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Chapter 4: Problem 75

A medical lab is testing a new anticancer drug on cancer cells. The drug stock solution concentration is \(1.5 \times 10^{-9} M,\) and 1.00 \(\mathrm{mL}\) of this solution will be delivered to a dish containing \(2.0 \times 10^{5}\) cancer cells in 5.00 \(\mathrm{mL}\) of aqueous fluid. What is the ratio of drug molecules to the number of cancer cells in the dish?

Short Answer

Expert verified
The ratio of drug molecules to the number of cancer cells in the dish is approximately \(4.517 \times 10^6\).

Step by step solution

01

Calculate the number of moles of drug in the solution

To calculate the number of moles (m) of the drug in the solution, we will use the equation: m = concentration (M) * volume (L) Remember that the concentration given in the exercise is \(1.5 \times 10^{-9} M\), and the volume is 1.00 mL. Since we need the volume in liters, we will convert milliliters to liters by dividing by 1000: 1.00 mL = 0.001 L Now, we can plug in our values and calculate the number of moles: m = \(1.5 \times 10^{-9} M * 0.001 L\) m = \(1.5 \times 10^{-12}\) mol
02

Calculate the number of drug molecules in the solution

Now that we have the number of moles, we will need to convert it to drug molecules. We will use Avogadro's number (6.022 \(\times 10^{23}\)) for this conversion. To calculate the number of drug molecules (N), we will use the equation: N = moles (mol) * Avogadro's number (molecules/mol) Plugging in our values: N = \(1.5 \times 10^{-12}\) mol * \(6.022 \times 10^{23}\) molecules/mol N = \(9.033 \times 10^{11}\) drug molecules
03

Calculate the ratio of drug molecules to cancer cells

Now that we have the number of drug molecules (N) and the number of cancer cells (given in the problem as \(2.0 \times 10^5\) cells), we can calculate the ratio: Ratio = \(\frac{\text{Drug molecules}}{\text{Cancer cells}}\) Ratio = \(\frac{9.033 \times 10^{11}}{2.0 \times 10^5}\) When we divide these numbers, we get: Ratio = \(4.517 \times 10^6\) This means that there are approximately \(4.517 \times 10^6\) drug molecules for every cancer cell in the dish.

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Most popular questions from this chapter

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