Unit 5: Kinetics

Rate Definition: Measure of how a property changes over time.
- Analogous to speed measuring distance traveled per unit time.
- Rate of reaction measures change in concentration per unit time (usually seconds).
- Measurement Methods:
- Measuring gas pressure if a product is a gas in liquid solution.
- Measuring light absorption to observe color changes in solution.
Rate Expression: Change in concentration over change in time.
- Formula: $Rate = \frac{\Delta [R]}{\Delta t} = \frac{[C]<em>f - [C]</em>i}{t<em>2 - t</em>1}$
- Where ( \Delta ) signifies change and brackets denote concentration.
- Reactant concentrations decrease (negative) while product concentrations increase (positive).

Rates must obey stoichiometric coefficients.
Example: Combustion of ammonia with a ratio 4:5:4:6.
- Assign coefficients to rate expressions:
- Ammonia: -1/4
- Oxygen: -1/5
- Nitrogen monoxide: +1/4
- Water: +1/6
Instantaneous Rate: Rate at a specific moment.
Initial Rate: Rate at the beginning of the reaction.
Instantaneous rates can be determined from average rates or slope of tangent lines.
Factors Influencing Rate of Reaction:
- Reactant concentration
- Temperature
- Surface area
- Catalysts

Rate Law General Form: $Rate = k imes [A]^m imes [B]^n$
- ( k ) = rate constant
- Molar concentrations of reactants raised to exponents (reaction orders).
- Exponents are determined experimentally and not directly from stoichiometry.
Reaction Order:
- First Order: If ( m = 1 ) → first order with respect to A.
- Zero Order: If ( n = 0 ) → zero order in B.
- Overall Reaction Order: Sum of individual orders.

Example Reaction:
- Reaction of nitrogen dioxide (NO2) and carbon monoxide (CO) to produce nitrogen monoxide (NO) and carbon dioxide (CO2).
- Observed rate data indicate second order in NO2 and zero order in CO, leading to rate law:
  $Rate = k[NO2]^2$
Determination of Reaction Orders:
- Compare trials with varying initial concentrations (initial rates data).
Example Data Analysis:
- Double an initial concentration leads to doubled reaction rate, confirming first-order dependence on that reactant.

Integrated rate laws relate concentration of reactants over time.
Zero Order Reaction:
- Rate law: $Rate = k \implies [A] = -kt + [A]_0$
First Order Reaction:
- Rate law: $Rate = k[A] \implies ln[A] = -kt + ln[A]_0$
Second Order Reaction:
- Rate law: $Rate = k[A]^2 \implies \frac{1}{[A]} = kt + \frac{1}{[A]_0}$
Graphical representation:
- Zero Order: Concentration vs. time yields straight line.
- First Order: Natural log of concentration vs. time yields straight line.
- Second Order: Inverse of concentration vs. time yields straight line.

Units depend on the overall reaction order:
- Zero Order: M/s
- First Order: s⁻¹
- Second Order: M⁻¹·s⁻¹

Describes molecular-level interactions during reactions.
Postulates:
1. Rate proportional to the collision frequency of reactant molecules.
2. Specific orientation necessary for effective collision leading to a reaction.
3. Sufficient energy required to allow for bond formation (overcome activation energy).
Maxwell-Boltzmann Distribution: Shows kinetic energy distribution among molecules, affecting the proportion able to exceed activation energy.

Mechanism Definition: Pathway through which a reaction occurs, often composed of multiple steps (elementary reactions).
Elementary Reactions: Proceed exactly as written, not further divisible.
- Example: Ozone decomposition occurs in two steps, yielding the overall reaction.
Intermediate: A species that appears in the mechanism but not in the overall reaction.
Molecularity:
- Unimolecular Reactions: Involve the decomposition of one molecule.
- Bimolecular Reactions: Involve collisions between two molecules.
- Termolecular Reactions: Uncommon reactions involving three molecules.
Rate-Determining Step: Slowest step that limits overall reaction rate; dictates the rate law.

Assumes the concentration of intermediates remains constant, balancing production and consumption rates.

Energy diagrams depict potential energy changes during reactions.
Horizontal axis: Reaction coordinate (time).
Vertical axis: Potential energy.
Activation Energy: Energy required to reach transition state, represented by the hump in the energy profile.
Enthalpy Change: Difference in potential energy between reactants and products.
- If products > reactants: endothermic reaction.
- If products < reactants: exothermic reaction.

Catalysts lower activation energy, increasing reaction rates without being consumed.
Types of Catalysis:
- Acid-Base Catalysis: Transfers protons to increase reactivity.
- Surface Catalysis: Reaction occurs on the surface of a solid catalyst.
- Biological Catalysis: Enzymes facilitate reactions, forming enzyme-substrate complexes.

Relates activation energy to rate constant: $k = Ae^{-\frac{E_a}{RT}}$
- ( A ): Frequency factor; ( E_a ): Activation energy; ( R ): Ideal gas constant (8.314 J/mol·K); ( T ): Temperature in Kelvin.

Nuclear reactions involve changes within the nucleus, altering atomic identities.
Nuclide Symbols: Represent isotopes with atomic and mass numbers.
Band of Stability: Region indicating stable isotopes based on neutron-proton ratio.
Unstable nuclei undergo radioactive decay.
Types of Particles Emitted:
- Alpha particle (He nucleus), beta particle (high-energy electron), positron (anti-electron), neutrons, and gamma rays (high-energy photons).
Nuclear Reaction Balancing: Requires mass and charge conservation.
Half-Life Definition: Time for half of a radioactive substance to decay.
- For a first-order process, half-life = $\frac{0.693}{k}$ and is independent of concentration.

This review covered key concepts in kinetics, including reaction rates, rate laws, mechanisms, catalysts, and nuclear decay.