Chemical Kinetics

Introduction to Reaction Rates

Chemical kinetics is the study of the speed, or rate, at which chemical reactions occur. The reaction rate measures how quickly reactants are converted into products or how fast products are formed. It is defined as the change in concentration of a reactant or product per unit time.

• Reaction Rate: for a reaction .

• Example: The rate can be expressed in terms of the change in concentration of any component in the reaction.

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Reaction Rate Changes Over Time

The rate of a reaction typically decreases as reactants are consumed. The reaction may stop when reactants are depleted or equilibrium is reached.

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

• Instantaneous Rate: Rate at a particular moment, found by the slope of the tangent to a concentration vs. time curve.

Calculating Reaction Rates: Examples

• Example: For the reaction , if drops from 1.000 M to 0.868 M in 10.0 s, the average rate is calculated as .

Graphical Determination of Instantaneous Rate

• Instantaneous rate is determined by the slope of the tangent to the concentration vs. time curve at a specific time.

• For , the rate at 50 s is found from the slope of vs. .

Factors Affecting Reaction Rate

• Nature of Reactants: Type, size, reactivity, and phase influence rate.

• Temperature: Higher temperature generally increases rate.

• Catalysts: Substances that increase rate without being consumed.

• Reactant Concentration: Higher concentration (or pressure for gases) increases rate.

Rate Laws and Reaction Order

The Rate Law

The rate law expresses the relationship between the reaction rate and the concentrations of reactants. It must be determined experimentally.

• General form:

• and are the orders with respect to and .

• is the rate constant.

Reaction Order

• The order with respect to a reactant is the exponent of its concentration in the rate law.

• The overall order is the sum of the exponents.

• Example: For , (second order in NO, first order in H2, third order overall).

Example: Determining Rate Law and Effect of Concentration

• Given: Reaction is second order in NO2, zero order in CO at 100°C.

• Rate law:

• Doubling [NO2] quadruples the rate; doubling [CO] has no effect.

Determining the Rate Law: Initial Rate Method

• Run experiments varying one reactant at a time, measure initial rates, and deduce exponents in the rate law.

• Order cannot be deduced from stoichiometry; must be found experimentally.

Example: Using Experimental Data to Find Rate Law

• Given data for , deduce the order and rate constant .

The Rate Constant (k)

• k is determined experimentally and its units depend on the reaction order.

• For a zero-order reaction: (units: mol/L·s)

• For a first-order reaction: (units: s-1)

• For a second-order reaction: (units: L/mol·s)

Integrated Rate Laws

General Integrated Rate Laws

Integrated rate laws relate concentration to time and are used to determine reaction order from experimental data.

• Zero-order:

• First-order:

• Second-order:

Zero Order Reactions

• Rate law:

• Integrated:

• Plot of vs. is linear with slope .

First Order Reactions

• Rate law:

• Integrated:

• Plot of vs. is linear with slope .

Second Order Reactions

• Rate law:

• Integrated:

• Plot of vs. is linear with slope .

Graphical Methods for Determining Reaction Order

• Plot vs. : Linear for zero order.

• Plot vs. : Linear for first order.

• Plot vs. : Linear for second order.

Half-Life of a Reaction

The half-life () is the time required for the concentration of a reactant to decrease to half its initial value.

• First-order: (independent of initial concentration)

• Second-order: (inversely proportional to initial concentration)

• Zero-order: (directly proportional to initial concentration)

Theories of Reaction Rates

Collision Theory

• Reactant particles must collide to react.

• Increasing concentration increases collision frequency and reaction rate.

• Number of collisions depends on the product of reactant concentrations.

Activation Energy

• Collisions must have sufficient energy (activation energy, ) to be effective.

• Particles form an activated complex or transition state at the energy barrier.

• Lower means a faster reaction.

Temperature and the Rate Constant: Arrhenius Equation

• Rate constant increases exponentially with temperature.

• Arrhenius equation:

• Linear form:

Effect of Temperature on Collision

• Higher temperature increases the fraction of collisions with energy greater than .

Catalysts

Role and Effect of Catalysts

• A catalyst increases reaction rate by providing an alternative pathway with lower activation energy.

• Catalysts are not consumed in the reaction and do not affect the overall energy change ().

Reaction Mechanisms

Elementary Steps and Molecularity

• The mechanism is the sequence of elementary steps making up the overall reaction.

• Molecularity is the number of particles involved in an elementary step.

• The slowest step is the rate-determining step and controls the overall rate law.

Validating Mechanisms

• Elementary steps must sum to the overall reaction.

• Predicted rate law must match experimental rate law.

Energy Diagrams for Multistep Mechanisms

• Each step has its own activation energy and transition state.

• The step with the highest activation energy is rate-limiting.

Mixed Mechanisms (with Equilibrium Steps)

• Some mechanisms involve fast equilibrium steps followed by a slow step.

• Intermediates do not appear in the overall rate law.