A mouthwash contains 22.5% (v/v) alcohol. If the bottle of mouthwash contains 355 mL, what is the volume, in milliliters, of alcohol?

Verified step by step guidance

1. Identify the given percentage concentration: 22.5% (v/v) alcohol.
2. Understand that (v/v) means volume/volume, so 22.5% (v/v) means 22.5 mL of alcohol per 100 mL of solution.
3. Set up a proportion to find the volume of alcohol in 355 mL of mouthwash: \( \frac{22.5 \text{ mL alcohol}}{100 \text{ mL solution}} = \frac{x \text{ mL alcohol}}{355 \text{ mL solution}} \).
4. Solve the proportion for \( x \) by cross-multiplying: \( 22.5 \times 355 = 100 \times x \).
5. Divide both sides by 100 to isolate \( x \), which represents the volume of alcohol in milliliters.

Key Concepts

Volume/Volume Percentage (v/v)

Volume/Volume percentage (v/v) is a way of expressing the concentration of a solution. It indicates the volume of solute (in this case, alcohol) present in a certain volume of solution. For example, a 22.5% (v/v) alcohol solution means that there are 22.5 mL of alcohol in every 100 mL of the solution.

Calculating Volume of Solute

To find the volume of solute in a solution, you can use the formula: Volume of solute = (v/v percentage) × (total volume of solution). This calculation allows you to determine how much of the solute is present based on the total volume and the concentration expressed as a percentage.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this context, it is important to ensure that the units used for volume are consistent, particularly when dealing with milliliters (mL) and percentages. Understanding how to convert and manipulate these units is essential for accurate calculations.