Topic 16: Kinetics II：練習問題

A reaction is first order with respect to reactant \(\text{X}\). If the initial concentration of \(\text{X}\) is doubled, what happens to the half-life \((t_{1/2})\) of the reaction?

The Arrhenius equation is given by \(\ln k = -\frac{E_a}{RT} + \ln A\). A plot of \(\ln k\) against \(1/T\) for a specific reaction yields a straight line with a gradient of \(-1.20 \times 10^4\text{ K}\). What is the activation energy, \(E_a\), for this reaction in \(\text{kJ mol}^{-1}\)?
(\(R = 8.31\text{ J K}^{-1}\text{ mol}^{-1}\))

In a plot of \(\ln k\) against \(\frac{1}{T}\) for a specific reaction, the gradient of the line is found to be \(-8.5 \times 10^{3}\) K. Calculate the activation energy, \(E_{a}\), for this reaction in \(kJ\) \(mol^{-1}\).
(Gas constant \(R = 8.31\) \(J\) \(K^{-1}\) \(mol^{-1}\))

In the acid-catalyzed iodination of propanone, the rate equation is found to be:
\(\text{rate} = k[\text{CH}_3\text{COCH}_3]^1[\text{H}^+]^1[\text{I}_2]^0\)
Which of the following statements about the reaction mechanism is correct?

The decomposition of cyclobutane to ethene is a first-order reaction. Calculate the rate constant, \(k\), given that the half-life of cyclobutane is \(140\text{ seconds}\) at a specific temperature. Include units in your answer.

For the hydrolysis of \(2\)-bromo-\(2\)-methylpropane with aqueous hydroxide ions, the rate is found to be independent of the concentration of hydroxide ions. Deducing the likely mechanism (\(S_{N}1\) or \(S_{N}2\)), justify your answer by describing the rate-determining step.