Question

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

Short answer

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

Step-by-step solution

Given Information.

The following are the given information to find the milliliters:

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

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

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 $100mL$of solution.

$22.5\%(v/v)$written as:

localid="1653466843727" $100\mathrm{ml}\text{solution}=22.5\mathrm{ml}\mathrm{alcohol}$

localid="1653466857271" $\frac{22.5\mathrm{ml}\text{alcohol}}{100\mathrm{ml}\text{solution}}\text{and}\frac{100\mathrm{ml}\text{solution}}{22.5\mathrm{ml}\text{alcohol}}$

The volume of the solution using conventional factors is,

localid="1653466871340" $$\begin{gathered} =355\mathrm{ml}\text{sotuion}\times \frac{22.5\mathrm{ml}\text{alcohol}}{100\mathrm{ml}\text{sotulion}} \\ =79.9\mathrm{ml}\text{of alcohol} \end{gathered}$$