to rupture bonds in reactants and form new bonds in products.
– Symbol: (Ea)
– Effect on Rate of Reaction:
– Slower reaction with greater activation energy because fewer molecules have the sufficient energy to get over the barrier.
– Faster reaction with lesser activation energy because more molecules can achieve the energy for reaction.

Activation energy can be thought of as the “threshold” that needs to be crossed by reactant molecules for a successful collision to result in a chemical transformation. Graphically, activation energy is the same as the energy difference between the reactants and the transition state (the top of the reaction pathway).

ii. Collision Theory:

Collision theory explains chemical reactions and variations in reaction rates. This theory prescribes that the following conditions must be met for a reaction to occur:

a. Collisions of Molecules:
– Molecules must collide in order to produce a reaction.
– Not all collisions are successful because only those with enough energy and correct orientation will be successful.

b. Sufficient Energy (Activation Energy):
– When molecules collide, they must have enough energy to break the activation energy barrier. If the colliding molecules’ kinetic energy is lower than the activation energy, they will simply rebound from each other without reacting.

c. Correct Orientation:
– Molecules must collide in the correct orientation so that the reacting portions of the molecules can come together and react. Even if molecules collide with enough energy, but not in the correct orientation, the reaction will not occur.

iii. Activation Energy vs. Reaction Rate:

The Arrhenius equation is employed to express the relationship between reaction rate and activation energy:

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

Where:
– (k) is the rate constant.
– (A) is the frequency factor (also known as the pre-exponential factor), and is the number of collisions with the correct orientation.
– (Ea) is the activation energy.
– (R) is the universal gas constant.
– (T) is the temperature in units of Kelvin.

iv. Temperature Effect on Reaction Rate (via Activation Energy):

With increasing temperature:
a. Molecules move faster, so there are more collisions.
b. There will be more such collisions having enough energy to overcome the activation energy barrier.

Activation energy may be estimated by the Arrhenius plot as well. By drawing the graph of (ln k) versus (1/T) (where temperature is taken in Kelvin units), the negative slope of the straight line that would result yields (-E_a/R) so that the activation energy could be calculated.

A catalyst is a substance that raises the rate of a reaction without being consumed in the reaction. Catalysts work by using an alternative reaction path that involves less energy in order to create the transition state.

– Effect on Activation Energy: The activation energy is lowered by a catalyst, in such a way that reactant collisions having enough energy to provide products are favored.
– Effect on Reaction Rate: Since there are more collisions with sufficient energy to overcome the lower activation energy, the reaction rate is increased.

4. Reaction Mechanism:

A reaction mechanism outlines the step-by-step sequence of elementary reactions that lead to an overall chemical change. It details how reactants transform into products by breaking down the reaction into individual molecular events. By examining the mechanism, we can gain insights into the reaction’s rate law, intermediates, and the influence of various factors on the reaction rate.

i. Elementary Steps:

An elementary step represents a simple, indivisible action within the overall reaction. Each elementary step involves a direct molecular collision or interaction, which may include the breaking or forming of bonds, highlighting fundamental events during the reaction.

ii. Molecularity of Elementary Steps:
– Unimolecular: Involves the reaction of a single molecule (e.g., the decomposition of a molecule).

$$\text{Rate}=k[A]$$

– Bimolecular: Involves the collision between two molecules (e.g., two reactants reacting to produce a product).

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

– Termolecular: Involves the simultaneous collision of three molecules. These occurrences are rare due to the low probability of three molecules colliding at once.

$$\text{Rate}=k[A][B][C]$$