Consider some of the precautions that must be taken when conducting single-molecule

Chapter 14, Problem 14.11

(choose chapter or problem)

Consider some of the precautions that must be taken when conducting single-molecule spectroscopy experiments.

(a) What is the molar concentration of a solution in which there is, on average, one solute molecule in \(1.0 \mu \mathrm{m}^3\) (1.0 fL) of solution?

(b) It is important to use pure solvents in single-molecule spectroscopy because optical signals from fluorescent impurities in the solvent may mask optical signals from the solute. Suppose that water containing a fluorescent impurity of molar mass \(100 \mathrm{~g} \mathrm{~mol}^{-1}\) is used as solvent and that analysis indicates the presence of \(0.10 \mathrm{mg}\) of impurity per \(1.0 \mathrm{~kg}\) of solvent. On average, how many impurity molecules will be present in \(1.0 \mu \mathrm{m}^3\) of solution? You may take the density of water as \(1.0 \mathrm{~g} \mathrm{~cm}^{-3}\). Comment on the suitability of this solvent for single-molecule spectroscopy experiments.