 # Density Measurements With a Balance

By Aimee O'Driscoll, 18 December 2020

Density is an important parameter in many applications, in particular in quality control. For example, variations in the density of a solid can indicate air pockets that could jeopardize the integrity of the material. Similarly, a change in density could indicate that a liquid or solid is impure and contains contaminants.

Calculating density seems straightforward as it simply involves dividing the mass of the matter by its volume. However, in practice, the volume measurement can be tricky. Thankfully, there are methods available to help you accurately measure density.

One of the most popular methods is the buoyancy technique, which follows Archimedes’ principle:

“Any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force, the magnitude of which is equal to the weight of the fluid displaced by the body.”

The buoyancy technique can be carried out in a relatively straightforward manner using an analytical balance fitted with a special density kit.

In this post, we reveal how density measurements are performed for solids and liquids and discuss some of the density kit options available.

## How Solid Density Measurements Are Performed With a Balance

The most common setup involves a beaker placed on the balance with one weighing pan above the beaker and another suspended inside, as shown in the image below. The beaker is filled with a reference liquid of known density. Common reference liquids are water, ethanol, and sodium chloride solution. An Ohaus Density Kit for Solids.

The basic steps involved are:

1. Weigh the sample in air.
2. Weigh the sample again in the reference liquid.
3. Calculate the density based on these measurements.

Many balances will perform this calculation for you but here is the formula for reference:

ρ = (A / (A - B) ) . (ρ0 - ρL) + ρL

Where:

• ρ = Sample density
• A = Sample weight in air
• B = Sample weight in auxiliary liquid
• ρ0 = Auxiliary liquid density
• ρL = Air density

Note that the temperature of the reference liquid is important (more on that below), so you will need to input this for the balance to calculate an accurate density.

Here are some examples of density kits. These are typically compatible with a range of balances from their respective brands. A Radwag Density Determination KIT and a Density Kit for Sartorius Precision Balances.

When using these kits, the balance will guide you through the process to help minimize the chance of making errors when measuring density.

### Potential Issues When Measuring Solid Density

There are some issues you may come across when measuring solid density, but these can be overcome. Here are the main problems you might encounter:

• Limited wettability: This is one of the biggest barriers to surpass. When a solid is submerged in a liquid, it’s natural for bubbles to form on the surface of the solid. These can cause a buoyancy effect and introduce errors in the density calculation. Adding a few drops of wetting agent to the reference liquid can help avoid bubbles while having a negligible impact on the density of the liquid.
• Temperature: While small ambient temperature fluctuations have a negligible impact on the density of solids, they have a bigger effect on the density of liquids. A fluctuation of 1°C can cause a density change of 0.1–1 percent. There are tables available that tell you the densities of most common reference liquids at a given temperature. However, many balances that carry out the calculation for you will have these values stored, so you just need to input the temperature.
• Low-density solids: What if the density of the solid is lower than that of water, such that the solid floats? In some density kits, you can invert the basket so that it pushes the solid down and keeps it below the surface of the water. Others come with a separate piece of apparatus designed specifically for this purpose. If the buoyancy force is too great, you can use an additional weight on the pan. Note that you will have to start the whole measurement process over after placing the weight on the pan.

## How Liquid Density Measurements Are Performed With a Balance

Liquid density measurements use the same concept as solid density measurements but the process is different. This time, the beaker holds the sample liquid and you weigh a reference body (a glass sinker) of known volume. Below are some examples of glass sinkers: An Ohaus Sinker Glass Liquid Density Kit and the sinker from the Radwag Density Determination KIT.

Here are the basic steps:

1. Weigh the reference body in air.
2. Weigh the reference body in the sample liquid.
3. Calculate the density based on these measurements.

As with solid density, many balances will perform this calculation for you, but here is the formula for reference:

ρ = α . ( (A - B) / V ) + ρL

Where:

• ρ = Liquid sample density
• α = Weight correction factor (0.99985)*
• A = Reference body weight in air
• B = Reference body weight in sample liquid
• V = Reference body volume (known)
• ρL = Air density

*The weight correction factor takes into account the atmospheric buoyancy of the weight.

## Density Standards

Note that the equipment and process you use should conform with whichever standards you are following, if any.

Some standards you may be adhering to include:

## Density versus Bulk Density

Sometimes the intrinsic property of density can be confused with the bulk density of a material. However, there is a difference. The bulk density refers to the mass of a bulk quantity of the material divided by the volume it occupies. While the density of a material remains constant, the bulk density can change depending on how it is handled. For example, disturbing a container of powder could cause particles to settle in closer proximity to each other, increasing the bulk density.