Question

A medical lab is testing a new anticancer drug on cancer cells. The drug stock solution concentration is 1.5×10−9M, and 4.00 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

Here, the concentration of drug stock solution given is 1.5 X 10^-9 M i.e., 1.5 X 10^-9 moles of the drug is in 1 litre of solution.

Thus, the number of moles present in 4 ml of the solution would be = 4 X 10^-3 X (1.5 X 10^-9) moles = 6 X 10^-12 moles.

1 mole of the drug will contain 6.022 X 10²³ drug molecules.

Therefore, 6 X 10^-12 moles of the drug will contain, 6 X 10^-12 moles X 6.022 X 10²³ molecules/1 mole = 36.132 X 10¹¹ molecules.

The number of cancer cells given = 2.0 X 10⁵

Hence the ratio required = drug molecules/cancer cells

= 36.132 X 10¹¹/2.0 X 10⁵

= 18.066 X 10⁶