Chemical Kinetics for the DAT
/Learn key DAT concepts about chemical kinetics, plus practice questions and answers
Table of Contents
Part 1: Introduction to chemical kinetics
Part 2: Rate laws
a) Reaction orders
b) Determining rate laws from experimental data
c) Arrhenius equation
Part 3: Activation energy
a) Reaction coordinate diagrams
b) Thermodynamic and kinetic products
Part 4: Half-life
a) Half-life and exponential decay
Part 5: High-yield terms
Part 6: Questions and answers
----
Part 1: Introduction to chemical kinetics
Chemical kinetics, a branch of physical chemistry, explores the rates at which chemical reactions occur and the factors influencing their speed. By investigating the mechanisms and pathways through which reactants transform into products, chemical kinetics unveils the dynamic nature of chemical processes. This guide delves into the details of reaction kinetics, shedding light on the role of various factors such as concentration, temperature, and catalysts in influencing reaction rates. Understanding chemical kinetics not only provides insights into reaction mechanisms but also enables the prediction and control of reaction outcomes. As you study this guide, pay attention to any bolded terms and test your understanding with DAT-like practice questions at the end.
----
Part 2: Rate Laws
a) Reaction orders
Quantifying the speed at which a chemical reaction occurs is a valuable endeavor. This speed, termed the reaction rate, is gauged by monitoring either the rate of product generation or the rate at which reactants are used up. Determining the reaction rate involves measuring the change in concentration of a product within a specified time frame, often in seconds.
Reactions can be represented as aA + bB → cC + dD. In the following reaction, CH4 + 2O2→CO2 + 2H2O, a corresponds to 1, A is CH4, b is 2, B is O2, and so on. [A] would be the concentration of CH4, [B] is the concentration of O2, and so on as well. The rate law for a reaction takes the form k[A]x[B]y and is expressed in molarity per second. In this equation, k signifies a distinct rate constant that is influenced by factors such as temperature and the presence of a catalyst.
The exponents x and y, present in the rate law, can be combined to determine the reaction order. This reaction order elucidates how the rate of product formation correlates with the rate of reactant consumption.
| Reaction Order | Rate Law | Description |
|---|---|---|
| The rate of product formation is equal to the rate constant, k, and is independent of any changes to the concentrations of the reactants. | ||
Rate=k[B]1 |
The rate of product formation is directly proportional to one reactant. | |
Rate=k[B]2 Rate=k[A][B] |
The rate of product formation is proportional to the square of the concentration of one reactant or just the concentration of both reactants. |
b) Determining rate laws from experimental data
The DAT might assess your skill in deducing a rate law and reaction order based on a provided set of experimental data. To illustrate, consider an example involving data derived from the amalgamation of sodium (Na) and chlorine (Cl) to form sodium chloride (NaCl).
| Trial | [Na] | [Cl] | Initial Rate (M/s) |
|---|---|---|---|
Based on this information, how could we find the rate law?
First, look for two trials during which the concentration of only one substance was changed. In trials 1 and 2, [Na] increased by a factor of 2 from 2.00 x 10-2 to 4.00 x 10-2. [Cl] remained unchanged. The rate increased by a factor of 4 from 2.00 x 10-8 to 8.00 x 10-8. With this information, we can set up the following equation to express the relationship between the change in concentration of [Na] and the change in the rate.
Now, find two trials during which [Cl] changed but [Na] did not. During trials 2 and 3, [Cl] increased by a factor of 2 from 2.00 x 10-2 to 4.00 x 10-2. The rate also increased by a factor of 2 from 8.00 x 10-8 to 1.60 x 10-7. Set up an expression similar to the previous one for sodium.
To determine the rate constant (k), substitute values from any of the trials into the derived rate law and use algebra to solve. Let’s use trial 1.
Finally, plug the k value into the rate law formula.
c) Arrhenius equation
It's crucial to recognize that the rate constant (k) is determined through experimentation and is influenced by environmental factors, specifically temperature. In the absence of experimental data specifying the temperature or environmental conditions, the rate constant cannot be accurately determined.
However, if the activation energy of the reaction is known, the Arrhenius equation can be used to calculate the change in the rate constant (k):
----
Part 3: Activation energy
Transition state theory posits that when molecules collide, they give rise to an intermediate complex characterized by higher energy than both the reactants and products. In this framework, molecules and atoms are conceptualized as particles with substantial mass and energy, necessitating specific orientations for contact.
a) Reaction coordinate diagrams
The transition state comprises partially dissociated old bonds and partially formed new bonds. The difference in free energy between the transition state and the reactants is termed activation energy. As the transition state is indispensable for product formation, activation energy represents the minimum energy required for the progression of a reaction—a kind of hurdle the reaction must surmount. The higher the activation energy, the slower the reaction proceeds. Catalysts, such as enzymes, play a role in diminishing the activation energy, thereby accelerating the reaction rate. In a reaction coordinate diagram, the transition state is situated at the summit of the curve.
