Keith Mack
The rate law, also known as the rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of reactants. The rate law can be determined by finding the values of the exponents and the rate constant. While stoichiometric coefficients do not affect how the rate law is written, they do influence the value of the rate constant, which changes based on conditions affecting reaction rates such as temperature, pressure, and surface area. The rate of a reaction is directly proportional to the concentration of the reactants in elementary reactions, which describe what is happening at the molecular level. However, in overall reactions, the rate law cannot be determined from coefficients alone as these reactions may consist of multiple steps involving different molecules.
| Characteristics | Values |
|---|---|
| Rate law | A mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of the reactants |
| Rate constant | K, the reaction rate constant or the reaction rate coefficient, expresses the rate and direction of the chemical reaction |
| Exponents | Positive integers that determine the rate law along with the rate constant |
| Stoichiometric coefficient | Does not affect how the rate law is written but does affect the value of the rate constant |
| Reaction order | The value of the exponent in the rate law, which may differ from the coefficient in the balanced chemical reaction |
| Elementary reactions | Can be determined from coefficients because they describe what is happening at the molecular level |
| Overall reactions | Cannot be determined from coefficients because they may consist of multiple steps involving different molecules |
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What You'll Learn
- The rate law is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of reactants
- The rate of a reaction is defined by the rate constant multiplied by the concentration of the reactants, raised to their stoichiometric coefficients
- The stoichiometric coefficient does not affect how the rate law is written but does influence the value of the rate constant
- The rate law for elementary reactions can be determined from coefficients, but not for overall reactions
- The rate law can be written with stoichiometry if the reaction occurs in a single elementary step
The rate law is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of reactants
The rate law, also known as the rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of reactants. It is denoted by the reaction rate constant or the reaction rate coefficient, often represented as 'k'. The rate law is expressed as:
Rate = k[A]^m[B]^n[C]^p
Where:
- [A], [B], and [C] represent the molar concentration of the reactants
- K is the rate constant
- M, n, and p are exponents and positive integers
The rate law is influenced by the reaction rate constant, which indicates the speed of a chemical reaction. A smaller rate constant value suggests a slower reaction, while a larger rate constant indicates a faster reaction. The rate law can be determined for elementary reactions, which involve a single mechanistic step, as the rate of reaction depends directly on the concentration of the reactants. For instance, in a bimolecular elementary reaction, the rate law is proportional to the concentration of the reactants.
However, determining the rate law for overall reactions is more complex. Overall reactions may consist of multiple steps involving different molecules, making it challenging to establish a direct relationship between the coefficients and the rate law. In such cases, experimental data is required to determine the exponents in the differential rate law. By conducting experiments at the same temperature with varying concentrations of reactants and different rates, the exponents can be calculated.
While the stoichiometric coefficient does not directly influence how the rate law is written, it does impact the value of the rate constant (k). The value of the coefficient k is influenced by factors that affect reaction rate, such as temperature, pressure, and surface area.
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The rate of a reaction is defined by the rate constant multiplied by the concentration of the reactants, raised to their stoichiometric coefficients
The rate of a reaction is a fundamental concept in chemistry, and it can be mathematically expressed using the rate law or rate equation. This equation describes the relationship between the rate of a chemical reaction and the concentrations of the reactants. The general form of the rate law is given as:
> $rate = k[A]^m[B]^n[C]^p$
Here, $ [A], [B],$ and $[C]$ represent the molar concentrations of the reactants, and k is the rate constant. The exponents $m, n,$ and $p$ are positive integers that indicate the reaction orders with respect to each reactant.
Now, let's delve into the role of coefficients in the rate law. In a chemical reaction equation, the coefficients represent the relative numbers of molecules or moles of each substance involved in the reaction. For example, in the reaction:
> ${N_2}{O_4} \rightleftharpoons 2N{O_2}$
The coefficient of $N_2O_4$ is 1, and the coefficient of $NO_2$ is 2.
The coefficients in the balanced chemical equation can influence the rate law, but not directly. The rate law is determined by the reaction orders, which are the exponents ($m, n, p$) in the rate equation. These exponents are not always the same as the coefficients in the balanced equation. However, in certain cases, particularly for elementary reactions (reactions occurring in a single step), the reaction orders may indeed be the same as the stoichiometric coefficients.
To illustrate this, consider the reaction:
> $2A \rightarrow B$
According to the rate law, the rate of this reaction is given as:
> $rate = k[A]^2$
Here, the stoichiometric coefficient of $A$ is 2, and it also indicates a reaction order of 2 in the rate law.
In summary, while the stoichiometric coefficients in a balanced chemical equation do not directly determine the rate law, they can provide insights into the reaction orders, especially in elementary reactions. The rate of a reaction is defined by the rate constant ($k) multiplied by the concentration of the reactants, raised to their respective reaction orders, which may or may not be equal to the stoichiometric coefficients.
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The stoichiometric coefficient does not affect how the rate law is written but does influence the value of the rate constant
The rate law, also known as the rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of the reactants. The general rate law is given as:
> $rate = k{[A]^m}{[B]^n}{[C]^p}$
Where [A], [B], and [C] are the molar concentrations of the reactants, and K is the rate constant. The exponents m, n, and p are positive integers.
