Chemical Kinetics: Reaction Rates and Factors Affecting Rates

Chemical Kinetics and Reaction Rates

Introduction to Kinetics

Chemical kinetics is the branch of chemistry that studies the speed, or rate, at which chemical reactions occur and the factors that influence these rates. Understanding kinetics is essential for controlling reactions in industrial, laboratory, and biological settings.

• Kinetics: The study of how quickly reactions occur.

• Reaction Rate: A measure of how the concentration of a reactant or product changes over time.

• Mechanism: The sequence of elementary steps by which a chemical reaction proceeds.

Defining and Measuring Reaction Rates

Conceptual Definition and Uses

The reaction rate quantifies the speed of a chemical process. It is typically expressed as the change in concentration of a reactant or product per unit time.

• Proper Symbol and Unit Usage:

  • Rate is expressed as $\frac{\Delta [A]}{\Delta t}$, where $[A]$ is the molar concentration of substance A and $t$ is time.

  • Units: $\frac{\text{mol}}{\text{L} \cdot \text{s}}$ or $\text{M} \cdot \text{s}^{-1}$ (M = molarity).

• Appearance vs. Disappearance:

  • For a reaction $A \rightarrow B$:

  • Rate of disappearance of A: $-\frac{\Delta [A]}{\Delta t}$

  • Rate of appearance of B: $\frac{\Delta [B]}{\Delta t}$

Types of Reaction Rates

• Average Rate: Change in concentration over a finite time interval.

  • Example: $\text{Average rate} = \frac{[C_2H_4Cl_2]_{t=150s} - [C_2H_4Cl_2]_{t=0}}{150\,\text{s} - 0}$

  • Calculation: $\frac{0.6740\,\text{M} - 0.1000\,\text{M}}{150\,\text{s} - 0} = -1.727 \times 10^{-3}\,\text{M/s}$

• Instantaneous Rate: The rate at a specific moment, found as the slope of the tangent to a concentration vs. time curve.

• Initial Rate: The instantaneous rate at the very start of the reaction (time zero).

Factors Affecting Reaction Rates

Collision Theory and Effective Collisions

For a reaction to occur, reactant particles must collide with sufficient energy and proper orientation. The frequency and effectiveness of these collisions determine the reaction rate.

• Increase Temperature: Raises kinetic energy, leading to more frequent and energetic collisions.

• Increase Concentration: More particles per volume increases collision frequency.

• Adjust State of Matter: Reactions are generally faster in solutions or gases than in solids due to greater particle mobility.

• Use a Catalyst: Provides an alternative pathway with lower activation energy, increasing the rate without being consumed.

Additional info: Catalysts often work by orienting reactants favorably or by stabilizing the transition state.

Relative Rates and Stoichiometry

Correlation with Stoichiometry

The rates at which reactants are consumed and products are formed are related by the stoichiometric coefficients in the balanced equation.

• For the reaction: $2O_3(g) \rightarrow 3O_2(g)$

• Relative rates: $-\frac{1}{2}\frac{\Delta [O_3]}{\Delta t} = \frac{1}{3}\frac{\Delta [O_2]}{\Delta t}$

• If the rate of appearance of $O_2$ is $4.50\,\text{M/s}$, then the rate of disappearance of $O_3$ is:

  • $\frac{1}{3}\frac{\Delta [O_2]}{\Delta t} = -\frac{1}{2}\frac{\Delta [O_3]}{\Delta t}$

  • $\Rightarrow \frac{\Delta [O_3]}{\Delta t} = -\frac{2}{3} \times 4.50\,\text{M/s} = -3.00\,\text{M/s}$

Summary Table: Types of Reaction Rates

Type of Rate	Definition	How Determined
Average Rate	Change in concentration over a time interval	Secant (straight line) between two points on a graph
Instantaneous Rate	Rate at a specific instant	Slope of tangent to curve at a point
Initial Rate	Instantaneous rate at time zero	Slope at $t=0$

Key Equations

• General rate expression for $A \rightarrow B$:

  • $\text{Rate} = -\frac{\Delta [A]}{\Delta t} = \frac{\Delta [B]}{\Delta t}$

• Relative rates for $aA \rightarrow bB$:

  • $-\frac{1}{a}\frac{\Delta [A]}{\Delta t} = \frac{1}{b}\frac{\Delta [B]}{\Delta t}$