Respuesta :
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
The ratio of drug molecules to the number of cancer cells in the dish is [tex]\boxed{4.5 \times {{10}^6}}[/tex].
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:
[tex]{\text{Molarity of solution}} = \dfrac{{{\text{Moles }}\left( {{\text{mol}}} \right){\text{of solute}}}}{{{\text{Volume }}\left( {\text{L}} \right){\text{ of solution}}}}[/tex] …… (1)
Rearrange equation (1) to calculate moles of solute.
[tex]{\text{Moles of solute}} = \left( {{\text{Molarity of solution}}} \right)\left( {{\text{Volume of solution}}} \right)[/tex] …… (2)
Substitute [tex]1.5 \times {10^{ - 9}}{\text{ M}}[/tex] for molarity of solution and 1.00 mL for volume of solution in equation (2) to calculate moles of drug.
[tex]\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}[/tex]
According to Avogadro’s law, one mole of every substance has [tex]6.022 \times {10^{23}}{\text{ units}}[/tex]. These units can vary from question to question and can be atoms, molecules, or formula units. Since one mole of drug also contains [tex]6.022 \times {10^{23}}{\text{ molecules}}[/tex], number of molecules of drug present in [tex]1.5 \times {10^{ - 12}}{\text{ mol}}[/tex] can be calculated as follows:
[tex]\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}[/tex]
The ratio of drug molecules to the number of cancer cells in the dish can be evaluated as follows:
[tex]\begin{aligned}{\text{Required ratio}} &= \frac{{9.033 \times {{10}^{11}}}}{{2.0 \times {{10}^5}}} \\ &= 4.5 \times {10^6} \\ \end{aligned}[/tex]
Learn more:
- Calculation of volume of gas: https://brainly.com/question/3636135
- Determine how many moles of water produce: https://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.
