Chem 2990
Density and Specific Gravity
Dr. Edward Walker
Density, the ratio of mass/voume, has many applications in the chemical industry. The relationship
between mass and volume is an important aspect of the characterization and specification of both solids
and liquids. For example, valuable metals and gem stones are characterized by their densities. Bulk
chemicals are shipped in drums and totes weighing hundreds of pounds. Conversion of pounds to
gallons or into metric equivalents is a critical aspect of trade. Shipping costs are most often determined
by weight. Density can be used to quantify the dissolved solids in liquids. For example, high
concentrations of salt in brines increase the density of these solutions.
๐ท๐๐๐ ๐๐ก๐ฆ = ๐ = ๐
๐ , ๐คโ๐๐๐ ๐ = ๐๐๐ ๐ ๐๐๐ ๐ = ๐ฃ๐๐๐ข๐๐
The most common laboratory units for density are g/cm3 (g/mL), while industrially, a variety of different
units are encountered: lb/gal, lb/ft3, and lb/in3.
Specific gravity is the density of a substance divided by the density of water. The density units cancel,
leaving specific gravity a unitless number. Since we often assume the density of pure water to be 1.0
g/mL, the specific gravity usually agrees closely with density. Temperature changes affect the density of
water, resulting in differences between density and specific gravity of the material being tested.
๐๐๐๐๐๐๐๐ ๐บ๐๐๐ฃ๐๐ก๐ฆ = ๐ท๐๐๐ ๐๐ก๐ฆ ๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐ข๐๐
๐ท๐๐๐ ๐๐ก๐ฆ ๐๐ ๐ค๐๐ก๐๐
Density of Solids
Measurement of the density of an unknown solid is relatively easy. Determine both the mass and the
volume of a substance, then divide the mass by the volume to calculate its density.
Archimedes (ca. 287-212 BC) was a Greek mathematician who is credited with first discovering and
characterizing the mass-to-volume relationship of materials. The king Hiero supposedly challenged
Archimedes to find out if his goldsmith had replaced some of the kingโs gold with silver when making a
wreath-like crown. But, of course, the king will not allow Archimedes to ruin the crown by cutting into
it. While struggling with this, he notices that as he gets into a bathtub, the water rises up (overflows) by
a volume equal to his own bodyโs volume. Realizing he has found a way to measure the volume of
irregular objects such as the crown, he jumps from the tub and runs through the streets screaming
โEureka! Eureka!โ (โIโve found it!โ Iโve found it.โ) Knowing the mass and the volume allows the
calculation of density. By comparing the different densities of gold and other pure metals, he was able
to determine the purity of the gold in the crown. History is somewhat ambivalent on the fate of the
goldsmith.
Archimedes continued his studies and eventually went on to write his law of buoyancy, โThe buoyant
force on an object is equal to the weight of the fluid displaced by the object.โ So, in the case of water,
the mass of the water displaced is essentially also the volume of water displaced (assuming 1 mL of pure
water has a mass of 1 gram.) In other words, solid masses weigh less when submerged in water than
they do in air. The difference in the two masses is the mass of the displaced liquid and in the case of
water the volume of the mass. So, by dividing the mass of the solid in air by the difference between its
mass in air and its mass suspended in water, the density is obtained. Of course, if the liquid is not water,
