Q. 9.35 - An Introduction to General, Organic, and Biological Chemistry

Question

A mouthwash contains $22.5\% (v/v)$ alcohol. If the bottle of mouthwash contains $335 mL$, what is the volume, in milliliters, of alcohol?

Step-by-Step Solution

Answer

The volume of alcohol is $79.9 \text{ml of alcohol }$if the mouthwash contains $335 mL$

Step 1: Given Information.

The following are the given information to find the milliliters:

Mouthwash contains $22.5\% (v/v)$ alcohol.

If mouthwash contains $335 mL$, find the volume in milliliters.

Step 2: Explanation.

A conversion factor is a one-to-one ratio. Multiplying a quantity by a conversion factor keeps changing the units of measurement but does not change the original amount.

Equalities/conversion factor represents the milliliter of solute in $100 mL$ of solution.

$22.5\% (v/v)$ written as:

$100 \mathrm{ml}\text{ solution }=22.5 \mathrm{ml} \mathrm{alcohol}$

$\frac{22.5 \mathrm{ml}\text{ alcohol }}{100 \mathrm{ml}\text{ solution }}\text{ and }\frac{100 \mathrm{ml}\text{ solution }}{22.5 \mathrm{ml}\text{ alcohol }}$

The volume of the solution using conventional factors is,

$$\begin{gathered} =355 \mathrm{ml}\text{ sotuion }\times \frac{22.5 \mathrm{ml}\text{ alcohol }}{100 \mathrm{ml}\text{ sotulion }} \\ =79.9 \mathrm{ml}\text{ of alcohol } \end{gathered}$$