Physical chemistry
for which the experimental rate equation is: rate = k[CH3CH2CH2CH2Br][OH−] The second-order rate equation suggests a single-step nucleophilic substitution mechanism involving direct collision of a hydroxide ion with a molecule of bromobutane; no further explanation is needed. However, in the superficially identical hydrolysis of 2-bromo-2-methylpropane:
Essential Notes
(CH3)3CBr + OH− → (CH3)3COH + Br− the experimental rate equation is: rate = k[(CH3)3CBr] and the reaction is first order, clearly requiring a different reaction mechanism. A proposed reaction mechanism that would fit this rate equation is:
(CH3)3CBr
slow
(CH ) C+ + OH− 3 3
In a process that involves a sequence of steps, each dependent on the preceding one, the overall rate of conversion is limited by the speed of the slowest step.
(CH3)3C+ + Br− fast
(CH3)3COH
Definition The rate-determining step is the slowest step in a multi-step reaction sequence; it dictates the overall rate of reaction.
The first, slow step involving the formation of a carbocation determines the overall rate of reaction. It is called the rate-determining step. The rate-determining step above involves only a single parent molecule; this step can be written as: (CH ) CBr slow (CH ) C+ + Br− 3 3 3 3
rate = k1[(CH3)3CBr]
and the second step can be written as: (CH ) C+ + OH− fast 3 3
(CH3)3COH
rate = k2[(CH3)3C+][OH−]
However, the kinetics of this step are of no interest, as it can proceed only as fast as the carbocation is formed and then speedily consumed. The overall reaction is: (CH3)3CBr + OH− → (CH3)3COH + Br−
rate = k1[(CH3)3CBr]
According to this proposed scheme, the reaction is first order (as found experimentally), so the proposed reaction mechanism is in accord with the observed kinetics. This is an example of a reaction mechanism where the rate-determining step is the first step in the sequence, so only the reactants in this step can appear in the rate equation. In other cases (mentioned below) the rate-determining step follows after other fast steps; in such cases, the species involved in these fast steps may well appear in the experimental rate equation.
Notes It is likely that both mechanisms (the secondorder as well as the first-order) are in play in the hydrolysis of both compounds. For 1-bromobutane, the dissociation into ions will have much higher activation energy than will the approach of a hydroxide ion to the C––Br carbon, which is relatively exposed. So the second-order mechanism will dominate. However, for 2-bromo2-methylpropane, the interference of the three quite bulky methyl groups will play a significant role in raising the bimolecular activation energy, as also will their influence in stabilising the tertiary carbocation.
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