Question

A medical lab is testing a new anticancer drug on cancer cells. The drug stock solution concentration is 1.5×10−91.5×10−9 M, and 1.00 mL of this solution will be delivered to a dish containing 2.0×1052.0×105 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

Given drug stock solution concentration is 1.5×10⁻⁹ M; molarity = moles per liter (mol/L)

moles in 1 mL of this drug = 1 mL x 10^-3 L x 1.5×10⁻⁹ M = 1.5 x 10^-12 mol

1 mol of any substance will possess 6.02214129 × 10²³ molecules/mol, so

molecules of drug present in 1.5 x 10^-12 mol = 1.5 x 10^-12 mol x 6.02214129 × 10²³ molecules/mol = 9.033211935 x 10¹¹ molecules.

ratio of drug molecules to the number of cancer cells in the dish = 9.033211935 x 10¹¹ molecules / 2.0 ×10⁵ cancer cells = 4.5166059675 ~ 4.52 x 10⁶

ratio of drug molecules to the number of cancer cells in the dish = 4.52 x 10⁶

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