Chapter 2, Problem 112A

Interpretation Introduction

Interpretation:

The mass of dextromethorphan in 1 bottle of cough syrup needs to be determined.

Concept introduction:

Primarily, dextromethorphan is used as a cough suppressant for the temporary relief of the cough. The common brand of a cough syrup generally comes in a 4-fluid ounce bottle and the active ingredient is dextromethorphan. The standard dose for an adult is $2$ teaspoon but on exceeding the dosages, dextromethorphan acts as dissociative hallucinogen. Also, $\text{1}\text{fluid}\text{ounce}=\text{29}\text{.6}\text{mL}$ and $\text{1}\text{teaspoon}=\text{5}\text{.0}\text{mL}$.

Answer to Problem 112A

$\text{0}\text{.24 g}$ of dextromethorphan is present per bottle.

Explanation of Solution

To determine the number of grams of dextromethorphan present one bottle, convert the ounces to milliliters and then milliliters to teaspoon. After that, convert the teaspoon to milligram and then finally milligrams to grams.

$\begin{array}{c}\text{Amount}\text{of}\text{dextromethorphan}=\left(\frac{\text{4}\text{fluid}\text{ounces}}{\text{1}\text{bottle}}\right)\times \left(\frac{\text{9}\text{.6}\text{mL}}{\text{fluid}\text{ounce}}\right)\times \left(\frac{\text{1}\text{teaspoon}}{\text{5}\text{.0}\text{mL}}\right)\times \left(\frac{\text{20}\text{mg}}{\text{2}\text{teaspoon}}\right)\times \left(\frac{\text{0}\text{.001}\text{g}}{\text{1}\text{mg}}\right)\\ =0.24\text{g}\text{dextromethorphan}/\text{bottle}\end{array}$

Hence, $\text{0}\text{.24 g}$ of dextromethorphan is present per bottle.

Conclusion

Thus, $\text{0}\text{.24 g}$ of dextromethorphan is present per bottle.