Now, to understand how the stoichiometric coefficient affects the rate law, let's consider the following reaction:
> ${N_2}{O_4} \rightleftharpoons 2N{O_2}$
Each coefficient present is worked into the rate of appearance/disappearance:
> $- \dfrac{1}{\upsilon }\dfrac{{d[A]}}{{dt}} = \dfrac{1}{\upsilon }\dfrac{{d[B]}}{{dt}} = r(t) = k{[A]^{order}}$
Where:
- $\upsilon$ is the stoichiometric coefficient
- A is the reactant
- B is the product
In this reaction, ${N_2}{O_4}$ is the decomposing reactant, making it a first-order reaction. So, we get:
> $- \dfrac{{d[{N_2}{O_4}]}}{{dt}} = \dfrac{1}{2}\dfrac{{d[N{O_2}]}}{{dt}} = r(t) = k{[{N_2}{O_4}]^1}$
From the above equation, we can conclude that the stoichiometric coefficient does not influence how the rate law is written. However, it does impact the value of the rate constant K. The value of the coefficient k changes with the conditions that affect reaction rate, such as temperature, pressure, and surface area. A smaller rate constant value indicates a slower reaction, while a larger rate constant suggests a faster reaction.
It is important to note that the reaction order is not related to the stoichiometric coefficients. For instance, in the reaction:
> $\ce{2A + B → C}$
The rate expression is given as:
> $- \dfrac{1}{2} \dfrac{{d[A]}}{{dt}} = - \dfrac{1}{1} \dfrac{{d[B]}}{{dt}} = \dfrac{1}{1} \dfrac{{d[C]}}{{dt}}$
Here, the stoichiometric coefficients are in the denominator of the rate expression. This is because the rate for each substance should be divided by its stoichiometric coefficient to represent a standard rate of reaction where the rates concerning all substances are equal.
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The rate law for elementary reactions can be determined from coefficients, but not for overall reactions
The rate law, or rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of the reactants. It is expressed as:
> $rate = k{[A]^m}{[B]^n}{[C]^p}$
Where $[A]$, $[B]$, and $[C]$ are the molar concentrations of the reactants, k is the rate constant, and m, n, and p are positive integer exponents. The rate constant, k, represents the rate and direction of the chemical reaction.
Now, for elementary reactions, the rate law can be determined directly from its molecularity. This is because elementary reactions describe exactly what is happening at the molecular level. For example, in a bimolecular elementary reaction, two molecules come together and react. The rate of this reaction depends directly on the concentration of these two molecules, and thus, the rate law is proportional to the concentration of the reactants.
On the other hand, overall reactions are not a direct representation of what is happening at the molecular level. They could consist of several steps involving different molecules that are not apparent just by looking at the overall reaction. Therefore, the rate law for overall reactions cannot be determined from the coefficients alone. Instead, it is necessary to experimentally determine the values of the exponents (m, n, and p) and the rate constant (k) to establish the rate law for such reactions.
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The rate law can be written with stoichiometry if the reaction occurs in a single elementary step
The rate law, or rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of the reactants. It can be written as:
$$rate = k{[A]^m}{[B]^n}{[C]^p}$$
Where [A], [B], and [C] are the molar concentrations of the reactants, and k is the rate constant. The exponents m, n, and p are positive integers.
In certain cases, the rate law can be determined directly from the stoichiometry of the reaction equation. This is true if the overall reaction occurs in a single elementary step, meaning it consists of only one reaction with no intermediate steps or products. In such cases, the rate of the reaction depends directly on the concentration of the reactants. For example, in a bimolecular elementary reaction, two molecules come together and react, so the rate of reaction is directly proportional to the concentration of these two molecules.
However, it's important to note that the stoichiometric coefficient does not affect how the rate law should be written. Instead, it influences the value of the rate constant, k. The value of k changes with conditions that affect the reaction rate, such as temperature, pressure, and surface area. A smaller rate constant indicates a slower reaction, while a larger rate constant suggests a faster reaction.
Additionally, while the rate law for elementary reactions can be determined from the coefficients of the elementary step reaction equation, the same is not true for overall reactions. Overall reactions may consist of multiple steps involving different molecules, so the rate law cannot be determined from stoichiometry alone. Instead, the rate law for each elementary reaction in a mechanism can be written by inspection, and the rate law for the overall reaction can then be determined.
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Frequently asked questions
Yes and no. The rate law can be predicted using coefficients in some cases, such as when the reaction occurs in a single elementary step. In this case, the rate law can be written with the stoichiometry of the balanced chemical equation. However, when the reaction occurs in multiple steps, the exponents of the rate law can only be determined through experimental data.
The rate law, also known as the rate equation, is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of the reactants.
The stoichiometric coefficient does not affect how the rate law should be written. However, the coefficient does affect the value of the rate constant, K. A smaller rate constant value indicates a slower reaction, while a larger rate constant indicates a faster reaction.
To determine a rate law, you need to find the values of the exponents and the value of the rate constant, K. If the reaction orders are known, the values of the coefficients can be used to write the rate law.
