MediumChemistryHigh School (11–12)Organic Compounds with Functional Groups › Haloalkanes and HaloarenesNumerical

A tertiary bromide is dissolved in aqueous ethanol…

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A tertiary bromide is dissolved in aqueous ethanol. It reacts by the $S_{\text{N}}1$ mechanism and follows first-order kinetics. Its rate constant is $3.5 \times 10^{-3}\ \text{s}^{-1}$ at the temperature of the experiment (a value chosen for this problem). Take $\ln 2 = 0.693$ . Find the half-life, the time for $87.5\ \%$ of the bromide to react, and the percentage of the bromide left after $600\ \text{s}$ . The first-order law gives the fraction left as $e^{-kt}$ .

Need a reminder? The key ideaShow

$S_{\text{N}}1$ is first order, $\text{rate} = k[\text{RX}]$ , with half-life $t_{1/2} = \dfrac{0.693}{k}$ . A planar carbocation gives a racemic or partly racemic product. The enantiomeric excess is the difference of the two shares, and the observed rotation is the specific rotation times tube length times concentration times the excess. A carbocation can rearrange to a more stable one by a hydride shift.

The worked solution

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