Problem 2
For a reaction \(A \rightarrow\) products which is zero order with respect to \(A,\) sketch a graph of (a) rate of reaction against time, and (b) [A] against time. Repeat the exercise for reactions that are first and second order with respect to A.
Problem 3
For a reaction \(A \rightarrow\) products which is first order with respect to \(\mathrm{A},\) show that the units of the rate constant are \(s^{-1}\). Similarly, confirm that the units of the second order rate constant are \(\mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{s}^{-1}\).
Problem 4
What is meant by each of the following terms: (a) rate of reaction; (b) differential and integrated forms of a rate equation; (c) order of a reaction (both the overall order and the order with respect to a given reactant); (d) rate constant, pseudo-nth order rate constant and overall rate constant; (e) activation energy; (f) catalysis and autocatalysis; (g) unimolecular step; (h) bimolecular step?
Problem 5
Iron(III) oxidizes iodide according to the following equation: \\[ 2 \mathrm{Fe}^{3+}+2 \mathrm{I}^{-} \rightarrow 2 \mathrm{Fe}^{2+}+\mathrm{I}_{2} \\] Write down a rate equation for this reaction if doubling the iodide concentration increases the rate by a factor of four, and doubling the \(\mathrm{Fe}^{3+}\) ion concentration doubles the rate.
Problem 7
The kinetics of reactions between alkenes and \(\mathrm{I}_{2}\) depend upon the alkene and the solvent. The data below give the results of the reaction of pent-l-ene with \(\mathrm{I}_{2}\) in two different solvents; the alkene is always in vast excess. Determine the order with respect to iodine and the pseudo-nth order rate constant in each reaction. Reaction I: Solvent \(=1,2\) -dichloroethane $$\begin{array}{ll} \text { Time / s } & {\left[\mathrm{I}_{2}\right] / \mathrm{mol} \mathrm{dm}^{-3}} \\ 0 & 0.0200 \\ 1000 & 0.0152 \\ 2000 & 0.0115 \\ 3000 & 0.0087 \\ 4000 & 0.0066 \\ 5000 & 0.0050 \\ 6000 & 0.0038 \\ 7000 & 0.0029 \\ 8000 & 0.0022 \end{array}$$ Reaction II: Solvent = acetic acid $$\begin{array}{ll} \text { Time / s } & {\left[\mathrm{I}_{2}\right] / \mathrm{mol} \mathrm{dm}^{-3}} \\ & \\ 0 & 0.0200 \\ 1000 & 0.0163 \\ 2000 & 0.0137 \\ 3000 & 0.0119 \\ 4000 & 0.0105 \\ 5000 & 0.0093 \\ 6000 & 0.0084 \\ 7000 & 0.0077 \\ 8000 & 0.0071 \end{array}$$
Problem 11
The \(\left[\mathrm{MnO}_{4}\right]^{-}\) ion is an oxidizing agent and the kinetics of the alcohol oxidation: have been studied. \(\left[\mathrm{MnO}_{4}\right]^{-}\) absorbs at \(546 \mathrm{nm}\) and the change in absorbance at this wavelength during the reaction was used to monitor the reaction. If [alcohol] \(\gg\left[\mathrm{MnO}_{4}^{-}\right]\), use the following data to find the order of the reaction with respect to \(\left[\mathrm{MnO}_{4}\right]^{-}\) a Absorbance values have been corrected to allow for the fact that it does not reach zero when \(\left[\mathrm{MnO}_{4}^{-}\right]=0\). (Data from: R. D. Crouch (1994) J. Chem. Educ., vol. \(71,\) p. \(597 .\))
Problem 12
The rate equation for a reaction of the type: \(A+B \rightarrow\) products is of the form: \\[ -\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=k[\mathrm{A}]^{x}[\mathrm{B}] \\] If kinetic runs are carried out with \(A\) in vast excess with respect to \(\mathrm{B}\), the equation can be rewritten in the form: \\[ -\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=k_{\mathrm{obs}}[\mathrm{B}] \\] (a) Use the following kinetic data to determine values of \(x\) and \(k\) (b) What is the overall order of the reaction?
Problem 13
Kinetic data for the reaction: \\[ \begin{array}{r} 2\left[\mathrm{MnO}_{4}\right]^{-}+5\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}+16 \mathrm{H}^{+} \longrightarrow \\ 2 \mathrm{Mn}^{2+}+10 \mathrm{CO}_{2}+8 \mathrm{H}_{2} \mathrm{O} \end{array} \\] are tabulated below and show the results of an experiment in which the initial concentrations of \(\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}\) and \(\mathrm{H}^{+}\) greatly exceed that of \(\left[\mathrm{MnO}_{4}\right]^{-}\) (a) Which species is the reducing agent in the reaction? (b) Why were large initial concentrations of two reagents used? (c) Determine the order of the reaction with respect to \(\left[\mathrm{MnO}_{4}\right]^{-}\)
Problem 15
Indium- 115 is a \(\beta\) -particle emitter with a half-life of \(6 \times 10^{14} \mathrm{y}\). (a) Write an equation for the decay of \(^{115}\) In. (b) What is the rate constant for the decay?
Problem 16
Polonium-211 decays by \(\alpha\) -particle emission. (a) Write an equation for the decay process. (b) If the half-life of \(^{211}\) Po is 0.52 s, what is the rate constant for the decay?
