Rate Law and Reaction Intermediates- Kinetics Explained
What Rate Law Actually Means
Rate law describes how fast a chemical reaction proceeds. It's not a theory or approximation—it's a mathematical relationship between reactant concentrations and reaction speed. You measure it experimentally, not derive it from stoichiometry.
The general form looks like this:
Rate = k[A]m[B]n
Where k is the rate constant, and m and n are the reaction orders with respect to each reactant. These exponents are not necessarily the stoichiometric coefficients. That's the first thing students get wrong.
Reaction Order: What It Actually Tells You
Reaction order is the exponent in the rate law. It tells you how sensitive the reaction rate is to changes in concentration.
Zero Order
Rate doesn't change when you increase concentration. The reaction runs at constant speed until reactants are exhausted.
Rate = k (concentration terms disappear)
First Order
Rate doubles when concentration doubles. Linear decay over time.
Rate = k[A]
Second Order
Rate quadruples when concentration doubles. Concentration dependence is stronger.
Rate = k[A]2 or Rate = k[A][B]
Fractional and Negative Orders
Reactions can have orders like 0.5, -1, or 3/2. These aren't weird—they just reflect the actual mechanism. Negative orders mean increasing that reactant's concentration slows the reaction down (common with inhibitors).
Rate Constant k: The Numbers Matter
The rate constant k isn't a fixed number. It depends on temperature, and that's why temperature control matters in kinetics.
The Arrhenius equation connects them:
k = A·e(-Ea/RT)
A is the pre-exponential factor. Ea is activation energy. R is the gas constant. T is absolute temperature.
Higher temperature = larger k = faster reaction. This isn't suggestions—it's physics.
Reaction Intermediates: The Hidden Players
Most reactions don't happen in a single step. They go through intermediates—unstable species that form and then disappear during the reaction pathway.
You won't find intermediates in the overall balanced equation. They're invisible to stoichiometry but crucial to mechanism.
Why Intermediates Matter
- They explain why rate laws don't match stoichiometry
- They reveal the actual reaction pathway
- They help predict how reaction conditions affect outcomes
Common Examples
Enzyme-substrate complexes in biochemistry. Free radicals in combustion. Carbocations in organic reactions. Each forms temporarily, then reacts further.
How Rate Laws Reveal Intermediates
Here's the connection most textbooks gloss over: the rate law's form tells you about the mechanism and any intermediates involved.
If a reaction is elementary (single step), the rate law matches the molecularity:
- Unimolecular collision: Rate = k[A]
- Bimolecular collision: Rate = k[A][B]
If the rate law doesn't match the stoichiometry, intermediates are hiding somewhere. You need to propose a mechanism that explains what you measured.
Steady-State Approximation: Your Practical Tool
When intermediates form and consume rapidly, their concentration stays roughly constant during most of the reaction. That's the steady-state assumption.
d[Intermediate]/dt ≈ 0
This lets you eliminate intermediate concentrations from your rate equations and solve for the overall rate law.
Comparing Rate Law Forms
| Order | Rate Law | Integrated Form | Half-Life Dependency |
|---|---|---|---|
| Zero | Rate = k | [A] = [A]â‚€ - kt | Proportional to [A]â‚€ |
| First | Rate = k[A] | ln[A] = ln[A]â‚€ - kt | Independent of [A]â‚€ |
| Second | Rate = k[A]² | 1/[A] = 1/[A]₀ + kt | Proportional to 1/[A]₀ |
Getting Started: Determining a Rate Law Experimentally
You can't write a rate law from the balanced equation. You have to measure it.
Method of Initial Rates
Run the reaction multiple times with different initial concentrations. Measure the initial rate for each run. Compare.
Step 1: Run with [A] doubled, [B] constant. See how rate changes. That's the order in A.
Step 2: Run with [B] doubled, [A] constant. See how rate changes. That's the order in B.
Step 3: Combine. Rate = k[A]m[B]n
Step 4: Use any single run to solve for k.
Isolation Method
Use excess of all reactants except one. The reaction order in the isolated reactant becomes obvious because others don't change significantly.
Common Mistakes That Cost You Points
- Assuming rate law matches stoichiometry—it usually doesn't
- Forgetting that rate constant k depends on temperature
- Confusing molecularity with reaction order
- Trying to derive the mechanism instead of proposing one that fits the data
- Ignoring units when checking your rate law
Quick Reference: Rate Law to Mechanism
If your measured rate law is Rate = k[A][B] and the overall reaction is A + B → products, you can propose:
- An elementary bimolecular step
- Or a multi-step mechanism with a fast equilibrium followed by a rate-determining step
If the slow step involves both A and B, the rate law matches. If it doesn't, you need to dig deeper into the mechanism.
The rate-determining step controls the overall rate. Everything before it reaches equilibrium. Everything after it happens fast.