Chapter 15 lecture 1

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates at which chemical reactions occur and the factors that influence these rates. Understanding kinetics is essential for elucidating reaction mechanisms, optimizing industrial processes, and assessing environmental impacts.

• Reaction Mechanism: The step-by-step molecular pathway from reactants to products.

• Applications: Drug design (pharmacokinetics), industrial synthesis, and environmental chemistry (e.g., CFC removal from the atmosphere).

• Elimination Half-life: The time required for the concentration of a substance (e.g., drug) to decrease by half.

Example: The slow removal of chlorofluorocarbons (CFCs) from the atmosphere impacts ozone depletion.

Factors Affecting Reaction Rates

The rate of a chemical reaction depends on several key factors:

• Concentration of Reactants: Higher concentrations generally increase reaction rates.

• Temperature: Raising temperature typically increases the rate by providing more kinetic energy to molecules.

• Physical State: Reactions proceed faster when reactants are in the same phase or finely divided.

• Catalysts: Catalysts speed up reactions without being consumed.

Example: Comparing fast and slow reactions visually demonstrates how the fraction of molecules reacting changes over time.

Defining Reaction Rates

Average and Instantaneous Reaction Rates

The reaction rate is the change in concentration of a reactant or product per unit time. It can be expressed as either the appearance of products or the disappearance of reactants.

• Units: $\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1}$ or $\text{M} \cdot \text{s}^{-1}$

• Average Rate: Calculated over a time interval.

• Instantaneous Rate: Determined at a specific moment, often from the slope of a concentration vs. time graph.

Example: For the reaction $A \rightarrow B$:

• Average rate of product formation: $R = \frac{\Delta [B]}{\Delta t}$

• Average rate of reactant disappearance: $R = -\frac{\Delta [A]}{\Delta t}$

Instantaneous Rate: The slope of the tangent to the concentration-time curve at a given point.

Reaction Rates and Stoichiometry

Unique Average Reaction Rate

For reactions with non-1:1 stoichiometry, the rate of disappearance of reactants and appearance of products must be adjusted by their stoichiometric coefficients to ensure consistency.

• General Rate Expression: For $aA + bB \rightarrow cC + dD$:

$\text{Rate} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{c} \frac{\Delta [C]}{\Delta t} = \frac{1}{d} \frac{\Delta [D]}{\Delta t}$

• Application: Knowing the rate for one species allows calculation for others using stoichiometry.

Example: For $2A \rightarrow B$, the rate of formation of B is half the rate of disappearance of A.

The Rate Law, Rate Constant, and Reaction Order

Differential Rate Law

The rate law relates the reaction rate to the concentrations of reactants, each raised to a power (the reaction order), and multiplied by a rate constant.

$\text{Rate} = k [A]^m [B]^n [C]^p$

• k: Rate constant (temperature dependent)

• m, n, p: Reaction orders (experimentally determined, not necessarily equal to stoichiometric coefficients)

• Overall Order: $m + n + p$

Experimental Determination of the Rate Law

Determining Reaction Orders

Reaction orders are determined by varying the concentration of one reactant at a time and measuring the effect on the reaction rate. The exponents in the rate law are found by comparing rates from different experiments.

• Steps:

  1. Vary initial concentration of one reactant, keep others constant.

  2. Measure average rates.

  3. Compare rates to calculate reaction orders.

  4. Establish the rate law and calculate the rate constant.

Example: For the reaction $A + 3B + 2C \rightarrow D + 3E$, a series of experiments yields:

Exp.	[A], M	[B], M	[C], M	Rate, M/s
1	0.010	0.010	0.00050	1.40×10-6
2	0.020	0.010	0.00050	2.88×10-6
3	0.010	0.020	0.00050	2.95×10-6
4	0.010	0.010	0.00100	1.45×10-6

By comparing experiments, the reaction is found to be first order in A, first order in B, and zeroth order in C:

$\text{Rate} = k [A]^1 [B]^1 [C]^0 = k [A][B]$

Calculation of Rate Constant:

$\text{k} = \frac{\text{Rate}}{[A][B]} = \frac{1.40 \times 10^{-6} \text{ M/s}}{0.010 \text{ M} \times 0.010 \text{ M}} = 0.0140 \text{ M}^{-1}\text{s}^{-1}$

Overall Order: 2 (since 1 + 1 + 0 = 2)

Summary Table: Atmospheric Lifetimes of CFCs

The following table summarizes the atmospheric lifetimes of several chlorofluorocarbons (CFCs), illustrating the environmental impact of slow reaction rates in atmospheric chemistry.

CFC Name	Structure	Atmospheric Lifetime
CFC-11 (CCl3F) Trichlorofluoromethane	See molecular model	45 years
CFC-12 (CCl2F2) Dichlorodifluoromethane	See molecular model	100 years
CFC-113 (C2F3Cl3) 1,1,2-Trichloro-1,2,2-trifluoroethane	See molecular model	85 years
CFC-114 (C2F4Cl2) 1,2-Dichlorotetrafluoroethane	See molecular model	300 years
CFC-115 (C2F5Cl) Monochloropentafluoroethane	See molecular model	1700 years

Additional info: The long atmospheric lifetimes of CFCs highlight the importance of chemical kinetics in environmental chemistry, as slow reaction rates lead to prolonged environmental persistence and impact.