Chemical Kinetics: Reaction Rates and Factors Affecting Them

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the speed (rate) at which chemical reactions occur and the factors that affect these rates. Understanding kinetics allows chemists to control reactions and optimize conditions for desired outcomes.

• Chemical Kinetics: Study of factors affecting the rate or speed of motion of reacting molecules.

• Reaction Rate: Measure of speed in changing concentration (usually in M/s) of reactants or products over time.

Reaction Progress and Completion

• For reactions that go to completion, almost all reactants are converted to products.

• Uses a single arrow (→) to signify completion.

• Reaction rates decrease with time due to reduction in concentrations of reactants.

Example: The formation of carbon tetrachloride from chloroform: CHCl3(g) + Cl2(g) → CCl4(g) + HCl(g). The concentration of CCl4 increases over time, typically following a curve that levels off as the reaction completes.

Energy Changes in Reactions

Energy Diagrams

Energy diagrams illustrate the energies of reactants, products, and the transition state as a reaction occurs.

• Reactants: Found at the beginning of the diagram.

• Products: Found at the end.

• Transition State: The highest energy point along the reaction path; also called the activated complex.

• Reaction Coordinate: The progress of a reaction pathway plotted along the x-axis.

• Activation Energy (Ea): The minimum energy required for a reaction to occur.

Example: In an energy diagram, the energy value of the product is read at the end of the curve.

Speed of Reactions and Activation Energy

• The speed of a chemical reaction is based on the magnitude of the activation energy.

• The higher the activation energy, the slower the reaction; the lower the activation energy, the faster the reaction.

Example: Given three reactions with different activation energies, the one with the lowest Ea will occur in the shortest time.

Stability and Enthalpy

• The difference in overall energy between reactants and products determines the enthalpy change (ΔH) of a reaction.

• ΔE = E_{products} - E_{reactants}

• Negative ΔE: exothermic reaction (releases energy).

• Positive ΔE: endothermic reaction (absorbs energy).

Catalysts and Reaction Pathways

• A catalyst increases the rate of a reaction by lowering the activation energy (Ea) without being consumed.

• Energy diagrams for catalyzed reactions show a lower peak (lower Ea) compared to uncatalyzed reactions.

Example: If a catalyst lowers the activation energy by 10 kJ, the total energy difference between products and the transition state is reduced by 10 kJ.

Factors Affecting Reaction Rates

Major Factors

• There are four major factors that directly influence how fast a reaction proceeds:

Factor	Condition	Effect on Collisions	Increase Rate?
Concentration of Reactants	↑ [reactant]	↑ collision frequency	Yes
Surface Area of Reactants	↑ surface area (e.g., powder vs. solid chunk)	↑ collision frequency	Yes
Temperature	↑ temperature (°C or K)	↑ collision energy & frequency	Yes
Catalysts	Present	↓ activation energy (Ea)	Yes

Example: Increasing the temperature or surface area of reactants increases the rate of a chemical reaction.

Measuring Reaction Rates

Average Rate of Reaction

• Average (General) Rate: Change in concentration (M) of a reactant or product over a period of time.

• Change in concentrations: reactant is negative (decreases), product is positive (increases).

Average Rate	Expression
Reactant	$\text{Average Rate} = -\frac{\Delta [\text{A}]}{\Delta t}$
Product	$\text{Average Rate} = +\frac{\Delta [\text{B}]}{\Delta t}$

Example: For 2 C2H6OH (l) + 9 O2 (g) → 6 CO2 (g) + 8 H2O (g), the rate of disappearance of C2H6OH is $-\frac{1}{2}\frac{\Delta [\text{C}_2\text{H}_6\text{OH}]}{\Delta t}$ and the rate of appearance of CO2 is $+\frac{1}{6}\frac{\Delta [\text{CO}_2]}{\Delta t}$.

Rate Comparisons Using Stoichiometry

• If the rate of one compound is known, the rate of another can be calculated using stoichiometric comparison.

• Use the coefficients from the balanced equation to relate rates.

Example: For 2 NO (g) + 2 H2 (g) → N2 (g) + 2 H2O (g), if the rate of decomposition of H2 is known, the rate of formation of N2 can be calculated using the ratio of their coefficients.

Instantaneous Rate

• Instantaneous Rate: The rate of a reaction at any particular moment in time.

• Calculated using the slope of the tangent line to the concentration vs. time curve at that point.

Formula:

$\text{Instantaneous Rate} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Example: For the reaction CH3OH (aq) + HCl (aq) → CH3Cl (aq) + H2O (l), the instantaneous rate at a given time is found by calculating the slope between two close time points.

Collision Theory and Arrhenius Equation

Collision Theory

• A chemical reaction is successful when two reactants successfully collide with enough energy and proper orientation.

• Collision frequency: Number of molecular collisions per unit time.

• Successful collisions: Energetic collisions resulting in product formation.

Factors Influencing Collisions

Factor	Effect
Temperature	Increases energy of collisions
Activation Energy (Ea)	Lower Ea increases frequency of successful collisions
Concentration	Increases frequency of collisions
Orientation	Proper orientation increases chance of successful collision

Arrhenius Equation

The Arrhenius equation relates the rate constant (k) to temperature and activation energy:

$k = Ae^{-\frac{E_a}{RT}}$

• k: Rate constant

• A: Frequency factor (includes orientation and collision frequency)

• Ea: Activation energy (J/mol or kJ/mol)

• R: Gas constant (8.314 J/mol·K)

• T: Temperature (K)

Frequency Factor (A): Can be split into orientation factor (p) and collision frequency (z).

• Orientation factor (p): Fraction of collisions with correct orientation.

• Collision frequency (z): Number of collisions per unit time.

Example: H2 + I2 has a smaller orientation factor than H2 + H2 due to the need for proper alignment.

Summary Table: Key Equations and Concepts

Concept	Equation/Definition
Average Rate (Reactant)	$-\frac{\Delta [\text{A}]}{\Delta t}$
Average Rate (Product)	$+\frac{\Delta [\text{B}]}{\Delta t}$
Instantaneous Rate	$\frac{\Delta y}{\Delta x}$ (slope of tangent)
Arrhenius Equation	$k = Ae^{-\frac{E_a}{RT}}$
Activation Energy (Ea)	Minimum energy required for reaction
ΔE (Enthalpy Change)	$E_{products} - E_{reactants}$

Additional info: These notes cover the core concepts of chemical kinetics, including reaction rates, energy diagrams, factors affecting rates, and the Arrhenius equation, as relevant to a General Chemistry college course (Chapter 14: Chemical Kinetics).