Measuring Density with Laboratory Balance

Use Your Balance and a Density Kit to Determine the Density of Solid, Liquid and Viscous Substances

The best procedures for density determination of solids are the buoyancy and displacement methods, both of which are based on Archimedes' Principle. Prerequisite for these methods is the use of a liquid with known density that does not react with the sample material, but wets it thoroughly. A wetting agent can be added to the liquid.

The integrated balance application provides step-by-step instructions. Excellence level balances have workflows for 5 different density determination methods. Advanced and Standard level balances have workflows for 2.

In conjunction with the Density Kit, the optional 10 mL glass sinker enables you to determine the density of liquids. The difference of the weight of the sinker in air and in the liquid is used to calculate the density. Alternatively, a pycnometer or digital density meter can be used.

The weighing basket on the Density Kit can be inverted so that lighter samples are held under the liquid and cannot float to the surface. If you experience that the buoyancy force is greater than the basket apparatus, place an additional weight on the top weighing pan of the Density Kit and restart the density determination procedure. Alternatively, use a different reference liquid with a lower density.

Add a few drops of wetting agent to the reference liquid. Leave it standing overnight to release any dissolved gas. Use a soft brush to brush the bubbles off the sample and the Density Kit.

The accuracy of density measurement is influenced by the tolerance of the method (air bubbles etc.) and the temperature measurement as well as the accuracy of the weight measurements. Every measurement on ANY balance is subject to uncertainty. Understanding this uncertainty is the key to ensuring accurate weighing results. It is not the readability that determines the accuracy of a weighing instrument, but rather its repeatability and the minimum net sample weight.

To find the appropriate balance for your needs, you need to know the smallest amount you want to weigh and how accurately you need to weigh it (i.e. at what tolerance).

METTLER TOLEDO's global weighing standard, GWP^{^®} helps you choose the right balance to meet your application requirements. Ask your local representative for a free balance recommendation. Determine if your existing balance meets your quality requirements.

GWP Recommendation

ISO 1183-1 compliance requires a balance with a readability of 0.1 mg or less and specifies that the sample should preferably have a mass of at least 1 g. Weighing samples of at least 1 g on a balance with readability 0.1 mg will not generally violate the minimum net sample weight requirement of the balance. The required balance accuracy however, should be considered in conjunction with your required process tolerance. Our free GWP^{^®} Recommendation service can help you select the right balance for your specific needs.

GWP Recommendation

There are several steps in the density measurement process, and sometimes you need to wait a while for the balance to settle so it can be easy to get lost off, especially when you are busy with multiple tasks. The integrated balance application provides step-by-step instructions. You confirm each instruction by pressing the OK button, so you always know where you are.

Connect a barcode reader to your balance to enable meta-data, such as sample ID, lot number and order number etc. to be read-in directly without any errors. With the METTLER TOLEDO P-50 line of printers, the meta-data, plus the date and time of the measurement, can be printed out alongside the results.

When you have a series of density determinations to make, the statistics option on METTLER TOLEDO balances enables you to quickly identify trends in your data assisting you to make decisions on a course of action where appropriate.

XPE, XSE, MS-TS, ML-T and ME-T balances have a built-in density database for the most commonly used reference liquids. The density value is adjusted according to the temperature you input.

The density application on XPE, XSE and MS-TS balances does all the calculations for you. You only need to input the temperature and select the reference liquid used. The balance records the weight values and calculates the density automatically.

The density application on MS-TS, ML-T and ME-T balances allows you to create a report of your density determination series which you can print out or save on a USB stick. XPE and XSE balances in combination with LabX software offer a higher degree of report customization with graphs and charts, and the report can be sent straight to your LIMS or EPR.

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Measuring density of a sample is an important quality parameter of both raw materials and finished products. Various techniques enable the density of solid, viscous and liquid materials to be accurately determined e.g. metals, plastics, chemicals, lubricants and food.

