Anaya Nolan
When studying chemical kinetics, it is essential to understand the concept of intermediates and their role in the rate law of a reaction. An intermediate is a molecule or ion that is produced during one step of a reaction mechanism and is then consumed in a subsequent step. In other words, it is a transient species that is neither a reactant nor a product. To determine the overall rate law expression, one must identify the intermediates and write the rate law expression for each elementary reaction. This involves considering the sequence of individual steps, known as the reaction mechanism, by which reactants are converted into products. The overall rate of the reaction is dictated by the slowest step, known as the rate-determining step. While intermediates themselves do not appear in the overall rate law, they play a crucial role in understanding the kinetics of a reaction and can be approximated using methods like the steady-state approximation.
| Characteristics | Values |
|---|---|
| Definition of an intermediate | A molecule or ion produced in one step of a reaction mechanism and consumed in another |
| Steady-state approximation | A method used to derive a rate law, assuming the rate of production of an intermediate is equal to the rate of its consumption |
| Expression of rate law | Write out the relationships between the rates of producing and consuming the intermediate, then express the intermediate in terms of the concentration of reactants |
| Elementary reactions | Unimolecular reactions have first-order rate laws, while bimolecular reactions have second-order rate laws |
| Overall reaction | Sum the steps, cancel intermediates, and combine like formulas |
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What You'll Learn
- Intermediates are molecules or ions produced in one step of a reaction mechanism and consumed in another
- The steady-state approximation assumes the rate of production of an intermediate equals the rate of its consumption
- In an elementary reaction, the rate constant is multiplied by the concentration of the reactant
- The overall rate of a reaction is determined by the rate of the slowest step
- Bimolecular elementary reactions have second-order rate laws
Intermediates are molecules or ions produced in one step of a reaction mechanism and consumed in another
The sequence of individual steps, or elementary reactions, by which reactants are converted into products during the course of a reaction is called the reaction mechanism. The overall rate of a reaction is determined by the rate of the slowest step, known as the rate-determining step.
When a reaction involves one or more intermediates, the concentration of one of the intermediates remains constant at some stage of the reaction. This is known as the steady-state approximation, which assumes that the rate of production of an intermediate is equal to the rate of its consumption. This means that the concentration of the intermediate remains the same throughout the duration of the reaction.
To determine the overall rate law expression for a reaction, one must first identify all intermediates and write the rate law for each elementary reaction. For example, consider the reaction between H2 and I2 gases. While this is not a simple question, one can derive the rate law from the proposed mechanism. By expressing the rate of reaction in terms of concentration changes, we can propose a mechanism that takes into account the weak bonding between I-I.
In summary, intermediates are molecules or ions that are produced and consumed during different steps of a reaction mechanism. They play a crucial role in determining the overall rate law expression for a reaction, especially when using the steady-state approximation to assume constant intermediate concentrations.
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The steady-state approximation assumes the rate of production of an intermediate equals the rate of its consumption
The steady-state approximation is a method used to estimate the overall reaction rate of a multi-step reaction. It is based on the assumption that an intermediate in the reaction mechanism is consumed as fast as it is generated, resulting in a constant intermediate concentration throughout the reaction. In other words, the rate of production of an intermediate is equal to the rate of its consumption. This approach is particularly applicable when the first step of the reaction is significantly slower than the subsequent steps, ensuring no accumulation of intermediate products.
To illustrate this concept, consider the following reaction:
\[ \ce{N_2O_5} \underset{\Large{k_{\textrm b}}}{\overset{\Large{k_{\textrm f}}}\rightleftharpoons} \ce{NO_2 + NO_3} \tag{step 1} \]
\[ \ce{NO3 + NO2} \ce{->[\large{k_2}] NO + NO2 + O2} \tag{step 2} \]
\[ \ce{NO3 + NO} \ce{->[\Large{k_3}] 2 NO2} \tag{step 3} \]
In this reaction, \(\ce{NO}\) and \(\ce{NO3}\) are intermediates. By applying the steady-state approximation, we can set the rate of production of these intermediates equal to the rate of their consumption:
\(\textrm{production rate of NO} = k_2 \ce{ [NO3] [NO2]}\)
\(\textrm{consumption rate of NO} = k_3 \ce{ [NO3] [NO]}\)
Similarly, for \(\ce{NO3}\):
\(\textrm{production rate of NO3} = k_{\ce f} \ce{ [N2O5]}\)
\(\textrm{consumption rate of NO3} = k_2\ce{ [NO3] [NO2]} + k_3\ce{ [NO3] [NO]} + k_{\ce b}\ce{ [NO3] [NO2]}\)
By equating these rates of production and consumption, we can derive expressions for the concentration of intermediates in terms of the reactants, simplifying the overall kinetic expression for product concentration.
The steady-state approximation is a valuable tool in chemical kinetics, particularly when dealing with complex multi-step reactions. It allows us to determine the rate law of a reaction, making assumptions about the relative rates of the reaction steps and the concentrations of intermediates. This approximation was first applied by George E. Briggs and John B. S. Haldane in 1925 to determine the rate law of an enzyme-catalyzed reaction.
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In an elementary reaction, the rate constant is multiplied by the concentration of the reactant
The rate of a reaction is the measure of the change in concentration of reactants or products per unit time. The rate law is an expression that relates the rate of a reaction to the rate constant and the concentrations of the reactants. The rate constant, k, is a proportionality constant for a given reaction. The general rate law is usually expressed as:
> Rate = k [A]^m [B]^n
Where [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, and m and n are the partial orders of reaction. The sum of m and n is called the overall order of reaction.
For an elementary step, there is a relationship between stoichiometry and rate law, as determined by the law of mass action. Almost all elementary steps are either unimolecular or bimolecular. There are few examples of elementary steps that are termolecular or of a higher order, due to the low probability of three or more molecules colliding in their reactive conformations and in the correct orientation to react.
The rate constant can be calculated for elementary reactions by molecular dynamics simulations. One approach is to calculate the mean residence time of the molecule in the reactant state, although this is not widely applicable as reactions are often rare events on a molecular scale. Another approach is the Divided Saddle Theory, which introduces a new, highly reactive segment of the reactant, called the saddle domain, and the rate constant is factored.
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The overall rate of a reaction is determined by the rate of the slowest step
The rate of a chemical reaction is influenced by various factors, including the concentration of reactants and the rate constant. Temperature and catalysts are also factors that can influence the rate of a reaction. The rate equation is derived from the slowest step in the reaction. This slowest step is often referred to as the rate-determining step.
The rate-determining step is the slowest step of a chemical reaction that dictates the speed at which the overall reaction occurs. It can be likened to the neck of a funnel; the rate at which water flows through the funnel is dictated by the width of the neck, regardless of how quickly water is poured into the funnel. Similarly, the slow step in a reaction determines the rate of the overall reaction.
Not all reactions have a distinct rate-determining step. For a rate-determining step to exist, one step must be significantly slower than the other steps in the reaction. If the first step is the slowest, the entire reaction must wait for it, making it the rate-determining step.
For example, consider the reaction between carbon monoxide and nitrogen dioxide to form carbon dioxide and nitrogen oxide. The rate equation is typically expressed as r = k[NO2][CO], indicating a one-step reaction. However, if the reaction involves multiple steps, the rate equation may become r = k[NO2]2, suggesting that the reaction rate is determined by the step involving the collision of two nitrogen dioxide molecules. In this case, the first step, being the slowest, becomes the rate-determining step.
In conclusion, the overall rate of a reaction is indeed determined by the rate of its slowest step, known as the rate-determining step. This slowest step influences the speed at which the entire reaction proceeds, and its identification is crucial for understanding the kinetics of chemical reactions.
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Bimolecular elementary reactions have second-order rate laws
For a reaction to be considered a second-order reaction, two reactants (\(\ce{A}\) and \(\ce{B}\)) must combine in a single elementary step. The reaction order with respect to each reactant is 1, meaning that if the concentration of reactant A is doubled, the rate of the reaction will also double. This relationship holds true for any variations in the concentration of A or B.
Bimolecular elementary reactions are a type of second-order reaction. In these reactions, two molecules, or reactants, come together to form a single product. The rate of a bimolecular elementary reaction is directly proportional to the product of the concentrations of the two reactants. This can be expressed using the equation:
\[ \text{Rate} = k[\ce{A}][\ce{B}] \]
Where k is the rate constant, and [\ce{A}] and [\ce{B}] are the concentrations of the reactants A and B, respectively.
To determine if a reaction is a second-order reaction, we can use the differential (derivative) rate equation or the integrated rate equation. The differential rate law shows how the rate of reaction changes over time, while the integrated rate equation illustrates how the concentration of species varies over time. By plotting these equations, we can identify if the reaction exhibits characteristics of a second-order reaction.
For all second-order reactions, a linear plot of \(\dfrac{1}{ [\ce{A}]_t}\) versus time will yield a straight line. This graph is useful because it allows us to determine the reaction constant, k, by finding the slope of the line. Additionally, if we know the concentrations of the reactants at specific times, we can attempt to create a similar graph. If the graph forms a straight line, it confirms that the reaction is indeed second-order.
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Frequently asked questions
An intermediate is a molecule or ion produced in one step of a reaction mechanism and consumed in another. It is neither one of the reactants nor one of the final products.
Intermediates are important in determining the overall rate law expression. While they are included in the rate law expression for each elementary reaction, they are cancelled out when determining the overall rate law expression.
The steady-state approximation is a method used to derive a rate law when a reaction involves one or more intermediates. It assumes that the rate of production of an intermediate is equal to the rate of its consumption, resulting in a constant intermediate concentration during the reaction.
To determine the rate law expression, express the concentration of the intermediate in terms of the concentration of reactants. Use the steady-state approximation to write out the relationships between the production and consumption rates of the intermediate. Then, manipulate these equations to solve for the rate law expression.
