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. Step 1: Understand the problem. The mouthwash contains 22.5% alcohol by volume (v/v), meaning that 22.5 mL of alcohol is present in every 100 mL of mouthwash. The total volume of the mouthwash is 355 mL, and we need to calculate the volume of alcohol in this amount.
2. Step 2: Write the formula for calculating the volume of alcohol. The formula is: \( \text{Volume of alcohol} = \text{Total volume of solution} \times \frac{\text{Percentage of alcohol}}{100} \).
3. Step 3: Substitute the given values into the formula. The total volume of the solution is 355 mL, and the percentage of alcohol is 22.5%. The formula becomes: \( \text{Volume of alcohol} = 355 \times \frac{22.5}{100} \).
4. Step 4: Simplify the fraction \( \frac{22.5}{100} \) to make the calculation easier. This fraction represents the decimal form of the percentage, which is \( 0.225 \).
5. Step 5: Multiply the total volume of the solution (355 mL) by the decimal form of the percentage (0.225) to find the volume of alcohol. This will give the final answer 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 specific 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 one unit of measurement to another. In this context, it is important to ensure that the units used for volume are consistent, especially when calculating the volume of alcohol in milliliters. Understanding how to convert between different volume units is essential for accurate calculations.