# Determining concentration by weight and volume

Coolants, cleaners, and polymer quenchants are often mixed in the field using volume percent. But a lab usually figures concentrations by weight percent. Here is the difference between the methods.

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In this column, I will discuss the different types of concentration percentages and how to convert them to each other. This is really a companion article to the one published in the April 2023 issue of Gear Solutions (pp 26-27).

### Introduction

There are a variety of liquid-based fluids used in a typical manufacturing facility. Coolants, cleaners, forming and forging compounds, and quenchants may be water soluble and require concentration control. It is often up to the user to mix the purchased chemicals with water to the desired concentration.

In the laboratory it is customary practice to determine concentrations of polymer quenchants by weight. However, in the field, it is generally more practical to determine concentration by volume. For instance, if a customer has a quench tank of 5,000 gallons, and needs a 10 percent solution, it is generally easier to fill the quench tank with 4,500 gallons of water and then add 500 gallons of polymer quenchant. It is generally not practical to weigh out a 10 percent solution in the field.

Chemical concentrations are typically identified in several different methods and are expressed using percent composition by mass, volume percent, mole fraction, molarity, or normality. In this short white paper, we will focus on concentration by mass and concentration by volume.

### Concentration by Mass Percent (%m/m)

This is the mass of the solute divided by the mass of the solution (mass of the solute plus the mass of the solvent), multiplied by 100 to get percent:

Example: Determine the percent composition by mass of a 100-gram NaCl solution that contains 20 grams of NaCl.

Solution: 20 grams NaCl/100 g solution x 100 = 20% NaCl solution by weight.

### Concentration by Volume Percent (%v/v)

Volume percent is most often used when preparing solution of liquids. This is defined as:

Notice that the volume percentage is based on the volume of the solution and not the volume of the solvent. The liquid volumes are not necessarily additive. For instance, in some alcohol solutions in water, the total volume will be less than the sum of the solute and solvent.

Example: Determine the percent composition by volume of 20 ml of ethanol in 100 ml of solution.

Solution: 20 ml ethanol/100 ml solution (ethanol + water) x 100 = 20% ethanol solution by volume.

The calculation of volume percent is generally accurate for the calculation of liquids provided that the liquids have nearly the same specific gravity (Sp). If the two liquids to be mixed have different specific gravities, then there will be differences in the concentration by volume and the concentration by weight.

### Converting from Mass Percent to Volume Percent

Specific gravity is defined as:

where Sp is the specific gravity; ρ is the density of the substance, in kg/m3 and ρo is the density of pure water at 4°C (997 kg/m3). The density of water is often just rounded to 1,000 kg/m3.

Volume is mass/density or mass equals volume x density. If I know the specific gravity, I can determine the density from

Using these relationships above, the mass percent (%m/m) is:

While this is more complicated, it allows the conversion of volume percent to mass percent, provided that the densities of the solute and solvent are known. If the solvent is water, then ρ0 and Spsolvent = 1.0.

### Application to Polymer Quenchants

Water has a specific gravity (Sp) = 1.0. Polymer quenchants have a specific gravity greater than water. A table of typical specific gravities of polymer quenchants commonly used at Quaker Houghton are shown in Table 1. For other manufacturers, you should contact them for the specific gravity of their products. Depending on the product, the specific gravity is between 2-9 percent greater than water. At low concentrations, the errors can be as much as 8 percent. In other words, if you have a solution of 5 percent by volume, the concentration measured by the laboratory would be about 5.4 percent weight. At higher concentrations, the error decreases, but because of the higher overall concentration, the difference in the amount of polymer is greater.

For instance, a 20 percent concentration by volume would be equivalent to 21.3 percent by weight. Depending on the allowable concentration specification range, this variation may or may not be acceptable. This variation can also explain why there is a difference between field and laboratory determined concentrations.

### Conclusions

Often, coolants, cleaners, and polymer quenchants are mixed in the field using volume percent. However, a laboratory usually determines concentrations using weight percent. In this short article, the difference between mass percent and volume percent is described. If the density or specific gravity is known, then conversion from one type of measurement can be accomplished. This difference can often explain the difference between laboratory and field determined concentrations.