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A reaction goes at the speed of its slowest step, the one with the highest transition state; only species in or before it appear in the rate law, so an SN1 rate ignores the nucleophile and an SN2 rate depends on both partners.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will find the rate-determining step from a profile, predict rate changes for SN1 and SN2 reactions, match rate laws to mechanisms, and say which changes speed a reaction up.
You can read activation energies off a profile and count its steps. In a multi-step reaction, one step sets the pace for all of them.
The rate-determining step is the slowest step of a mechanism. A rate law says how the rate depends on concentrations, such as rate = k[A][B]. SN1 and SN2 are the two substitution mechanisms of unit 7: SN1 with a slow ionization first, SN2 in one step.
Every molecule must cross every transition state on the path. The one that stands highest above the reactants lets the fewest molecules through per second: that step is rate-determining, and the whole reaction goes at its speed.
The rate law records who is in that step. In the SN1 reaction of 2-bromo-2-methylpropane with water:
So rate = k[(CH3)3CBr]: doubling the water does nothing, because water arrives after the bottleneck. In an SN2 reaction the nucleophile and substrate meet in the only step, so rate = k[substrate][nucleophile].
Another way: steps
To use the slow step:
Chemists usually run this logic in reverse: measure how the rate depends on each concentration, then ask which mechanism fits. A rate that ignores the nucleophile says the substrate reacts alone first; a rate that depends on both says they meet in the slow step. A rate law cannot prove a mechanism — several mechanisms can share one — but it rules out every mechanism whose slow step contains the wrong species. And only a change that touches the slow step speeds the reaction: a polar solvent that stabilizes the forming ions helps an SN1; a stronger nucleophile does not.
Every step of a mechanism has the same rate. The slowest sets the pace.
The last step is the slowest. Any step can be.
Everything in the equation appears in the rate law. Only species in or before the slow step do.
A rate law proves a mechanism. It rules mechanisms out.
The slow step is the substrate ionizing, alone.
Find the bottleneck.
The nucleophile reacts in the fast second step.
After the bottleneck.
So doubling it leaves the rate unchanged: rate = k[substrate].
Only the slow step counts.
Is the nucleophile in the slow step?
Yes: SN2 has one step.
By what factor does the rate change?
It triples, since rate = k[substrate][nucleophile].
A two-step reaction's first transition state lies $50$ kJ/mol above the reactants and its second transition state $60$ kJ/mol above the reactants. Which step is rate-determining?
An SN1 reaction has rate $= k[\mathrm{substrate}]$. The substrate's concentration is multiplied by $2$ and the nucleophile's by $3$. By what factor does the rate change?
Answer:
Match each measured rate law to the mechanism it points to.
| SN1: the substrate ionizes in the slow step | SN2: nucleophile and substrate react in one step | E2: base and substrate react in one step | |
|---|---|---|---|
| rate = k[RBr], substitution product | |||
| rate = k[RBr][Nu−], substitution product | |||
| rate = k[RBr][base], alkene product |
The SN1 reaction of 2-bromo-2-methylpropane with water has its slow step in the substrate ionizing to a carbocation. Mark every change that would speed it up.
This task has no paper form; do it on a device.
In the body, an enzyme converts a drug D using a cofactor C, and experiments give rate = k[D][C] when the enzyme is plentiful. What does that say about the slowest step?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
An SN2 reaction has rate $= k[\mathrm{substrate}][\mathrm{nucleophile}]$. The substrate's concentration is multiplied by $4$ and the nucleophile's by $4$. By what factor does the rate change?
The rate rises by a factor of a.
You can say which step controls a reaction's rate. Tell someone why doubling the nucleophile does nothing in an SN1 reaction. Next unit: stereochemistry, the shape of molecules in three dimensions.
8. Your turn: an SN2 reaction with the nucleophile tripled, step 3