?Two neutral species, A and B, with diameters 655 pm and 1820 pm, respectively, undergo

Distinguish between a diffusion-controlled reaction and an activation-controlled reaction. Do both have activation energies?

Describe the role of the encounter pair in the cage effect.

A typical diffusion constant for small molecules in aqueous solution at \(25^{\circ} \mathrm{C}\) is \(6 \times 10^{-9} \mathrm{\ m}^{2} \mathrm{\ s}^{-1}\) . If the critical reaction distance is 0.5 nm, what value is expected for the second-order rate constant for a diffusion-controlled reaction? Text Transcription: 25^circ C 6 times 10^-9 m^2 s^-1

Suppose that the typical diffusion coefficient for a reactant in aqueous solution at \(25^{\circ} \mathrm{C}\) is \(5.2 \times 10^{-9} \mathrm{\ m}^{2} \mathrm{\ s}^{-1}\) . If the critical reaction distance is 0.4 nm, what value is expected for the second-order rate constant for the diffusion-controlled reaction? Text Transcription: 25^circ C 5.2 times 10^-9 m^2 s^-1

Calculate the magnitude of the diffusion-controlled rate constant at 298 K for a species in (i) water, (ii) pentane. The viscosities are \(1.00 \times 10^{-3} \mathrm{\ kg} \mathrm{\ m}^{-1} \mathrm{\ s}^{-1} \) and \(2.2 \times 10^{-4} \mathrm{\ kg} \mathrm{\ m}^{-1} \mathrm{\ s}^{-1}\) , respectively. Text Transcription: 1.00 times 10^-3 kg m^-1 s^-1 2.2 times 10^-4 kg m^-1 s^-1

Calculate the magnitude of the diffusion-controlled rate constant at 298 K for a species in (i) decylbenzene, (ii) concentrated sulfuric acid. The viscosities are 3.36 cP and 27 cP, respectively.

Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in water, for which \(\eta=0.89 \mathrm{\ cP}\). Assuming the concentration of the reacting species is \(1.5 \mathrm{\ mmol} \mathrm{\ dm}^{-3}\) initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary. Text Transcription: eta=0.89 cP 1.5 mmol dm^-3

Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in benzene, for which \(\eta=0.601 \mathrm{\ cP}\). Assuming the concentration of the reacting species is \(2.0 \mathrm{\ mmol} \mathrm{\ dm}^{-3}\) initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary Text Transcription: eta=0.601 cP 2.0 mmol dm^-3

Two neutral species, A and B, with diameters 655 pm and 1820 pm, respectively, undergo the diffusion-controlled reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{P}\) in a solvent of viscosity \(2.93 \times 10^{-3} \mathrm{\ kg} \mathrm{\ m}^{-1} \mathrm{\ s}^{-1}\) at \(40^{\circ} \mathrm{C}\). Use eqn 18B.3 to calculate the initial rate d[P]/dt, given that the initial concentrations of A and B are \(0.170 \mathrm{\ mol} \mathrm{\ dm}^{-3}\) and \(0.350 \mathrm{\ mol} \mathrm{\ dm}^{-3}\) , respectively. Then repeat the calculation by using eqn 18B.4. Comment on the validity of the approximation that leads to eqn 18B.4. Text Transcription: A+B rightarrow P 2.93 times 10^-3 kg m^-1 s^-1 40^circ C 0.170 mol dm^-3 0.350 mol dm^-3

Two neutral species, A and B, with diameters 421 pm and 945 pm, respectively, undergo the diffusion-controlled reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{P}\) in a solvent of viscosity 1.35 cP at \(20^{\circ} \mathrm{C}\). Use eqn 18B.3 to calculate the initial rate d[P]/ dt, given that the initial concentrations of A and B are \(0.155 \mathrm{\ mol} \mathrm{\ dm}^{-3}\) and \(0.195 \mathrm{\ mol} \mathrm{\ dm}^{-3}\) , respectively. Then repeat the calculation by using eqn 18B.4. Comment on the validity of the approximation that leads to eqn 18B.4. Text Transcription: A+B rightarrow P 20^circ C 0.155 mol dm^-3 0.195 mol dm^-3

Confirm that eqn 18B.8 is a solution of eqn 18B.7, where [J] is a solution of the same equation but with \(k_{\mathrm{r}}=0\) and the same initial conditions. Text Transcription: k_r=0

Use mathematical software or a spreadsheet to explore the effect of varying the value of the rate constant \(k_{\mathrm{r}}\) on the spatial variation of \([\mathrm{J}]^{*}\) (see eqn 18B.8 with [J] given in eqn 18B.9) for a constant value of the diffusion coefficient D. Text Transcription: k_r [J]^*

Confirm that if the boundary condition is \([\mathrm{J}]=[\mathrm{J}]_{0}\) at t > 0 at all points on the yz-plane, and the initial condition is [J] = 0 at t = 0 everywhere else, then the solutions \([\mathrm{J}]^{\star}\) in the presence of a first-order reaction that removed J are related to those in the absence of reaction, [J], by \([\mathrm{J}]^{*}=k_{\mathrm{r}} \int_{0}^{t}[\mathrm{J}] \mathrm{e}^{-k_{\mathrm{r}} t} \mathrm{\ d} t+[\mathrm{J}] \mathrm{e}^{-k_{\mathrm{r}} t}\) Base you answer on eqn 18B.7. Text Transcription: [J]=[J]_0 [J]^* [J]^* = k_r int_0^t [J] e^-k_r t dt + [J] e^-k_r t

The compound \(\alpha \text {-tocopherol }\), a form of vitamin E, is a powerful antioxidant that may help to maintain the integrity of biological membranes. R.H. Bisby and A.W. Parker (J. Amer. Chem. Soc. 117, 5664 (1995)) studied the reaction of photochemically excited duroquinone with the antioxidant in ethanol. Once the duroquinone was photochemically excited, a bimolecular reaction took place at diffusion-limited rate. (a) Estimate the rate constant for a diffusion-limited reaction in ethanol. (b) The reported rate constant was \(2.77 \times 10^{9} \mathrm{\ dm}^{3} \mathrm{\ mol}^{-1} \mathrm{\ s}^{-1}\) . Estimate the critical reaction distance if the sum of diffusion coefficients is \(1 \times 10^{-9} \mathrm{\ m}^{2} \mathrm{\ s}^{-1}\) . Text Transcription: alpha-tocopherol 2.77 times 10^9 dm^3 mol^-1 s^-1 1 times 10^-9 m^2 s^-1