CHEM 1036: Chapter 16

Chapter 16: Kinetics - Rates and Mechanisms of Chemical Reactions

Dr. Shamindri M. Arachchige Email: arachsm@vt.edu

Key Concepts of Kinetics

To understand chemical reactions, it's essential to analyze reaction rates from three fundamental perspectives:

• Rate Laws: Mathematical expressions defining the relationship between reaction rates and reactant concentrations. They provide insight into how changes in concentration affect the rate of a reaction.

• The Arrhenius Equation: Describes how temperature and activation energy influence reaction rates, illustrating the temperature dependence of reaction kinetics.

• Collision Theory: A theory that explains how molecules must collide with enough energy and proper orientation to result in chemical reactions, which helps in understanding factors that affect reaction rates.

Expressing Reaction Rates

• Rate of Reaction: Defined as the change in concentration of reactants or products over time, expressed in molarity per second (M/s). Reactants decrease in concentration while products increase, indicating the progress of the reaction.

• Example formula for rate for a general reaction (A → B):Rate = −( \frac{D[A]}{Dt} ) = ( - \frac{[A_2] - [A_1]}{t_2 - t_1} )This indicates the rate at which reactant A is consumed.

• For product formation, a positive value can be expressed as:( \frac{D[B]}{Dt} = \frac{[B_2] - [B_1]}{t_2 - t_1} )

The Wide Range of Reaction Rates

Chemical reactions can occur at vastly different rates, ranging from extremely slow processes (like the rusting of iron) to very rapid reactions (such as the combustion of fuels). Understanding this variability highlights the importance of kinetics in different chemical contexts.

Example: Reaction Rates with N2O5

Consider the reaction:( \text{N2O5} \leftrightarrow 2 \text{NO2} + \frac{1}{2} \text{O2} )

A concentration versus time graph of this reaction would illustrate the changing concentrations of N2O5, NO2, and O2 over time. Observing the slope of this graph provides valuable information regarding the rates at which reactants are consumed and products are formed.

Rate Relationships

The rate relationship between reactants and products follows stoichiometric ratios:

• Rate(N2O5) = 1 x Rate(NO2) = 0.5 x Rate(O2).This means if the N2O5 is consumed at a certain rate, you can determine the corresponding rates at which NO2 and O2 are produced based on their stoichiometry.

Problem Solving - Expressing Rates

For example, at a consumption rate of (0.68 M/s) for N2O5, you calculate the production rates as follows:

• Rate of NO2: 1.36 M/s (2 times the rate of N2O5)

• Rate of O2: 0.34 M/s (0.5 times the rate of N2O5)

Reaction Order and Rate Laws

• The general form of chemical reactions can be represented as:( aA + bB \rightarrow cC + dD ).

• The Rate Law is expressed as:Rate = k[A]^m[B]^nwhere:

  • k: the rate constant, which varies under different conditions (temperature, presence of catalysts).

  • m, n: orders of reaction, determined experimentally and indicating how the rate is affected by the concentration of each reactant.

Types of Reaction Rates

• Average Rate: This represents the change in concentration over a specified time interval.

• Instantaneous Rate: The rate at a specific moment, typically found using the slope of the tangent line to the curve on a concentration versus time graph.

• Initial Rate: The rate of reaction measured at the very beginning (time = 0) of the reaction.

Integrated Rate Laws

Different reaction types exhibit different integrated rate laws:

• Zero Order: Reaction rate is constant.Integral: [A]t = [A]0 - kt

• First Order: Rate depends linearly on single reactant concentration.Integral: ln[A]t = ln[A]0 - kt

• Second Order: Rate depends on the square of a concentration.Integral: \frac{1}{[A]t} = \frac{1}{[A]0} + kt

• Half-life (t_{1/2}): Time required for the concentration of a reactant to reduce to half of its initial concentration:

  • Zero Order: t_{1/2} = \frac{[A]0}{2k}

  • First Order: independent of concentration, t_{1/2} = \frac{0.693}{k}

  • Second Order: t_{1/2} = \frac{1}{k[A]0}

Collision Theory

For a chemical reaction to occur, reactants must collide with adequate energy and in the correct orientation. Key factors influencing reaction rates include:

• Concentration of Reactants: Higher concentrations lead to more frequent collisions, thus increasing the rate of reaction.

• Activation Energy (Ea): This is the minimum energy threshold that must be exceeded for a reaction to take place.

Temperature Effects on Reaction Rates

Increasing temperature enhances the kinetic energy of molecules, leading to:

• More frequent and forceful collisions.

• Greater probability of successful collisions that surpass the activation energy barrier.The Arrhenius Equation, expressed as:k = A e^(-Ea/RT), illustrates the relationship between the rate constant and temperature, where A is the pre-exponential factor, Ea is activation energy, R is the universal gas constant, and T is the temperature in Kelvin. A plot of ln(k) versus 1/T will yield a straight line, allowing for the determination of Ea from the slope.

Catalysts

Catalysts serve to lower the activation energy of a reaction, consequently increasing its rate without being consumed in the process. There are two main types of catalysts:

• Homogeneous Catalysts: These exist in the same phase as the reactants, typically found in liquid-phase reactions.

• Heterogeneous Catalysts: These are in a different phase than the reactants, such as solid catalysts in gas or liquid reactions.

Example Problems and Applications

Engagement with practice problems can illuminate how factors like activation energy, catalysts, and temperature variations affect reaction kinetics. Additionally, analyzing case studies on catalysts' effects can deepen understanding of reaction speed and direction.