Kara Sears
In chemistry, a mechanism describes how a chemical reaction proceeds, including the individual reactions that take place. The rate law, on the other hand, describes the mathematical relationship between the reaction rate and the concentrations of the reactants. A mechanism is consistent with a rate law if the rate law can be derived from the mechanism. This involves expressing the rate law in terms of the reactants and ensuring that the stoichiometry of the mechanism matches the observed stoichiometry. For elementary reactions, the order of reaction for a reactant is equal to its stoichiometric coefficient. The slow step in a reaction mechanism is often the rate-limiting step, and the rate law for this step must match the experimental rate law. While a mechanism that explains experimental results can be considered valid, it is not proof that the mechanism is correct.
| Characteristics | Values |
|---|---|
| Rate law | \(rate = k\ce{ [H2][I2]}\) |
| Mechanism | \(\ce{ I2_{(g)} <=> 2I_{(g)} \quad\quad [fast]}\tag {i }\) |
| \(\ce{H2_{(g)} + I_{(g)} <=> H2I_{(g)} [fast]\tag{ii}}\) | |
| \(\ce{ H2I_{(g)} + I_{(g)} -> 2HI_{(g)} [slow]}\tag{iii}\) | |
| Stoichiometry | Must match the observed stoichiometry |
| Reaction order | Same as molecularity for elementary reactions |
| Rate-determining step | Slowest step in the reaction mechanism |
| Rate law expression | Expressed in terms of reactants |
| Rate law consistency | Must match the observed rate law |
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What You'll Learn
- The rate law deduced from the mechanism must match the observed rate law
- The stoichiometry of the mechanism must match the observed stoichiometry
- The slow step is rate-limiting
- The rate law for the slowest overall reaction must give the experimentally determined rate law
- The rate law cannot be determined from the balanced chemical equation for the overall reaction
The rate law deduced from the mechanism must match the observed rate law
The rate law deduced from a mechanism must match the observed rate law. This is because the rate law for the slowest overall reaction is the same as the rate law for the slowest step in the reaction mechanism, which is the rate-determining step. This rate-determining step limits the speed of the reaction, and thus the overall reaction rate.
For example, consider the reaction between hydrogen and iodine, with the rate law:
> $rate = k\ce{[H2][I2]}$
The long-accepted mechanism for this reaction was a single bimolecular step, thought to be elementary. However, in the 1960s, evidence showed the presence of free I atoms during the reaction, leading to a proposed three-step mechanism. The rate law deduced from this new mechanism must still match the observed rate law for the reaction.
To determine if a proposed mechanism is consistent with experimental data, the rate laws for elementary reactions must be used appropriately. The stoichiometry of the mechanism must match the observed stoichiometry, and the rate law cannot be determined from the balanced chemical equation for the overall reaction unless it is a single-step mechanism. For elementary reactions, the order of reaction for a reactant equals its stoichiometric coefficient.
It is important to note that even if a mechanism explains experimental results, it is not proof that the mechanism is correct. Chemists may propose multiple mechanisms that are consistent with available data, but if a proposed mechanism predicts the wrong experimental rate law, it must be incorrect.
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The stoichiometry of the mechanism must match the observed stoichiometry
The stoichiometry of a chemical reaction is the quantitative relationship between the reactants and the products, expressed in terms of the number of atoms, molecules, or formula units. It is essential that the stoichiometry of the mechanism matches the observed stoichiometry to ensure that the reaction is balanced and follows the law of conservation of mass.
In the context of reaction mechanisms and rate laws, stoichiometry plays a crucial role in understanding the kinetics of a reaction. When proposing a reaction mechanism, it is essential to ensure that the stoichiometry of the mechanism aligns with the observed stoichiometry of the overall reaction. This means that the coefficients of the reactants and products in the elementary steps of the mechanism must sum up to the coefficients in the overall reaction equation.
For example, consider the reaction between hydrogen and iodine, with the rate law: $rate = k\ce{[H2][I2]}$. The long-accepted mechanism for this reaction involved a single bimolecular step. However, in the 1960s, spectroscopic evidence revealed the presence of free I atoms during the reaction. As a result, kineticists proposed a three-step mechanism that accounted for these observations:
$$\co: 2>\ce{ I2_{(g)} <=> 2I_{(g)} \quad\quad [fast]}\tag {i }$$
$$\co: 2>\ce{H2_{(g)} + I_{(g)} <=> H2I_{(g)} [fast]\tag{ii}}$$
$$\co: 2>\ce{ H2I_{(g)} + I_{(g)} -> 2HI_{(g)} [slow]}\tag{iii}$$
In this example, the proposed mechanism satisfies the criterion of matching the observed stoichiometry. The overall reaction is: $\ce{H2 + I2 -> 2 HI}$, and the sum of the elementary steps in the mechanism also yields this equation, with the correct stoichiometric coefficients.
It is important to note that while matching the observed stoichiometry is a necessary criterion for a valid reaction mechanism, it is not sufficient on its own. The mechanism must also meet other criteria, such as having physically reasonable elementary steps and correlating with the experimentally determined rate law.
