Explanations 
Flashcards 
StudySmarter AI 
Notes 
Study Plans 
Study Sets 
Exams 
Magazine 
Find a job 
Mobile App 
Jump to a key chapter
Rate Determining Steps - Definition
The concept of the rate determining step is fundamental in the study of chemical reactions. When you analyze complex reactions, you'll find that they consist of multiple steps that occur in sequence. Among these steps, there often exists one particular step that has a significant impact on the overall rate of the reaction.
Understanding the Role of the Rate Determining Step
The rate determining step is the slowest step in a reaction mechanism, essentially acting as a bottleneck. It controls the speed at which the entire reaction progresses. You can compare it to a sequence of players passing a basketball down the court; the slowest player determines the pace at which the team's play advances.
In chemical terms, the rate of a complex reaction is primarily dependent on this single step. The involved molecules require either the most energy, or participate in the most intricate coordination, which results in the slow progression of that step.
Mathematically, the rate of the entire reaction (\text{Rate}) can often be approximated by just the rate of the rate determining step:
\[ \text{Rate} = k[\text{Reactant}]^n \]
Where:
- k is the rate constant for the rate determining step.
- [\text{Reactant}] represents the concentration of the involved reactants.
- n is the order with respect to that reactant in the rate determining step.
The rate determining step is the slowest step in a reaction mechanism, and it governs the rate of the entire chemical reaction process. Identifying this step is crucial for understanding reaction kinetics.
Consider the decomposition of hydrogen peroxide:
\[ 2H_2O_2 \rightarrow 2H_2O + O_2 \]
This reaction occurs via two steps. Initially, hydrogen peroxide decomposes into water and an oxygen molecule (the slower step), and subsequently, the free oxygen radical reacts to form the stable molecule. The first step is the rate determining step of the reaction.
How to Find Rate Determining Step
Finding the rate determining step in a multi-step reaction is crucial for chemical kinetics analysis. This enables you to predict the rate of the overall reaction and understand the reaction mechanism better.
To identify this step, you generally analyze the reaction mechanism and the energy profile.
Steps to Identify the Rate Determining Step
To determine the rate determining step, follow this systematic approach:
- Analyze the Mechanism: Study the hypothesized sequence of steps in the reaction mechanism.
- Determine Activation Energies: Each step has an associated activation energy; the step with the highest activation energy usually acts as the rate determining step.
- Use Experimental Data: Compare experimental rate data with the steps to identify the slowest one.
- Identify Reaction Intermediates: Focus on steps involving intermediates that require higher energy consumption.
- Consider Rate Laws: Evaluate which step aligns with the overall observed rate law.
Let's consider the hypothetical reaction:
The reaction mechanism is:
- Step 1: \(A + B \rightarrow C \) (slow)
- Step 2: \(C \rightarrow D \) (fast)
In this case, Step 1 is the rate determining step. The rate of the reaction \([R]\) can be expressed based on the rate law:
\[ \text{Rate} = k[A][B] \]
The activation energy of a chemical reaction is the minimum energy barrier that reactants must overcome to convert into products. This concept is intricately tied to the rate determining step. Activation energy can be visualized using energy profile diagrams which plot the potential energy changes as a function of the reaction coordinate.
The step on the energy profile with the highest peak is usually the rate determining step, as it necessitates the most energy investment. This peak corresponds to the transition state of the slowest step.
The relationship between activation energy \( E_a \) and temperature is elucidated by the Arrhenius equation:
\[ k = Ae^{-\frac{E_a}{RT}} \]
Where:
- k is the rate constant.
- A is the pre-exponential factor.
- R is the gas constant.
- T is the temperature in Kelvin.
Techniques to Determine Rate Determining Step
To effectively predict and control chemical reactions, understanding the rate determining step is crucial. This step dictates the kinetics of the entire reaction mechanism.
Here we will explore methods to pinpoint this critical step.
Kinetic Analysis of Multi-Step Reactions
When assessing a complex reaction, you must first identify the individual steps that compose it. Each step has its own specific rate constant and activation energy.
Mathematically, the relation can be given as:
\[ \text{Rate}_{\text{overall}} = k \cdot [\text{Reactants}]^{n} \]
Where \( k \) is predominantly controlled by the rate determining step. By determining which step has the highest \( E_a \) (activation energy), it’s typically feasible to identify the rate controlling stage.
