The reaction between ethyl iodide and hydroxide ion in ethanol
\(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) solution,
\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(a l c)+\mathrm{OH}^{-}(a l c)
\longrightarrow\) \(\mathrm{C}_{2} \mathrm{H}_{5}
\mathrm{OH}(l)+\mathrm{I}^{-}(\) alc \()\) has an activation energy of \(86.8
\mathrm{~kJ} / \mathrm{mol}\) and a frequency factor of \(2.1 \times 10^{11}
\mathrm{M}^{-1} \mathrm{~s}^{-1}\) (a) Predict the rate constant for the
reaction at \(30^{\circ} \mathrm{C}\). (b) A solution of KOH in ethanol is made
up by dissolving \(0.500 \mathrm{~g} \mathrm{KOH}\) in ethanol to form \(500
\mathrm{~mL}\) of solution. Similarly, \(1.500 \mathrm{~g}\) of \(\mathrm{C}_{2}
\mathrm{H}_{5} \mathrm{I}\) is dissolved in ethanol to form \(500 \mathrm{~mL}\)
of solution. Equal volumes of the two solutions are mixed. Assuming the
reaction is first order in each reactant, what is the initial rate at
\(30^{\circ} \mathrm{C} ?(\mathbf{c})\) Which reagent in the reaction is
limiting, assuming the reaction proceeds to completion? ((d) Assuming the
frequency factor and activation energy do not change as a function of
temperature, calculate the rate constant for the reaction at \(40^{\circ}
\mathrm{C} .\)