The recommended dose of aspirin will yield approximately 100.0 micrograms/mL in the blood. How many molecules of aspirin (C9H8O4) are in a drop (0.100 mL) of blood?

3.34x10¹⁶ molecules of aspirin are in a drop of blood

Explanation:

The recomended dose of aspirin in blood is 100.0μg/mL =

1x10⁻⁴g aspirin / mL of blood.

In a drop (0.100mL) there are:

0.100mL ₓ (1x10⁻⁴g aspirin / mL of blood) = 1x10⁻⁵g aspirin.

Molecular mass of aspirin is:

9C = 12.01g/mol ₓ 9 = 108.09g/mol

8H = 1.01g/mol ₓ 8 = 8.08g/mol

4O = 16g/mol ₓ 4 = 64g/mol

108.09 + 8.08 + 64 = 180.17g/mol

Thus, moles of aspirin in 1x10⁻⁵g are:

1x10⁻⁵g ₓ (1mol / 180.17g) = 5.55x10⁻⁸ moles of aspirin

In 1 mole, you have 6.022x10²³ molecules, thus:

5.55x10⁻⁸ moles of aspirin ₓ (6.022x10²³ molecules / 1 mole) =

3.34x10¹⁶ molecules of aspirin are in a drop of blood