Question

For a reaction A + B → Products, the rate law is $\mathrm{Rate = k[A][B]^{3/2}}$. Write the overall order of the reaction. Can this reaction be an elementary reaction ? Give reason in support of your answer.

Hint:

Order = sum of powers = 1 + 3/2 = 2.5; a fractional order means a multi-step reaction.

Answer 1

(a)
The fastest isomer in an $\mathrm{S_N1}$ reaction is the one that can form the steadiest carbocation, because the slow step in $\mathrm{S_N1}$ is the breaking away of the halide to leave a positive carbon behind. Among the $\mathrm{C_4H_9Br}$ isomers, 2-bromo-2-methylpropane, $\mathrm{(CH_3)_3C{-}Br}$ (tert-butyl bromide), loses its bromide to give a tertiary carbocation $\mathrm{(CH_3)_3C^+}$. Three alkyl groups push electron density onto the positive carbon and steady it, so this cation forms most easily. That makes tert-butyl bromide the most reactive towards $\mathrm{S_N1}$.

(b)
In the Wurtz reaction two alkyl halide pieces join together at their carbon ends with sodium metal in dry ether. To end up with 2,5-dimethylhexane we split that product down the middle: each half is a four carbon piece, $\mathrm{(CH_3)_2CHCH_2{-}}$, which comes from 1-bromo-2-methylpropane, $\mathrm{(CH_3)_2CHCH_2Br}$ (isobutyl bromide). Two of these isobutyl pieces coupling end to end give the symmetrical product:
\[ 2(CH_3)_2CHCH_2Br + 2Na \rightarrow (CH_3)_2CHCH_2CH_2CH(CH_3)_2 + 2NaBr \]
So the required isomer is isobutyl bromide.