Density for Quality Control

A variation in a raw material, indicated by a change in the density, may have a detrimental outcome on the functioning or quality of the final product. Density measurement of raw materials can be used to confirm the purity of the material. If a substance has been adulterated with a cheaper alternative, the measured density of the composite material will be different from the pure substance.

Density can also be used to ensure homogeneity. If a manufactured part is not homogenous, key performance attributes such as strength and crack resistance can be affected. For example, an internal air bubble could ultimately cause a part to fail when placed under stress. Random sampling of parts is a simple and cost-effective way to monitor ongoing quality.

Why Accurate Weighing is Crucial

Common laboratory gravimetric procedures for determining density are the buoyancy technique, the displacement principle and the pycnometer method.

The most widely used method is the buoyancy technique which utilizes Archimedes' principle: a body immersed in fluid indicates an apparent loss in weight equal to the weight of the fluid it displaces. This ancient principle, from around 200 BC, is precisely what is used nowadays to determine density gravimetrically. Accurate density measurement therefore is highly dependent upon accurate weight values.

Jump to one of the following section to explore and learn more:

Application Workflow and Challenges
METTLER TOLEDO Solutions
FAQ's

Workflow of the Determination of Density in Solids Samples

Buoyancy Method - Archimedes' Principle in Action

Archimedes' principle states that a body immersed partially or fully in fluid experiences a buoyant force acting upwards on it. The magnitude of this force is equivalent
to the weight of the fluid displaced by the body.

The solid is weighed in air (A) and then again (B) in the auxiliary liquid with a known density. The density of the solid ρ can be calculated as follows:

Calculation formula for density in solid sample

ρ = Density of the sample

A = Weight of the sample in air

B = Weight of the sample in the auxiliary liquid

ρ₀ = Density of the auxiliary liquid

ρ_L = Density of air

The temperature of the liquid must be taken into account as this can cause density changes of the order of magnitude 0.001 to 0.1 per °C, the effect
of which can be seen in the third decimal place of the result.

	Gravimetric, Buoyancy	Gravimetric, Displacement	Pycnometer	Digital Density Meter
Methods	Beaker for auxiliary liquid stands on a platform or below the balance.	Beaker for auxiliary liquid stands on the balance.	Glass beaker of defined volume.	Oscillating tube technology
Suitable for	Solids Liquids (with glass sinker)	Pasty substances(with gamma sphere) Liquids (with glass sinker) Solids	Liquids, Dispersions Powder Granules	Liquids Gases
Advantages	Quick process Flexible with regards to sample size Weighing instrument already available	Quick process Weighing instrument already available	Accurate method Weighing instrument already available	Quick process Exact temperature control by Peltier elements Automatic density measurement Small sample volumes
Disadvantages	Temperature sensitive Sample must be wet very carefully Air bubbles must not be trapped	Temperature sensitive Large sample volume required	Temperature sensitive Labour-intensive Time-consuming Air bubbles must not be trapped	Viscous samples require a viscosity correction (available in modern instruments).

If you know the mass and volume of a sample (solids or liquids), its density can be calculated from:

Calculation of density by mass and volume

The Difficulty with Volume

It's quite simple to weigh a sample accurately, but determining the volume of a sample accurately can be challenging.

Buoyancy

The buoyancy method avoids the problem of determining volume because it involves weighing the sample twice in two different mediums (air and a liquid). The volume can therefore be assumed to be constant in both situations.

Displacement

In the simplest application of the displacement method, the volume of a solid sample is determined by observing the increase in the level of the liquid in which the sample is submerged.
Conversely, when an object of known volume is submerged in a liquid with unknown density, the difference in the weight values (in air and in the liquid) can be used to determine the density of the liquid.

Pycnometer

A pycnometer is a specially designed glass flask, usually with a defined volume. It is most often used to determine the density of liquids. The pycnometer is first weighed empty and then full of the liquid under investigation. The difference (i.e. the mass of the sample) divided by the volume of the pycnometer is the density of the sample.
The pycnometer method can also be used for determining the density of powder samples or granulates.

Digital Density Meter

A hollow glass tube vibrates at a certain frequency. The frequency changes when the tube is filled with different substances: the higher the mass of the sample, the lower the frequency. Digital density meters work by measuring the frequency and converting it into density.

Please see the table below for a comparison of these four different methods.

	Gravimetric, Buoyancy	Gravimetric, Displacement	Pycnometer	Digital Density Meter
Methods	Beaker for auxiliary liquid stands on a platform or below the balance.	Beaker for auxiliary liquid stands on the balance.	Glass beaker of defined volume.	Oscillating tube technology
Suitable for	Solids Liquids (with glass sinker)	Pasty substances(with gamma sphere) Liquids (with glass sinker) Solids	Liquids, Dispersions Powder Granules	Liquids
Measuring principle for a solid sample	The sample is weighed once in air and once immersed in the auxiliary liquid with known density. Density of the solid sample can be determined from the known density of the liquid and the two mass values. ρ,= Density of the sample A,= Weight of the sample in air B,= Weight of the sample in the auxiliary liquid ρ0,= Density of the auxiliary liquid ρL,= Density of air	The auxiliary liquid with known density is weighed before and after immersing the sample (tare can be used to measure mass difference directly). Using the mass difference and the liquid density the volume of the sample can be determined. This is then used together with the mass of the sample to calculate its density.	The pycnometer is first weighed empty and then again full with the reference liquid of known density. The powder is added to the cleaned and dried pycnometer. It is weighed to determine the weight of the powder sample. The pycnometer is then topped up with the same liquid in which the powder must be completely insoluble. The pycnometer is weighed again. The weight of the displaced liquid can then be determined, and hence the density of the powder calculated.	n/a
Measuring principle for a liquid sample	The reference body with known volume (glass sinker) is weighed once in air and once in the liquid with unknown density. Density of the liquid can be determined from the known volume of the reference body and the two mass values. ρ,= Density of the liquid sample α,= Weight correction factor (0.99985), to take the atmospheric buoyancy of the adjustment weight into account A,= Weight of the reference body in air B,= Weight of the reference body in the liquid V,= Known volume of the reference body ρL,= Density of air	The weight of the liquid with the unknown density is measured before (tare) and after immersing the reference body (gamma sphere or glass sinker). Using the mass difference and the known volume of the reference body, the density of the liquid sample can be determined.	The pycnometer is first weighed empty and then again full with the liquid sample. The mass difference divided by the volume of the pycnometer is the density of the liquid.	The sample is added to a U-shaped hollow glass tube in the device. The density of the sample is determined by measuring the frequency of vibration of the tube. The lower the frequency of vibration, the higher the density of the sample.

Density Determination of Liquids with Digital Density Meters

If more than just the density is of interest, digital density meters measure density, specific gravity and other related attributes of liquid samples (i.e. alcohol%, BRIX°, API degrees) with high precision and short measuring time.

Measurement with Digital Density Meters

Density Standards

Many standards and norms exist for the determination of density in solids samples. Some of the most commonly used are:

ISO 1183-1: Plastics — Methods for determining the density of non-cellular plastics
OIML G 14: Density measurement according OIML
ASTM-D-792: Standard Test Methods for Density and Specific Gravity Standard

ISO 1183-1 specifies the use of a 4-decimal place analytical balance.

The Confusion with Bulk Density

Bulk density is a measure of how many particles, parts or pieces are contained within a measured volume. Bulk density is not a property of the material itself. Bulk density includes the spaces between the particles or items as well as any voids within the items themselves. Bulk density can vary depending on how the material is handled; shaking a container, for example, allows parts to settle, increasing the overall bulk density.

Do You Need Support?

Measurement of density is an extremely important quality parameter of both raw materials and finished products. We understand there are many factors which must be considered to ensure accurate density results. If you need support with density determination or want advice on which balance or Density Kit to purchase, our team of experts is here to help.
Do not hesitate to contact us for assistance.

Challanges of Density Measurement of Solids

The Challenges of Accurate Density Measurement of Solids

Bubbles

By far, the biggest source of error in density measurement is the limited wettability of the sample. When the sample is submerged in liquid, it is crucial that all bubbles adhering to the sample and equipment are removed. Any remaining bubbles will cause a buoyancy effect and distort the density calculation. (A bubble with a 1 mm diameter causes a buoyancy of 0.5 mg.) We recommend:

Use a wetting agent or organic liquids (the density change experienced by distilled water by the addition of a few drops of wetting agent can be neglected).
Degrease solvent-resistance solids
Clean equipment regularly
Do not touch parts to be submerged with bare hands
Use a fine brush to remove stubborn air bubbles

Temperature

Solids are generally so insensitive to ambient temperature fluctuations that the corresponding density changes are of no consequence. However, as density determination is carried out with an auxiliary liquid, temperature must be taken into account. Temperature has a greater effect with liquids and causes density changes of order of magnitude 0.1 to 1‰ per °C.

This effect is already apparent in the third decimal place of the result. To obtain accurate results, we recommend that you always take the temperature of the auxiliary liquid into account in all density determinations. Values are available in dedicated books of tables. The densities of the most important reference liquids (H₂O and Ethanol) are stored in the balance.

Weighing

As mentioned above, weighing plays an important part in the accurate determination of density so it is critical that the balance used meets the needs of the density application. For small samples, the minimum net sample weight of the balance must be considered – weighing a sample below this weight cannot be trusted to be of the required level of accuracy.

Data Handling

Manual transcription of sample data, weight values and density calculations is time consuming and prone to error.

METTLER TOLEDO Solution to Determine the Density of Samples Gravimetrically

Most METTLER TOLEDO analytical and precision balances with 1 mg or higher readability can be easily used to determine density via the buoyancy technique with the use of a density kit which is mounted on the balance in a few simple steps.

To measure density of solids using a balance is an easy and convenient process that delivers highly reliable results when compared to other methods in which the volume of the part is determined independently of the weight. By converting a standard laboratory balance with the addition of a Density Kit, you avoid the necessity to purchase a dedicated piece of equipment to carry out this straightforward procedure. This makes the purchase of the Density Kit accessory a very cost-effective investment. With the addition of a glass sinker of known volume, the Density Kit can also be used for determining the density of liquid samples.

The built-in Density application provides step-by-step instructions making it easy for even untrained operators to use. Benefit further from:

High flexibility to accommodate individual process needs
Automatic density calculations for solids and liquids including temperature adjustment of the reference liquid
Statistic evaluation of multiple samples
All results, including User, Sample ID, Lot Number, Time and Date can either be printed or saved on a USB stick.

Measure Density of Bulky Samples

For bulky samples, which do not fit into the Density Kit, METTLER TOLEDO precision balances with 0.1 g and 0.01 g readability can be converted to weigh below the balance through the addition of a dedicated hook. The density measurement principle is exactly the same; the sample is weighed in air and again in a reference liquid.

Video: Density Determination in Action

Watch how simple it is to measure density on your METTLER TOLEDO laboratory balance. The Density Kit enables you to determine the density of solid, liquid, porous and viscous substances. With step-by-step instructions and automatic calculations, the whole process is easy.

Density determination for plastics quality

Free Application Note: Easy Density Determination for Consistent Plastics Quality

The determination of density in plastic is essential for consistent plastic quality. The application note describes how the density of solid plastic parts can be easily determined using the integrated application on a METTLER TOLEDO MS-TS, ML-T or ME-T analytical balance with a Density Kit.

Extended Data Management and Process Security

LabX Software connects all instruments

The combination of a METTLER TOLEDO Excellence level balance and LabX software offers a higher level of data management and process security. Excellence analytical and precision balances can be set up with a Density Kit for density determination. LabX ensures that your density SOP is followed precisely. LabX records all weight values, performs all calculations and saves all results securely in a central database. All the data related to your density application can be transferred directly to your internal data management system.