page_title: Relative density
section_title: Pycnometer
hierarchical_section_title: Relative density / Measurement / Pycnometer
caption_attribution_description: An empty pycnometer, photographed on 5 mm squares.
context_page_description: Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage.
  If a substance's relative density is less than one then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.
  Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm. Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry.
context_section_description: A pycnometer (from Greek: πυκνός (puknos) meaning "dense"), also called pyknometer or specific gravity bottle, is a device used to determine the density of a liquid.  A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus.  This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water or mercury, using an analytical balance.
  If the flask is weighed empty, full of water, and full of a liquid whose relative density is desired, the relative density of the liquid can easily be calculated. The particle density of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample.  The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble.  The weight of the displaced liquid can then be determined, and hence the relative density of the powder.
  A gas pycnometer, the gas-based manifestation of a pycnometer, compares the change in pressure caused by a measured change in a closed volume containing a reference (usually a steel sphere of known volume) with the change in pressure caused by the sample under the same conditions.  The difference in change of pressure represents the volume of the sample as compared to the reference sphere, and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above, or for porous materials into which the liquid would not fully penetrate.
  When a pycnometer is filled to a specific, but not necessarily accurately known volume, V and is placed upon a balance, it will exert a force
  where mb is the mass of the bottle and g the gravitational acceleration at the location at which the measurements are being made. ρₐ is the density of the air at the ambient pressure and ρb is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is, of course, filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted on the pan of the balance becomes:
  If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain.
  where the subscript n indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now:
  where ρₛ is the density of the sample. The ratio of the sample and water forces is:
  This is called the Apparent Relative Density, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a hydrometer (the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does RDA depend on the actual volume of the pycnometer.
  Further manipulation and finally substitution of RDV, the true relative density (the subscript V is used because this is often referred to as the relative density in vacuo), for ρₛ/ρw gives the relationship between apparent and true relative density.
  In the usual case we will have measured weights and want the true relative density. This is found from
  Since the density of dry air at 101.325 kPa at 20 °C is 0.001205 g/cm³ and that of water is 0.998203 g/cm³ we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where the relative density of the sample is close to that of water (for example dilute ethanol solutions) 
caption: An empty glass pycnometer and stopper
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