How To Calculate Volume Using Specific Gravity

The specific gravity of a substance is the ratio of the density of the substance, generally at a standard temperature of 20 degrees C (68 degrees F), to the density of water at a temperature of 4 degrees C (39.2 degrees F).

Density is temperature dependent, so temperatures are usually specified when referring to density.  The reason why the density of the substance being compared to water is at 20 degrees C is because this is a convenient room temperature for handling the substance.  The reason why water density is determined at 4 degrees C is because this is the temperature at which water reaches its maximum density.

The density of a substance is its mass divided by its volume at a given temperature (p=m/v where "p" equals density, "m" equals mass, and "v" equals volume). Since specific gravity is a ratio that compares the same type of units, specific gravity has no units associated with it, i.e. the specific gravity of water at 4 degrees C is 1.0000.  It is widely used in industry to determine the concentrations of solutions such as acids, brines, and sugar solutions (syrups, juices, and beverage bases).

The specific density (and therefore specific gravity) of a substance can be determined using various tools.  One way to determine specific gravity is to use a digital refractometer to measure the refractive index which is converted using a chart, to specific gravity.  Another method to determine specific gravity is to use a hydrometer. The hydrometer has a scale which is read while "floating" the instrument in the liquid.  A digital density meter or oscillating U-tube meter is also often used in laboratories to determine specific gravity.

If the specific gravity and mass of a liquid is known, the volume of that liquid can be determined mathematically with simple algebra, using the formula V=M x SG (where V= volume, M= mass, and SG= specific gravity).  To determine the volume of a liquid using specific gravity:

1. Obtain the specific gravity of the liquid using a refractometer, digital density meter, hydrometer, or a reference chart.
2. Determine the mass of the substance (weigh it using a gram scale) or assign a fictitious amount that is convenient (such as 100 grams).
3. Assign the values in the formula and solve for V (volume).  For example:  What is the volume of 100 grams of 100% Sulfuric Acid (H2SO4)?  The specific gravity of 100% Sulfuric Acid is about 1.84. Using the formula V=M x SG, the volume of 100 grams of sulfuric acid = 184 ml.

Note:  In reality acids are generally not 100% pure, so when using the specific gravity of an acid to calculate volume, be certain that the specific gravity pertains to the exact concentration of the acid.