How to Remove an Intermediate in a Rate Law
Understanding how to remove an intermediate in a rate law is a fundamental concept in chemical kinetics. Intermediates are species formed during a reaction mechanism but do not appear in the overall balanced equation. Their presence in a rate law can complicate analysis, so chemists use specific methods to eliminate them and express the rate law in terms of reactants or products. This article explains the steps to remove intermediates, provides a detailed example, and explores the scientific principles behind the process.
Steps to Remove an Intermediate in a Rate Law
To eliminate an intermediate from a rate law, follow these steps:
1. Write the Rate Law from the Slow Step
- The rate law is determined by the slowest step (rate-determining step) in a reaction mechanism.
- If the slow step includes an intermediate, its concentration will initially appear in the rate expression.
2. Use the Fast Step(s) to Express the Intermediate’s Concentration
- If the intermediate is part of a fast equilibrium step, use the equilibrium constant ((K)) to relate its concentration to other species in the mechanism.
- For intermediates in fast non-equilibrium steps, the steady-state approximation may be applied.
3. Substitute the Intermediate’s Expression into the Rate Law
- Replace the intermediate’s concentration with the expression derived from step 2.
- Simplify the equation to obtain the rate law in terms of measurable concentrations.
Example: Removing an Intermediate in a Rate Law
Consider the reaction between nitrogen dioxide ((\text{NO}_2)) and fluorine gas ((\text{F}_2)) to form nitrogen tetrafluoride ((\text{NF}_4)) and oxygen ((\text{O}_2)):
[
2 \text{NO}_2 + \text{F}_2 \rightarrow 2 \text{NF}_4 + \text{O}_2
]
Proposed Mechanism:
-
Fast equilibrium step:
[ \text{NO}_2 + \text{F}_2 \rightleftharpoons \text{NF}_4 + \text{O}_2 \quad (\text{fast}) ]
(This step is reversible and rapid.) -
Slow step:
[ \text{NF}_4 \rightarrow \text{NF}_3 + \text{F} \quad (\text{slow}) ]
(This step determines the reaction’s rate.)
Step 1: Rate Law from the Slow Step
The slow step involves (\text{NF}_4), so the initial rate law is:
[
\text{Rate} = k[\text{NF}_4]
]
Step 2: Express ([\text{NF}_4]) Using the Fast Equilibrium
From the equilibrium step:
[
K = \frac{[\text{NF}_4][\text{O}_2]}{[\text{NO}_2][\text{F}_2]}
]
Rearranging for ([\text{NF}_4]):
[
[\text{NF}_4] = K \cdot \frac{[\text{NO}_2][\text{F}_2]}{[\text{O}_2]}
]
Step 3: Substitute into the Rate Law
Substitute ([\text{NF}_4]) into the rate expression:
[
\text{Rate} = k \cdot K \cdot \frac{[\text{NO}_2][\text{F}_2]}{[\text{O}_2]} = k' \cdot \frac{[\text{NO}_2][\text{F}_2]}{[\text{O}_2]}
]
Here, (k' = k \cdot K) becomes the effective rate constant Surprisingly effective..
Final Rate Law:
[
\text{Rate} = k' \cdot \frac{[\text{NO}_2][\text{F}_2]}{[\text{O}_2]}
]
This rate law excludes the intermediate (\text{NF}_4) and is expressed in terms of reactants and products in the overall reaction Small thing, real impact..
Scientific Explanation: Why Intermediates Are Removed
Intermediates are transient species that exist only during the reaction mechanism. Their concentrations are not measurable experimentally because they do not appear in the stoichiometry of the overall reaction. Rate laws must reflect experimentally observable quantities, so
Rate laws must reflect experimentally observable quantities, so their concentrations must be eliminated by expressing them in terms of the concentrations of reactants or products that are present in the overall reaction. Plus, their transient nature means their concentrations fluctuate rapidly during the reaction, making them inaccessible to standard experimental techniques. This substitution is critical because intermediates, by definition, are not part of the stoichiometric equation and cannot be directly measured. By leveraging equilibrium relationships or the steady-state approximation, chemists can mathematically remove intermediates from rate laws, ensuring the final expression depends only on species whose concentrations can be tracked experimentally That's the part that actually makes a difference. Less friction, more output..
Honestly, this part trips people up more than it should.
Key Considerations in the Example
The derived rate law for the NO₂ + F₂ reaction provides several insights:
- This could arise from the equilibrium step, where O₂ is a product. Here's the thing — Inverse Dependence on [O₂]: The presence of oxygen in the denominator suggests that increasing oxygen concentration slows the reaction. Plus, if O₂ accumulates, it shifts the equilibrium backward (via Le Chatelier’s principle), reducing the concentration of NF₄ and thus the overall reaction rate. 2.
Most guides skip this. Don't Worth keeping that in mind..
