Chapter 10, Problem 148A

Pain Relief Acetaminophen, a common aspirin substitute, has the formula ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}{\text{NO}}_{\text{2}}$ . Determine the number of molecules of acetaminophen in a 500-mg tablet.

Interpretation Introduction

Interpretation:

The number of molecules of acetaminophen present in 500 mg tablet should be calculated.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 148A

Number of molecules of acetaminophen = $1.99\times 10\text{molecules}$

Explanation of Solution

Mass of tablet = 500 mg

Convert the mass in mg to g.

Since, 1 g = 1000 mg

Thus, the mass of tablet in g = $\text{500 mg}\times \frac{1\text{ g}}{1000\text{ mg}}$

= $0.5\text{ g}$

Molecular formula of acetaminophen = ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}{\text{NO}}_{\text{2}}$

Molar mass of ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}{\text{NO}}_{\text{2}}$

= $8\left(12.01\text{ g/mole}\right)+9\left(1.0078\text{ g/mole}\right)+1\left(14.01\text{ g/mole}\right)+2\left(15.999\text{ g/mole}\right)$

= $151.2\text{ g/mole}$

Number of moles of ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}{\text{NO}}_{\text{2}}$ = $\frac{\text{ 0}\text{.5 g}}{151.2\text{ g/mole}}$

= $\text{0}\text{.00330 mole}$

Number of molecules of acetaminophen = $\text{Number of moles × 6}\text{.022}\times {\text{10}}^{23}\frac{\text{molecules}}{\text{mole}}$

Number of molecules of acetaminophen = $\text{0}\text{.00330 mole}\times \text{ 6}\text{.022}\times {\text{10}}^{23}\frac{\text{molecules}}{\text{mole}}$

= $1.99\times 10\text{molecules}$