Most reactions happen in a series of steps, and the overall rate can be no faster than the slowest one. The rate equation is a fingerprint of that slow step, so it lets you test whether a proposed mechanism could be right.
The rate-determining step is the slowest step in a mechanism. Only species that take part in the rate-determining step, or in fast steps before it, appear in the rate equation, and the order of each matches the number of its particles involved. A species with zero order joins the reaction after the slow step. An intermediate is made in one step and used up in a later one, so it never appears in the overall equation; a catalyst is used in one step and regenerated later, so it can appear in the rate equation but not in the overall equation. A mechanism is consistent with the data if its steps add up to the overall equation and its slow step matches the rate equation.
Work through each example: write the steps, check they add up to the overall equation, then read the rate equation off the slow step.
| Overall reaction | Experimental rate equation | Mechanism consistent with it |
|---|---|---|
| NO2 + CO → NO + CO2 (below 500 K) | rate = k[NO2]2 | step 1 (slow): 2NO2 → NO3 + NO; step 2 (fast): NO3 + CO → NO2 + CO2 |
| 2NO + 2H2 → N2 + 2H2O | rate = k[NO]2[H2] | step 1 (slow): 2NO + H2 → N2 + H2O2; step 2 (fast): H2O2 + H2 → 2H2O |
| CH3COCH3 + I2 → CH3COCH2I + HI (H+ catalyst) | rate = k[CH3COCH3][H+] | slow step involves propanone and H+; I2 reacts in a later fast step, so it is zero order |
Compare the one-step and two-step hydrolysis mechanisms in the simulator and note which species is present in the slow step.
| Halogenoalkane | Rate equation | Mechanism | Slow step |
|---|---|---|---|
| bromoethane (primary) | rate = k[CH3CH2Br][OH−] | SN2: one step | OH− attacks as Br− leaves, through a single transition state |
| 2-bromo-2-methylpropane (tertiary) | rate = k[(CH3)3CBr] | SN1: two steps | (CH3)3CBr → (CH3)3C+ + Br−; then fast (CH3)3C+ + OH− → (CH3)3COH |
The rate equation tells you about the slow step, not the overall equation, so do not copy coefficients from the overall equation. A reactant that is zero order is still needed: it reacts in a fast step after the rate-determining step. An intermediate is formed then used up; a catalyst is used then regenerated. Do not call the transition state an intermediate: a transition state is a peak on the energy profile, an intermediate sits in a dip.
Four quick checks. Each correct answer earns XP and records this skill on your profile.
What is the rate-determining step in a mechanism?
2-bromo-2-methylpropane is hydrolysed by OH−. What is the rate equation?
In the mechanism 2NO2 → NO3 + NO, then NO3 + CO → NO2 + CO2, what is NO3?
The iodination of propanone is zero order with respect to iodine. What does this show?
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For 2A + B → C, rate = k[A][B]. Which mechanism is consistent with this?
Overall: H2O2 + 2I− + 2H+ → I2 + 2H2O; rate = k[H2O2][I−]. Which species are NOT in the rate-determining step?
Rate = k[CH3COCH3][H+] for the iodination of propanone. How does H+ act?
Doubling [OH−] has no effect on the rate of hydrolysis of a halogenoalkane. Which halogenoalkane is most likely?
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