Chapter 10, Problem 108A

Interpretation Introduction

Interpretation: The number of molecules of compound present in an athlete’s urine needs to be determined.

Concept Introduction: The relation between the number of moles, mass, and molar mass of a substance is as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Also, according to Avogadro’s law, in 1 mol of a substance, there are $6.022\times {10}^{23}$ units of that substance.

Explanation of Solution

The molar mass compound found in an athlete’s urine is 312 g/mol. The mass of the compound is 30.0 mg. The number of moles can be calculated as follows:

  $n=\frac{m}{M}$

Putting the values,

  $\begin{array}{c}n=\frac{30.0\text{ mg}\left(\frac{{10}^{-3}\text{ g}}{1\text{ mg}}\right)}{312\text{ g/mol}}\\ =9.615\times {10}^{-5}\text{ mol}\end{array}$

Therefore, the number of moles of the compound is $9.615\times {10}^{-5}\text{ mol}$ .

The number of molecules can be calculated as follows:

  $\begin{array}{c}N=9.615\times {10}^{-5}\text{ mol}\left(\frac{6.022\times {10}^{23}\text{ molecules}}{1\text{ mol}}\right)\\ =5.8\times {10}^{19}\text{ molecules}\end{array}$

Therefore, the number of molecules of the compound is $5.8\times {10}^{19}\text{ molecules}$ .