Question

A medical lab is testing a new anticancer drug on cancer cells. The drug stock solution concentration is 1.5×10−9m, 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?

Answer 1

The concentration of the drug stock solution is 1.5*10^-9 M i.e. 1.5 * 10^-9 moles of the drug per Liter of the solution

Therefore, the number of moles present in 1 ml i.e. 1*10^-3 L of the solution would be =  1 *10^-3 L * 1.5 * 10^-9 moles/1 L = 1.5 * 10^-12 moles

1 mole of the drug will contain 6.023*10^23 drug molecules

Therefore, 1.5*10^-12 moles of the drug will correspond to :

    1.5 * 10^-12 moles * 6.023*10^23 molecules/1 mole = 9.035 * 10^11 molecules

The number of cancer cells = 2.0 * 10^5

Hence the ratio = drug molecules/cancer cells

                          = 9.035 *10^11/2.0 *10^5

                          = 4.5 * 10^6

Answer 2

The ratio of drug molecules to the number of cancer cells in the dish is $\boxed{4.5 \times {{10}^6}}$.

Further Explanation:

Concentration of various solutions can be expressed by various concentration terms. Some of such concentration terms are listed below.

• Molarity
• Mole fraction
• Molality
• Parts per million
• Mass percent
• Volume percent
• Parts per billion

Molarity is defined as moles of solute present in one litre of solution. It is represented by M and its unit is mol/L. The expression for molarity of solution is as follows:

${\text{Molarity of solution}} = \dfrac{{{\text{Moles }}\left( {{\text{mol}}} \right){\text{of solute}}}}{{{\text{Volume }}\left( {\text{L}} \right){\text{ of solution}}}}$                 …… (1)

Rearrange equation (1) to calculate moles of solute.

${\text{Moles of solute}} = \left( {{\text{Molarity of solution}}} \right)\left( {{\text{Volume of solution}}} \right)$                         …… (2)

Substitute $1.5 \times {10^{ - 9}}{\text{ M}}$ for molarity of solution and 1.00 mL for volume of solution in equation (2) to calculate moles of drug.

$\begin{aligned}{\text{Moles of drug}} &= \left( {1.5 \times {{10}^{ - 9}}{\text{ M}}} \right)\left( {1.00{\text{ mL}}} \right)\left( {\frac{{{{10}^{ - 3}}{\text{ L}}}}{{1{\text{ mL}}}}} \right) \\ &= 1.5 \times {10^{ - 12}}{\text{ mol}} \\\end{aligned}$  

According to Avogadro’s law, one mole of every substance has $6.022 \times {10^{23}}{\text{ units}}$. These units can vary from question to question and can be atoms, molecules, or formula units. Since one mole of drug also contains   $6.022 \times {10^{23}}{\text{ molecules}}$, number of molecules of drug present in $1.5 \times {10^{ - 12}}{\text{ mol}}$ can be calculated as follows:

$\begin{aligned}{\text{Molecules of drug}} &= \left( {1.5 \times {{10}^{ - 12}}{\text{ mol}}} \right)\left( {\frac{{6.022 \times {{10}^{23}}{\text{ molecules}}}}{{1{\text{ mol}}}}} \right) \\ &= 9.033 \times {10^{11}}{\text{ molecules}} \\ \end{aligned}$  

The ratio of drug molecules to the number of cancer cells in the dish can be evaluated as follows:

$\begin{aligned}{\text{Required ratio}} &= \frac{{9.033 \times {{10}^{11}}}}{{2.0 \times {{10}^5}}} \\ &= 4.5 \times {10^6} \\ \end{aligned}$  

Learn more:

1. Calculation of volume of gas: brainly.com/question/3636135
2. Determine how many moles of water produce: brainly.com/question/1405182

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Concentration

Keywords: concentration, concentration terms, solutions, molarity, Avogadro’s law, drug molecules, cancer cells, 4.5*10^6, one mole, atoms, molecules.