medical lab is testing a new anticancer drug on cancer cells. The drug stock solution concentration is 1.5 * 10-9 M, and 1.00 mL of this solution will be delivered to a dish containing 2.0 * 105 cancer cells in 5.00 mL of aqueous fluid. What is the ratio of drug molecules to the number of cancer cells in the dish?

검증된 단계별 안내

Calculate the total volume of the solution in the dish by adding the volume of the drug solution to the volume of the aqueous fluid: 1.00 \(\text{ mL}\) + 5.00 \(\text{ mL}\).

Determine the concentration of the drug in the dish by using the dilution formula: C_1V_1 = C_2V_2, where C_1 is the initial concentration, V_1 is the initial volume, C_2 is the final concentration, and V_2 is the final volume.

Calculate the number of moles of the drug in the dish using the final concentration and the total volume of the solution in liters.

Convert the number of moles of the drug to the number of molecules using Avogadro's number (6.022 \(\times\) 10^{23} \(\text{ molecules/mol}\)).

Find the ratio of the number of drug molecules to the number of cancer cells by dividing the number of drug molecules by the number of cancer cells (2.0 \(\times\) 10^5).

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주요 개념

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

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, the drug's concentration is given as 1.5 x 10^-9 M, indicating that there are 1.5 x 10^-9 moles of the drug in one liter of solution. Understanding molarity is essential for calculating the total amount of drug in a specific volume, which is crucial for determining the ratio of drug molecules to cancer cells.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This concept is vital for converting moles of the drug into actual molecules. By using Avogadro's number, we can determine how many drug molecules are present in the delivered volume, allowing us to compare this quantity to the number of cancer cells.

Dilution

Dilution refers to the process of reducing the concentration of a solute in a solution, typically by adding more solvent. In this scenario, the drug is delivered in a total volume of 5.00 mL, which affects the final concentration of the drug in the dish. Understanding dilution is important for accurately calculating the effective concentration of the drug when mixed with the aqueous fluid and determining the ratio of drug molecules to cancer cells.