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The slow step is rate-limiting
In chemical kinetics, the rate-determining step is the slowest step of a chemical reaction, determining the speed at which the overall reaction proceeds. It can be compared to the neck of a funnel, where the rate at which water flows is determined by the width of the neck and not the rate at which water is poured. Similarly, the slow step of a reaction dictates its rate.
The rate equation is derived from the slowest step in the reaction. For instance, in the reaction between hydrogen and iodine, the long-accepted mechanism was a single bimolecular step, but in the 1960s, spectroscopic evidence revealed the presence of free iodine atoms during the reaction. Kineticists then proposed a three-step mechanism, with the third step being the rate-determining step:
$$\co: 13>\ce{H2_{(g)} + I_{(g)} → H2I_{(g)} [fast]}$$
$$\co: 13>\ce{H2I_{(g)} + I_{(g)} -> 2HI_{(g)} [slow]}$$
In another example, the reaction between oxalic acid and chlorine in aqueous solution has multiple steps, with the rate-determining step being the one that precedes the transition state:
$$\co: 10>\ce{Cl2 + H2C2O4 -> Cl2 + H2C2O4 - 2H+ - Cl- + x·H2O}$$
The rate-determining step is not always the first step of a reaction. In the reaction:
$$\co: 9>\ce{NO2 + CO → NO + CO2}$$
The rate equation suggests that the rate is determined by a step in which two NO2 molecules react, with the CO molecule entering in another, faster step. The rate-determining step is the second elementary step:
$$\co: 9>\ce{NO3 + CO → NO + CO2 [slow]}$$
In some cases, the second step of a reaction is the rate-limiting step, meaning it is slower than the first step in the reverse direction.
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The rate law for the slowest overall reaction must give the experimentally determined rate law
Rate laws are determined experimentally and cannot be predicted by reaction stoichiometry. They provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. The rate law for the slowest overall reaction must give the experimentally determined rate law.
Consider the reaction between hydrogen and iodine, with the rate law: $rate = k\ce{[H2][I2]}$. The long-accepted mechanism had a single bimolecular step, meaning the overall reaction was thought to be elementary. However, in the 1960s, spectroscopic evidence revealed the presence of free I atoms during the reaction, leading kineticists to propose a three-step mechanism. The third reaction, $\ce{H2I + I->2HI}$, is the rate-determining step, and the mechanism must be consistent with the rate law.
The rate constant k and the exponents m, n, and p are determined experimentally by observing how the reaction rate changes as reactant concentrations vary. The reaction orders m and n describe the mathematical dependence of the rate on reactant concentrations. For instance, if m = 1 and n = 2, the reaction is first order in A and second order in B. The overall reaction order is the sum of the orders for each reactant.
To experimentally determine the rate law, the method of initial rates is often employed. This involves measuring reaction rates for multiple trials with different initial reactant concentrations. By comparing the measured rates, the reaction orders and rate constant can be determined, which together formulate the rate law.
In some cases, a mechanism may be consistent with the rate law, but later work may show it to be incorrect. This highlights the importance of experimental validation in determining the validity of a proposed mechanism and its consistency with the experimentally determined rate law.
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The rate law cannot be determined from the balanced chemical equation for the overall reaction
The rate law for a reaction cannot be determined from the balanced chemical equation for the overall reaction. This is because the rate law is dependent on the reaction mechanism, which is not always apparent from the balanced equation. The rate law describes the mathematical relationship between the rate of a chemical reaction and the concentrations of the reactants. It is determined experimentally and can be expressed as:
$$\text Rate = k [A]^m [B]^n$$
Where:
- Rate is the rate of the reaction
- K is the rate constant
- [A] and [B] are the concentrations of the reactants A and B
- M and n are the reaction orders with respect to A and B, respectively
The reaction orders, m and n, cannot be determined from the balanced chemical equation alone. They depend on the reaction mechanism, which may involve multiple steps and intermediates that are not apparent from the overall reaction equation.
For example, consider the reaction between hydrogen and iodine:
$$\ce H2 + I2 -> 2HI$$
The rate law for this reaction is:
$$\text Rate = k [H2] [I2]$$
However, the reaction mechanism may involve multiple steps, such as the following three-step mechanism:
$$\ce I2 <=> 2I \quad[fast]$$
$$\ce H2 + I -> HI \quad[fast]$$
$$\ce HI + I -> 2HI \quad[slow]$$
In this mechanism, the overall reaction is the sum of the three individual steps, but the rate-determining step is the slow final step. The reaction orders, m and n, in the rate law are determined by the concentrations of the reactants in the rate-determining step, which may not be the same as the concentrations in the overall reaction.
Even when a mechanism appears to be consistent with the rate law, further experimental evidence may show it to be incorrect. It is important to validate proposed mechanisms through multiple lines of experimental evidence.
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Frequently asked questions
The rate law deduced from the mechanism must match the observed rate law. The stoichiometry of the mechanism must also match the observed stoichiometry.
An example of a rate law is the reaction between hydrogen and iodine: $rate = k\ce{ [H2][I2]}$.
A rate-determining step is the slowest step in a reaction mechanism, which limits the speed of the reaction.
To derive a rate law from a mechanism, you must use the rate laws for the elementary reactions appropriately.
A mechanism is a proposal from which a rate law can be deduced. The fact that a mechanism explains experimental results does not prove that the mechanism is correct.
