Table of Contents

## Definition of Volume Percentage

The volume percentage of a solution is defined as the ratio of the volume of solute present in a solution relative to the volume of the solution as a whole.

Volume/volume percentage (v/v percent) measures the concentration of a substance in a solution. It is expressed as the ratio of the volume of the solute to the total volume of the solution multiplied by 100.

Volume percent is usually used when the solution is made by mixing two fluids, such as liquids or gases. However, percentages are the only additive for ideal gases.

## Volume Percent Equations

The volume percent of a solution is defined as the ratio of the volume of solute present in a solution relative to the volume of the solution as a whole.

- Additionally, this type of concentration, which is typically calculated for liquid- and gas-phase solutions, is expressed as a percentage. This proportion must be multiplied by 100, as shown below.

Volume Percent = V_{solute} (mL)/ V_{solution} (mL) × 100

- Because a solution comprises both a solute and a solvent. The volume of a solution, as a whole, is equal to the sum of the volumes of the solute and the solvent that it contains. Therefore, we can also use the following equation to calculate the volume percent of a solution.

Volume Percent = V_{solute} (mL)/solute(mL)+ V_{solution} (mL) × 100

While these two equations are equivalent, the first equation should be applied to determine. And the volume percent of a solution if a numerical quantity is associated with the word “solution” in a given problem.

In contrast, the second equation should be utilized when the amount of solvent present in the solution is specified.

The Percent solutions can be in the form of weight/volume percentage, volume/volume percentage or, weight/weight percentage.

In each case, the concentration in percentage is calculated as the fraction of the volume or weight of the solute related to the total volume or weight of the solution.

Not only for a solution where concentration needs to be expressed in volume percent (v/v%) when the solute is a liquid. But it is also applicable to the numerator in weight units and the denominator in volume units and called weight/volume percent.

## Mass/Volume Percent

Another version of a percentage concentration is mass/volume percent. Which measures the mass or weight of solute in grams (e.g., in grams) vs. the volume of solution (e.g., in mL).

**For** **example**– 0.9%( w/v) NaCl solution in medical saline solutions that contains 0.9g of NaCl for every 100mL of solution. The mass/volume percent is used to express the concentration of a solution when the mass of the solute and volume of the solution is given.

## Properties of Mass/Volume Percent

- Since the numerator and denominator have different units, and this concentration unit is not a true relative unit (e.g., percentage). However, it is often used as an easy concentration unit since volumes of solvent and solutions are easier to measure than weights. Moreover, since the density of dilute aqueous solutions is close to 1 g/mL. If the volume of a solution is measured in mL (as per definition), then this well approximates the mass of the solution in grams (making a true relative unit (m/m)).
- Mass percentage and volume percent can be calculated using an alternative equation. The masses or volumes, respectively, of the solute and the solvent contained in a solution are added to obtain the mass or volume, respectively, that solution, as a whole.
- While mass per cents are typically reported for solid- and liquid-phase solutions, and volume percents are usually determined for liquid- and gas-phase solutions. A mass/volume percent concentration is most often calculated for solutions that are specifically prepared by dissolving solid solutes in liquid solvents. In order to create this type of solution, and the solid solute particles must overcome the attractive forces that exist between the liquid solvent molecules.
- The percentage by volume (vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt.%) and mole fraction (percentage by moles, mol%) are others.

## Examples of Volume Percentage

Here are some examples of volume percentage;

### Example-1

Determine the volume/volume percent solution made by combining 25 mL of ethanol with enough water to produce 200 mL of the solution.

**Solution: **Given parameters are Volume of solute is 25 mL Volume of the solution is 200 mL Substitute the values in the given formula,

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

= {25 mL / 200 mL }x 100%

Therefore, the Volume percent = 12.5 %

### Example-2

A solution is prepared by dissolving 90 mL of hydrogen peroxide in enough water to make 3000 mL of solution. Identify the concentration of the hydrogen peroxide solution.

**Solution:** The given parameters are Volume of solute is 90 mL Volume of solution is 3000 mL. Substitute the values in the given formula,

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

= 90 mL/ 3000mL x 100%

Therefore, the Volume percent = 3 %

### Example-3

A solution of propanol (CH_{3}CH_{2}CH_{2}OH) is prepared by dissolving 67 mL in enough water to have a final volume of 250 mL. What is the volume percent of the ethanol?

**Solution:** First, it should be identified

Volume of solute = 67 mL

Volume of solution = 250 mL

% V/V = (67 mL/ 250 mL) x 100% = 26.8%

How many mL of HNO_{3} concentrate are needed to prepare 250 mL of solution 4%?

First, identify the data available:

Volume of solute =?

Volume of solution = 250 mL

% V/V = 4% Volume_{solute} = %V/V x Volume_{solution} / 100%

Therefore, the Volume_{solute} = 4% x 250 mL / 100% = 10 mL of HNO3 are needed for preparing

### Example-4

What is the % v/v of a solution that has 5.0 mL of hydrochloric acid (HCl) diluted to 100 mL with deionized water?

**Solution:**

X % = 5.0 mL HCl/100 mL of solution

X/100 = 5.0/100

Cross multiplying,

100X = 500 X = 5.0% % v/v

## Use of Volume Percentage

It is a common formula in chemistry. As the same as molar concentration, it is used for expressing the concentration of solutes in solution. The percent by volume is also widely used in the pharmaceutical field for expressing the concentration of different components in solution.

### When Is Volume Percent Used ?

- Volume percent (vol/vol% or v/v%) should be used whenever a solution is prepared by mixing pure liquid solutions. In particular, it’s useful where miscibility comes into play, as with volume and alcohol.
- Acid and aqueous base reagents are usually described using weight percent (w/w%). An example is concentrated hydrochloric acid, which is 37% HCl w/w. Dilute solutions are often described using weight/volume % (w/v%). An example is 1% sodium dodecyl sulfate. Although it’s always good to cite the units used in percentages and it seems common for people to omit them for w/v%. Also, note “weight” is mass.

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