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.

검증된 단계별 안내

Determine the number of moles of calicheamicin gamma-1 needed to kill 1.0 \(\times\) 10^8 bacteria, knowing that one molecule kills one bacterial cell. Use Avogadro's number (6.022 \(\times\) 10^{23} molecules/mol) to convert the number of molecules to moles.

Calculate the volume of the stock solution required to obtain the moles of calicheamicin gamma-1 needed. Use the formula: \( C_1V_1 = C_2V_2 \), where \( C_1 \) is the concentration of the stock solution, \( V_1 \) is the volume of the stock solution needed, \( C_2 \) is the concentration of the desired solution, and \( V_2 \) is the volume of the desired solution.

Rearrange the formula to solve for \( V_1 \): \( V_1 = \frac{C_2V_2}{C_1} \). Substitute the known values: \( C_1 = 5.00 \times 10^{-9} \text{ M} \), \( V_2 = 25.00 \text{ mL} \), and \( C_2 \) is the concentration calculated from the moles needed.

Convert the volume \( V_1 \) from liters to milliliters if necessary, as the final preparation will be in milliliters.

Carefully measure \( V_1 \) mL of the stock solution using a pipette and dilute it with distilled water in a volumetric flask to a final volume of 25.00 mL to prepare the desired solution.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.