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Measurement of density

For a homogeneous solid object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate weighing scale or balance and the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid.

A very simple and commonly used instrument for directly measuring the density of a liquid is the hydrometer. A less common device for measuring fluid density is a pycnometer and a similar device for measuring the absolute density of a solid is a gas pycnometer.

Another instrument used to determine the density of a liquid or a gas is the digital density meter, based on the oscillating U-tube principle.

Density of irregular shaped solid object heavier than water

One of the many statements attributed to the Archimedes principle is that an object immersed in a fluid apparently loses weight by an amount equal to the weight of the fluid displaced. That principle makes it possible to determine of the density of a solid object that is denser than water and is so irregular in shape that its volume cannot be measured directly.

First, the object's dry weight in air, $W_{d}$, is measured. Next, the weight of the object while submerged in water, $W_{s}$, is measured. Then the submerged object is removed from the water, the excess surface water is removed and the wet weight in air, $W_{w}$, is measured. The density of the object, $\rho _{o}$, is then obtained from:

$\rho _{o}={\frac {m}{V}}={\frac {W_{d}}{(W_{w}-W_{s})/\rho _{water}}}={\frac {W_{d}\cdot \rho _{water}}{W_{w}-W_{s}}}$

and the volumetric porosity fraction, $p$ can be obtained from:

$p={\frac {W_{w}-W_{d}}{W_{w}-W_{s}}}$

Density of solid objects by x-ray diffraction crytallography

For some crystalline materials, density can be calculated using this equation which is based the molecular mass of the material and on information provided by x-ray crystallography:

${\mbox{density}}={\frac {M\cdot N}{L\cdot a\cdot b\cdot c}}$

where:

M is molecular mass

N is the number of ions, atoms or molecules in a unit cell

L is Loschmidt or Avogadro's constant

a, b, c are the lattice parameters

Figure 1: Cubic lattice structure of crystalline sodium chloride

For example, the cubic lattice structure of crystalline sodium chloride (NaCl) is depicted in the Figure 1.