Exhaustive Notes on Collision Theory and Chemical Kinetics

Definition and Scope: Collision theory explains how chemical reactions occur and why reaction rates vary under different conditions. It was proposed in the early twentieth century to provide a detailed view of chemical kinetics beyond what simple chemical equations can show.
Requirement for Success: For a reaction to be successful, it is not enough for reactant particles to simply hit each other. Only a certain fraction of collisions result in products.

Collision Event: Reacting species must physically encounter one another.
Sufficient Energy: Molecules must possess enough energy to break existing chemical bonds and form new ones. This minimum energy requirement is known as the Activation Energy ( $E_a$ ).
Molecular Orientation: The "bits" of the molecules that need to interact must be correctly positioned in relation to one another. Even if molecules have sufficient energy, incorrect orientation will result in a failed reaction. This acts as a probability factor in the reaction rate.
The Rate Equation Components: The rate of a reaction is equal to the product of: - The number of collisions per second. - The fraction of collisions possessing enough energy to react (e.g., perhaps only $10\%$ or $20\%$ of species). - The orientation/probability factor.

Concentration: Increasing the concentration of reactants ( $A + B \rightarrow \text{Products}$ ) results in more collisions per volume of space, leading to a higher frequency of successful collisions.
Temperature: Increasing temperature increases the kinetic energy of the system, which raises collision frequency and the fraction of molecules with energy exceeding $E_a$ .
Catalysts: These provide an alternative reaction pathway with a lower activation energy.
Solvent: The medium in which a reaction occurs can significantly impact the rate, particularly in processes like hydrolysis.
Phase and Surface Area: This is specifically relevant for materials in a solid state. Increasing the surface area (breaking down a solid) increases the sites available for reaction, thereby increasing the rate.

High vs. Low Concentration: In low-concentration environments, there are fewer collisions between species ( $\text{green and red molecules}$ ) in a given volume.
Statistical Probability: If conditions (temperature, orientation probability) are constant, and only $20\%$ of collisions are successful, a larger absolute number of collisions at high concentration will yield a much higher reaction rate than the same percentage of a smaller number at low concentration.

Activation Energy ( $E_a$ ): Represented on an energy versus reaction progress diagram ( $x\text{-axis} = \text{time}$ , $y\text{-axis} = \text{energy}$ ). It is the energy barrier or "hurdle" that prevents reactants from spontaneously and instantaneously turning into products.
Units of $E_a$ : Measured in Joules per mole ( $J\,mol^{-1}$ ) or Kilojoules per mole ( $kJ\,mol^{-1}$ ).
Maxwell-Boltzmann Distribution Curvature: - $x\text{-axis}$ : Kinetic Energy. - $y\text{-axis}$ : Number of particles with a particular kinetic energy ( $E$ ). - The area under the curve represents the total population of molecules. - The Activation Energy Line: Only the molecules in the shaded area to the right of the $E_a$ line have sufficient energy for a potential reaction.
Effect of Temperature Increase: - Increasing temperature does not decrease or shift the activation energy. - Instead, it shifts the entire population curve to the right (rightwards shift). - This results in a larger fraction of the population possessing energy greater than $E_a$ .

Concentration: If 10 students are blindfolded in Brooklyn Hall, they will bump into each other occasionally. If 130 students are in the room, they will bump into each other much more frequently.
Temperature: If students in Brooklyn Hall walk, collisions occur occasionally. If those same students run (higher kinetic energy), the frequency of collisions increases significantly.
Relationship: Both factors—more people (concentration) and faster movement (temperature)—increase the rate of reaction through higher collision frequency.
Rule of Thumb: For every $10^{\circ}C$ increase in temperature, the reaction rate approximately doubles (though this is a non-absolute approximation).

Exponential Form: Quantifies the influence of temperature ( $T$ ) on kinetics.
Formula: $k = A e^{-\frac{E_a}{RT}}$ - $k$ : Reaction rate constant. - $A$ : Frequency factor (probability factor related to orientation and entropy of activation). - $E_a$ : Activation energy. - $R$ : Universal gas constant ( $8.314\,J\,K^{-1}\,mol^{-1}$ ). - $T$ : Absolute temperature (must be in Kelvin).
Logarithmic (Linearized) Form: $\ln(k) = \ln(A) - \frac{E_a}{R} \times \frac{1}{T}$ - This form allows for the determination of kinetic parameters through graphical analysis.

The Plot: Graphing $\ln(k)$ on the $y\text{-axis}$ versus $\frac{1}{T}$ (inverse Kelvin) on the $x\text{-axis}$ .
Extricating Values: - Slope: Equals $-\frac{E_a}{R}$ . Use this to calculate activation energy. - $-y\text{-intercept}$ : Equals $\ln(A)$ . Use this to find the frequency factor.
Extrapolation: Researchers often measure kinetics at high temperatures (e.g., $70^{\circ}C$ , $80^{\circ}C$ , or $90^{\circ}C$ ) to get data in a useful amount of time. They then extrapolate this data back to find the rate constant ( $k$ ) at room temperature ( $25^{\circ}C$ or $298\,K$ ) or storage temperatures ( $4^{\circ}C$ ) to predict product stability.
Point-to-Point Comparison: Comparing two rate constants ( $k_1, k_2$ ) at two different temperatures ( $T_1, T_2$ ) using the rearranged Arrhenius expression, provided $E_a$ is known.

Mechanism: A catalyst provides an alternative reaction pathway.
Energy Barrier: It lowers the activation energy ( $E_a$ ) required for the reaction, and in some cases, the barrier may disappear entirely.
Biological Example: Enzymes in the body act as catalysts. They "lock" reacting species into the correct orientation and position relative to one another.
Necessity: Catalysts are vital in physiological conditions where increasing the temperature to provide energy for a reaction is not possible.

Ester Hydrolysis: The influence of pH on ester hydrolysis will be addressed in subsequent videos and is part of the Aspen hydrolysis experiment.