## Pycnometer

### Pycnometer

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[citation needed].

If the flask is weighed empty, full of water, and full of a liquid whose specific gravity is desired, the specific gravity 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 specific gravity of the powder.

There is also a gas-based manifestation of a pycnometer known as a gas pycnometer. It 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

$F_b = g(m_b - ho_a{m_bover ho_b})$

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:

$F_w = g(m_b - ho_a{m_bover ho_b} + V ho_w - V ho_a).$

If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain.

$F_{w,n} = gV( ho_w - ho_a)$

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:

$F_{s,n} = gV( ho_s - ho_a)$

where ρs is the density of the sample. The ratio of the sample and water forces is:

$SG_A = {gV( ho_s - ho_a) over gV( ho_w - ho_a)} = {( ho_s - ho_a) over ( ho_w - ho_a)}.$

This is called the Apparent Specific Gravity, 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 SGA depend on the actual volume of the pycnometer.

Further manipulation and finally substitution of SGV, the true specific gravity (the subscript V is used because this is often referred to as the specific gravity in vacuo), for ρs/ρw gives the relationship between apparent and true specific gravity.

$SG_A= {{ ho_s over ho_w}-{ ho_a over ho_w} over 1 - { ho_a over ho_w}} ={SG_V-{ ho_a over ho_w} over 1 - { ho_a over ho_w}}$

In the usual case we will have measured weights and want the true specific gravity. This is found from

$SG_V = SG_A - { ho_a over ho_w }(SG_A-1)$

Since the density of dry air at 101.325 kPa at 20 °C is[7] 0.001205 g/cm3 and that of water is 0.998203 g/cm3 we see that the difference between true and apparent specific gravities for a substance with specific gravity (20°C/20°C) of about 1.100 would be 0.000120. Where the specific gravity 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 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 änd heavy oils, 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

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