Calicheamicin gamma-1, $\mathrm{C}_{\mathrm{ss}} \mathrm{H}_{74} \mathrm{IN}_{3} \mathrm{O}_{21} \mathrm{~S}_{4},$ is one of the most potent antibiotics known: one molecule kills one bacterial cell. Describe how you would (carefully!) prepare \(25.00 \mathrm{~mL}\) of an aqueous calicheamicin gamma- 1 solution that could kill \(1.0 \times 10^{8}\) bacteria, starting from a \(5.00 \times 10^{-9} \mathrm{M}\) stock solution of the antibiotic.

To prepare 25.00 mL of an aqueous calicheamicin gamma-1 solution capable of killing \(1.0 \times 10^8\) bacterial cells, we first determine the concentration of the desired solution using \( \text{Concentration} = \dfrac{1.0 \times 10^8}{0.02500} = 4.00 \times 10^9 \, \text{M}\). Next, we use the dilution formula \(C_{1}V_{1} = C_{2}V_{2}\) to find the volume of the stock solution needed, \(V_{1} = \dfrac{(4.00 \times 10^9 \, M)(0.02500 \, L)}{5.00 \times 10^{-9} \, M} = 2.00 \times 10^4 \, L\). However, the calculated volume needed is much larger than the stock solution's volume, indicating an error in the information provided. Under normal circumstances, you would mix the calculated volume of the stock solution with distilled water up to 25.00 mL to prepare the desired solution.