Steady State Approximation- Khan Academy’s Kinetic Modeling Guide
What the Steady State Approximation Actually Is
The steady state approximation is a shortcut for solving reaction mechanisms that have intermediate species — compounds that form during the reaction but don't appear in the overall balanced equation.
Instead of tracking every intermediate's concentration moment by moment, you assume its concentration stays roughly constant after an initial buildup. The intermediate forms at about the same rate it disappears.
This sounds like a hand-wavy assumption. It is. But it works surprisingly well for many real reaction networks.
Why You Need This Approximation
Most interesting reaction mechanisms involve multiple steps. Solving them with differential equations gets messy fast. The steady state approximation cuts through that math without losing too much accuracy.
You encounter this most often with:
- Chain reactions
- Enzyme kinetics (Michaelis-Menten)
- Atmospheric chemistry
- Catalytic mechanisms
If you're working through Khan Academy's kinetics unit, you'll hit this concept around the intermediate steps section. It's tested constantly on exams.
The Core Assumption in Plain Terms
For an intermediate I:
Rate of formation ≈ Rate of consumption
Mathematically:
d[I]/dt ≈ 0
This doesn't mean [I] is literally zero. It means the concentration changes so slowly relative to reactants and products that you can treat it as approximately constant during the measurement window.
When the Approximation Breaks Down
Don't apply this blindly. The steady state assumption fails when:
- The intermediate accumulates faster than it decomposes
- You're looking at the very beginning of the reaction (pre-equilibrium period)
- The intermediate is actually a reactant or product in disguise
- Concentrations are extremely low (noise dominates)
Enzyme-substrate complexes often violate this early in the reaction. That's why Michaelis-Menten derivations specify certain conditions.
Step-by-Step: Applying the Approximation
1. Identify the intermediate
Look for species that appear in elementary steps but not in the overall reaction. Common examples include free radicals (Cl•, Br•), enzyme complexes (ES), and transient species.
2. Write the rate law for the intermediate
Sum up all formation pathways. Sum up all consumption pathways. Set them equal.
3. Solve for the intermediate's concentration
Isolate [I] in terms of reactant concentrations. Plug back into the overall rate law.
4. Check your assumptions
Does the result match experimental data? Does the pre-equilibrium approximation give a similar answer? If yes, you're probably on track.
Comparing Approximation Methods
| Method | Best When | Accuracy | Complexity |
|---|---|---|---|
| Steady State | Intermediate forms and decomposes rapidly | Good for most mechanisms | Medium |
| Pre-Equilibrium | Reverse reaction is fast relative to overall rate | Excellent when valid | Medium |
| Rate-Determining Step | One step is much slower than all others | Depends on mechanism | Low |
| Exact Integration | All concentrations are measurable | Perfect | High |
The steady state and pre-equilibrium approximations often give identical results when both are valid. If they diverge, something's wrong with your mechanism.
Khan Academy's Approach to This Topic
Khan Academy breaks this down into digestible chunks. The videos walk you through:
- Writing rate laws for multi-step mechanisms
- Identifying when intermediates qualify for the approximation
- Deriving rate laws using the d[I]/dt ≈ 0 assumption
- Connecting the math to physical intuition
The practice problems are worth doing twice. The first pass, you learn the method. The second pass, you catch the mistakes you made the first time.
One thing Khan Academy does well: they show the algebra step-by-step without skipping steps. This is where most students get lost in textbooks.
Common Mistakes That Will Cost You Points
Forgetting to express everything in terms of observable species. Your final rate law should only contain reactants and products you can measure. If you still have intermediate concentrations in your final equation, you haven't finished.
Applying steady state to reactants or products. This only works for intermediates. Always.
Rounding too early. Keep symbols in your equations until the final step. Substituting numbers too soon introduces errors that compound through the calculation.
Confusing steady state with equilibrium. They're different assumptions. Steady state says the net change is zero. Equilibrium says forward and reverse rates are equal. Don't mix them up.
A Quick Worked Example
Consider the mechanism:
Step 1: A + B → I
Step 2: I → C
Apply steady state to I:
d[I]/dt = k₁[A][B] - k₂[I] ≈ 0
Solve for [I]:
k₁[A][B] = k₂[I]
[I] = (k₁/k₂)[A][B]
Rate of product formation:
rate = k₂[I] = k₁[A][B]
The overall rate law matches Step 1. This tells you Step 1 is the rate-determining step, which you'd expect since I is in steady state.
What to Do Next
Go to Khan Academy's kinetics section. Find the steady state approximation video. Watch it once at 1.5x speed to see the whole derivation. Then watch it again at normal speed with paper ready.
Work through at least five practice problems before moving on. The pattern clicks after you've made your own mistakes a few times.
If you're preparing for an exam, focus on being able to derive rate laws from mechanisms without looking anything up. That's the skill they're testing.