The activation energy \( E_a \) is the minimum energy required to initiate a reaction, influencing the reaction rate significantly, especially for the rate determining step.
Consider the following reaction sequence:
– \( A \rightarrow B \) (slow)
– \( B \rightarrow C \) (fast)
Since the first step is slower, it becomes the rate determining step, thus, establishing the reaction rate.
The rate law observed experimentally would be:
\[ \text{Rate} = k[A] \]
Always compare the predicted rate laws derived from your mechanism with experimental data to confirm the rate determining step.
Energy Profile Diagrams
Energy profile diagrams provide a visual representation of the energy changes during a chemical reaction. These diagrams can highlight which step demands the most energy, thus pointing out the rate determining step.
These diagrams plot the potential energy of the system against the reaction coordinate, with peaks representing energy barriers.
| Transition State | The maximum peak in energy for any given step. |
| Intermediate | Stable species formed between transitions, with energy lower than the peaks. |
To relate the concept of transition state theory, consider a reaction path as resembling a mountain range. The transition state can be compared to the highest mountain peak separating two valleys. It's during this peak where the potential energy of reactants rises before falling into valleys of stable intermediates and products.
The height of this peak (activation energy) directly affects the overall reaction rate, exemplifying the importance of the rate determining step in kinetic studies.
Rate Determining Step Examples
Understanding rate determining steps through examples can significantly enhance your comprehension of complex reaction mechanisms. These examples demonstrate how various factors contribute to the overall reaction rate and how the slowest step dictates the pace.
Example 1: Decomposition of Nitrogen Dioxide
Consider the decomposition of nitrogen dioxide, \( \text{NO}_2 \), a classical example for identifying the rate determining step:
\[ 2\text{NO}_2 \rightarrow 2\text{NO} + \text{O}_2 \]
This reaction proceeds through a two-step mechanism:
- \( \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \) (slow)
- \( \text{NO}_3 \rightarrow \text{NO} + \text{O}_2 \) (fast)
The first step is the rate determining step, as it is the slowest; hence, the overall rate law is:
\[ \text{Rate} = k[\text{NO}_2]^2 \]
In this reaction, since the experimental rate law corresponds to the hypothesis, with the concentration of \( \text{NO}_2 \) squared, the initial collision event is evidently the bottleneck, thus deciding the reaction rate overall.
In terms of molecular dynamics, the slow formation of \( \text{NO}_3 \) involves significant internal rearrangements and energy requirements. This explains why it acts as the governing step in the kinetic sequence, validating both thermodynamic and kinetic control principles.
Example 2: Hydrolysis of Ester
The hydrolysis of esters, such as ethyl acetate, provides another prime example:
The reaction is expressed as:
\[ \text{CH}_3\text{COOC}_2\text{H}_5 + \text{H}_2\text{O} \rightarrow \text{CH}_3\text{COOH} + \text{C}_2\text{H}_5\text{OH} \]
Here is the two-step mechanism:
- Formation of the tetrahedral intermediate (slow).
- Breakdown of the tetrahedral intermediate to the final products (fast).
In this mechanism, the first step holds the biggest energy barrier, becoming the rate determining step. Consequently, the experimental rate law is:
\[ \text{Rate} = k[\text{CH}_3\text{COOC}_2\text{H}_5][\text{H}_2\text{O}] \]
In many organic reactions, the formation of a high-energy intermediate is often the rate determining step, characterized by a relatively high activation energy.
rate determining steps - Key takeaways
- Rate Determining Step Definition: The rate determining step is the slowest step in a reaction mechanism, controlling the overall reaction rate.
- Mathematical Relation: The reaction rate can often be approximated by the rate of the rate determining step: \[ \text{Rate} = k[\text{Reactant}]^n \]
- Techniques to Determine Rate Determining Step: Analyze the mechanism, determine activation energies, use experimental data, identify reaction intermediates, and consider rate laws.
- Energy Profile Diagrams: Illustrate energy changes during reactions; the highest energy peak corresponds to the rate determining step.
- Rate Determining Step Example 1: Decomposition of hydrogen peroxide involves a slow initial step determining the reaction rate.
- Rate Determining Step Example 2: Hydrolysis of an ester involves the slow formation of an intermediate, dictating the reaction rate.
Learn faster with the 12 flashcards about rate determining steps
Sign up for free to gain access to all our flashcards.
Frequently Asked Questions about rate determining steps
About StudySmarter
StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn more