Editing Relative density (section)

===Pycnometer===
[[File:PycnometerEmpty.jpg|thumb|upright|An empty glass pycnometer and stopper]]
[[File:Pycnometer full.jpg|thumb|upright|A filled pycnometer]]
{{see also|Gas pycnometer}}
A '''pycnometer''' (from {{langx|grc|πυκνός|puknos|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 joint|ground glass]] [[stopper (plug)|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 (element)|mercury]], using an [[analytical balance]].<ref>{{Cite web |title=Pycnometer |url=https://www.che.utah.edu/academic_program/projects_lab/pycnometer/ |access-date=2025-05-30 |website=Chemical Engineering {{!}} University of Utah |language=en-US}}</ref>

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 (packed density)|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
<math display="block"> F_\mathrm{b} = g\left(m_\mathrm{b} - \rho_\mathrm{a}\frac{m_\mathrm{b}}{\rho_\mathrm{b}}\right),</math>
where ''m''<sub>b</sub> is the mass of the bottle and ''g'' the [[gravitational acceleration]] at the location at which the measurements are being made. ''ρ''<sub>a</sub> is the density of the air at the ambient pressure and ''ρ''<sub>b</sub> 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#Archimedes' principle|Archimedes Principle]] must be subtracted. The bottle is 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:
<math display="block"> F_\mathrm{w} = g\left(m_\mathrm{b} - \rho_\mathrm{a} \frac{m_\mathrm{b}}{\rho_\mathrm{b}} + V\rho_\mathrm{w} - V\rho_\mathrm{a}\right). </math>

If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain.
<math display="block">F_\mathrm{w,n} = gV( \rho_\mathrm{w} - \rho_\mathrm{a}),</math>
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:
<math display="block">F_\mathrm{s,n} = gV(\rho_\mathrm{s} - \rho_\mathrm{a}),</math>
where ''ρ''<sub>s</sub> is the density of the sample. The ratio of the sample and water forces is:
<math display="block">SG_\mathrm{A} = \frac{gV(\rho_\mathrm{s} - \rho_\mathrm{a})}{gV( \rho_\mathrm{w} - \rho_\mathrm{a})} = \frac{\rho_\mathrm{s} - \rho_\mathrm{a}}{\rho_\mathrm{w} - \rho_\mathrm{a}}. </math>

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 ''RD''<sub>A</sub> depend on the actual volume of the pycnometer.

Further manipulation and finally substitution of ''RD''<sub>V</sub>, the true relative density (the subscript V is used because this is often referred to as the relative density {{lang|la|in vacuo}}), for ''ρ''<sub>s</sub>/''ρ''<sub>w</sub> gives the relationship between apparent and true relative density:

<math display="block">RD_\mathrm{A}= {{\rho_\mathrm{s} \over \rho_\mathrm{w}}-{\rho_\mathrm{a} \over \rho_\mathrm{w}} \over 1 - {\rho_\mathrm{a} \over \rho_\mathrm{w}}} ={RD_\mathrm{V}-{\rho_\mathrm{a} \over \rho_\mathrm{w}} \over 1 - {\rho_\mathrm{a} \over \rho_\mathrm{w}}}.</math>

In the usual case we will have measured weights and want the true relative density. This is found from
<math display="block">RD_\mathrm{V} = RD_\mathrm{A} - {\rho_\mathrm{a} \over \rho_\mathrm{w} }(RD_\mathrm{A}-1).</math>

Since the density of dry air at 101.325&nbsp;kPa at 20&nbsp;°C is<ref>DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density</ref> 0.001205&nbsp;g/cm<sup>3</sup> and that of water is 0.998203&nbsp;g/cm<sup>3</sup> we see that the difference between true and apparent relative densities for a substance with relative density (20&nbsp;°C/20&nbsp;°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) the correction is even smaller.

The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and [[ASTM International|ASTM]] standard: ASTM D854.

'''Types'''

* [[Gay-Lussac]], pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 mL
* as above, with ground-in [[thermometer]], adjusted, side tube with cap
* Hubbard, for [[bitumen]] and [[heavy crude oil]]s, cylindrical type, [[ASTM]] D 70, 24 mL
* as above, conical type, ASTM D 115 and D 234, 25 mL
* Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL