# Percent by Volume Definition and Example (% v/v)

Percent by volume is a way of expressing the concentration of a chemical solution that is the volume of solute divided by the total volume of the solution, multiplied by 100%. It is also known as volume percent (vol%) or % v/v.

percent by volume = volume of solute / volume of solution x 100%

Because the volume units cancel out, percent by volume is a unitless quantity. Percent by volume is common in chemistry and the food and beverage industry. For example, alcoholic beverages often list the amount of alcohol in terms of percent by volume.

### When to Use the Volume of Solution

You might think the total volume of the solution is the sum of the volume of the solute and the volume of the solvent:

percent by volume = volume of solute / (volume of solute + volume of solvent) x 100%

This works when mixing gases. However, use the total volume of the solution and not the sum of its components when mixing liquids or solids. The reason is because mixing a solution changes its volume. For example, mixing ethanol and water results in a solution that has a lower volume than the sum of the volume of alcohol and volume of water. These two chemicals are miscible in one another and intermolecular forces draw the molecules in the mixture close together.

Similarly, mixing together sugar and water gives a different volume than the sum of the volumes of the components. The air space between solid solute particles goes away when the solid dissolves in a liquid.

### Making a Percent by Volume Solution

When you prepare a solution using percent by volume, measure the volume of solute and then dilute it with solvent to reach the total volume.

• Correct: Make a 12% v/v alcohol solution by pouring 12 milliliters of alcohol into a container and diluting it with water to reach 100 milliliters.
• Incorrect: Mixing 12 milliliters of alcohol and 88 milliliters of water.

### Percent by Volume Example Problems

#### Example #1

For example, find the amount of alcohol in a 750 milliliter bottle of wine that is 12% ABV (alcohol by volume, which is volume percent).

percent by volume = volume of solute / volume of solution x 100%
12% = volume alcohol / 750 ml x 100
or
0.12 = volume / 750 ml

volume of alcohol = 12 x 750 / 100 = 90 milliliters

#### Example #2

For example, find the volume of HNO3 you need to make 250 ml of 4% v/v aqueous solution.

For this problem, you know the total volume of the solution is 250 milliliters and the concentration is 4%.

percent by volume = volume of solute / volume of solution x 100%
4% = volume of HNO3 / 250 x 100

Rearranging the terms:

volume of HNO3 = 4 x 250 / 100 = 10 milliliters