(a) For an electron donor/acceptor pair at 298 K, $H_{a}(d)=0.04\ \mathrm{cm}^{-1}, \Delta_{r} G^{\ominus}=-0.185\ \mathrm{eV},$ and $k_{n}=37.5\ \mathrm{s}^{-1}.$ Use mathematical software to estimate the value of the reoryanization energy. (b) For an electron donor/acceptor pair at 298 K, $k_{a}=2.02 \times 10^{3}\ \mathrm{s}^{-1}$ and $\Delta_{r} G^{\ominus}=-0.665\ \mathrm{eV}.$ The standard reaction Gibbs energy changes to $\Delta_{r} G^{\ominus}= -0.975\ \mathrm{eV}$ when a substituent is added to the electron acceptor and the rate constant for electron transfer changes to $k_{n}=3.33 \times 10^{6}\ \mathrm{s}^{-1}.$ Assume that the distance between donor and acceptor is the same in both experiments and estimate the values of $H_{\mathrm{n}}(d)$ and $\Delta E_{\mathrm{R}}.$

21. Euglena are photosynthetic protists that live in fresh water. How would their photosynthetic properties help stabilize a pond ecosystem? Suppose they and all the other photosynthetic organisms disappeared from the pond, How might their disappearance affect other organisms that lived in the pond?

The rate constant (k) depends on which of the following? (There may be more than one answer.) a. the concentration of the reactants b. the nature of the reactants c. the temperature d. the order of the reaction Explain.

Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

(a) By how much does $H_{n}(d)^{2}$ change when d is increased from 1.0 nm to 2.0 nm, with $\beta=9\ \mathrm{nm}^{-1} ?$ (b) By how much does $H_{n}(d)^{2}$ change when d is increased from 1.0 nm to 2.0 nm, with $\beta=30\ \mathrm{nm}^{-1} ?$