Kinetics: Reaction Rates, Rate Laws, Integrated Rate Laws, Collision Theory, Mechanisms, and Catalysis

Kinetics Overview

17.1 Chemical Reaction Rates

Kinetic Information: Represents chemical changes over time.
- Observable as the disappearance of reactants and appearance of products.
- Rate of a reaction: Defined as the change in the amount of a reactant or product per unit time.
- Amount is often expressed in terms of concentration (typically in molarity, M).
  - Square brackets [ ] denote molarity (e.g., [0.45] means $0.45 ext{ M}$ ).
- Rate expression: A mathematical representation of the rate of reaction.
  - Can be written in terms of either reactant or product concentration.
Variety of Reaction Rates: Chemical reactions occur at vastly different rates.
- Slow reactions: Geological reactions (e.g., formation of rocks) occur over millions of years.
- Fast reactions: Acid-base reactions can happen in nanoseconds to microseconds.
Importance in Pharmaceuticals: Reaction rates are crucial for pharmaceutical dosing.
- Determining the frequency of doses to maintain an effective medication concentration.
- Preventing overdose when doses are repeated.
Kinetics: The study of the rate (or speed) of chemical reactions.
- Provides insights into the reaction mechanism: A step-by-step description of how reactants transform into products.
Determining Reaction Rates (Graphical Interpretation):
- A graph of concentration versus time shows the progress of a reaction.
- The rate at any instant is equal to the opposite of the slope of a line tangential to this curve at that time (for reactant concentration).
- Initial rate: Slope of the tangent at $t = 0$ hours.
- Instantaneous rate: Slope of the tangent at any specific time t > 0 hours.
- Example: For the decomposition of $H2O2$ , 2H2O2(aq)
 ightarrow 2H2O(l) + O2(g), the rate can be determined from the slope of the concentration versus time curve.
Relative Rates of Reaction:
- Reaction rate can be expressed in terms of the change in concentration of any reactant or product.
- Stoichiometric factors from a balanced chemical equation are used to relate the rates of different species.

17.2 Factors Affecting Reaction Rates

Chemical Nature of the Reactants:
- Different substances react at different speeds due to their inherent chemical properties.
- Example: Alkali metals react at a faster rate with water as you move down the group (e.g., Cs reacts faster than Li).
Particle Size of the Reactants (Surface Area):
- The rate of most reactions increases with increasing surface area contact between reactants.
- Smaller particle size means larger surface area, leading to more frequent collisions.
Temperature of the Reactants:
- Reaction rates ordinarily increase with temperature.
- Higher temperature means molecules have more kinetic energy, leading to more frequent and energetic collisions.
Concentration of the Reactants:
- Reaction rates ordinarily increase with increasing concentration of reactants.
- Higher concentration means more reactant molecules per unit volume, increasing collision frequency.
Presence of a Catalyst:
- Catalysts increase reaction rates without being consumed in the reaction (discussed in more detail later).

17.3 Rate Laws

Definition: A mathematical expression that relates the rate of a reaction to the concentrations of reactants.
- For a generic reaction A + B
  ightarrow products, the rate law is typically expressed as: $ext{rate} = k[A]^m[B]^n$ .
Components of a Rate Law:
- Reactants Only: Only reactants appear in a rate law.
- Rate Constant (k):
  - Specific for a particular reaction at a particular temperature.
  - Independent of reactant concentration.
  - Must be determined experimentally.
- Reaction Orders (m, n):
  - $m$ is the order with respect to reactant A.
  - $n$ is the order with respect to reactant B.
  - Must be determined experimentally; they are NOT the stoichiometric coefficients from the balanced equation.
  - Usually positive integers ( $0$ , $1$ , $2$ ), but can also be fractions or negative numbers.
- Overall Order of the Reaction: The sum of the individual reaction orders ( $m + n$ ).
  - Provides an understanding of how all reactants contribute to the rate.
  - Dictates the units of the rate constant ( $k$ ) for that reaction.
Experimental Determination of Rate Laws:
- Cannot be predicted from the balanced chemical equation alone.
- Experiments must be performed to determine the rate law, often by measuring the initial rate at different initial reactant concentrations.
**Example 1: N2O5(g) ightarrow 2NO2(g) + rac{1}{2}O2(g)
- Experimental rate law: $ext{rate} = k[N2O5]$
 - This reaction is first order with respect to $N2O5$ and overall first order.
**Example 2: NO2(g) + CO(g) ightarrow NO(g) + CO2(g) (at $100^ ext{o}C$ )
- Experimental findings: second order in $NO_2$ and zero order in $CO$ .
- Rate law: $ext{rate} = k[NO2]^2[CO]^0 = k[NO2]^2$
 - If $[NO_2]$ doubles, the rate increases by a factor of $2^2 = 4$ .
 - If $[NO_2]$ triples, the rate increases by a factor of $3^2 = 9$ .
Example 3: 2NO + 2H2 ightarrow N2 + 2H_2O
- Using initial rates from multiple experiments, the rate law was determined to be: $ext{Rate} = k[NO]^2[H_2]$
  - This means the reaction is second order with respect to $NO$ , first order with respect to $H_2$ , and overall third order.
Calculating the Rate Constant (k):
- Once the rate law is determined, use one set of experimental data (concentrations and initial rate) to solve for $k$ .
- For the $NO/H_2$ example, $k = 6.32 ext{ M}^{-2} ext{s}^{-1}$ .
Units of the Rate Constant (k):
- The units of $k$ depend on the overall order of the reaction.
- Zero order: $ext{M s}^{-1}$
- First order: $ext{s}^{-1}$
- Second order: $ext{M}^{-1} ext{s}^{-1}$
- Third order: $ext{M}^{-2} ext{s}^{-1}$

17.4 Integrated Rate Laws

Purpose: Integrated rate laws relate the concentration of a reactant to time.
General Notes for Integrated Rate Laws:
- The