Calicheamicin gamma-1, C55H74IN3O21S4, is one of the most potent antibiotics known: one molecule kills one bacterial cell. Describe how you would (carefully!) prepare 25.00 mL of an aqueous calicheamicin gamma-1 solution that could kill 1.0 * 108 bacteria, starting from a 5.00 * 10-9M stock solution of the antibiotic.

Key Concepts

Molarity and Dilution

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. To prepare a specific concentration from a stock solution, the dilution equation (C1V1 = C2V2) is used, where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the desired concentration and volume of the diluted solution. Understanding this concept is crucial for accurately preparing the required solution.

Bacterial Cell Count

To determine how much calicheamicin gamma-1 is needed to kill a specific number of bacteria, one must understand the relationship between the antibiotic's potency and the bacterial cell count. In this case, the problem states that one molecule of calicheamicin can kill one bacterial cell, so to kill 1.0 * 10^8 bacteria, you need 1.0 * 10^8 molecules of the antibiotic. This translates to calculating the required molarity based on Avogadro's number.

Volume Calculation

Once the required concentration of the antibiotic solution is determined, the next step is to calculate the volume of the stock solution needed to achieve this concentration in the final volume of 25.00 mL. This involves using the dilution equation to find V1, which represents the volume of the stock solution to be diluted. Accurate volume measurement is essential for ensuring the solution's effectiveness in killing the targeted bacterial cells.