Distance Learning Math Index
Websites for Those Who Need Help
Homepage

Expressions of Concentrations
Density and Specific Gravity

Density means weight per unit volume.  There are 62.4 pounds of water per 1 cubic foot.  This means that a tank of volume 1 cubic foot, filled with water, would contain 62.4 pounds of water.  The density of all substances depends on the temperature.  For example, at 32°F the density of water is 62.41 pounds/ft3;  at 62°F the density of water is 62.36 pounds/ft3.  For most practical purposes the density of water can be considered equal to 62.4 pounds/ft3.  The following table lists weight-volume relationships of water in different units:

 Weight-Volume Water Relationships 1 cubic foot = 62.4 pounds 1 gallon = 8.33 pounds 1 liter = 1000 grams  =  1 kg 1 milliliter = 1 gram

Specific gravity is defined as the ratio of the density of a substance to the density of water.  Written mathematically:

Example 1:

The density of lead is 708 pounds per cubic foot.  What is the specific gravity of lead?

Solution:  Using the above equation,

Substances with higher specific gravity will settle more quickly than substances with lower specific gravity  A grit chamber is designed to remove particles with larger specific gravity than a settling tank.

Concentrations

The strengths of pollutants or substances in water are expressed in a number of ways:

1. parts per million (ppm)
2. milligrams per liter (mg/L)
3. percent (%)

Parts per million, formerly used most frequently, can, in most cases, be considered equivalent to milligrams per liter.  Parts per million is a weight to a weight ratio.  For example, a suspended solids concentration of 200 ppm is equivalent to saying there exists 200 lbs of suspended solids for every one million pounds of sampled water.

Milligrams per liter is a weight to volume ratio.  A suspended solids concentration of 200 mg/L means that one liter of sampled water will contain 200 milligrams of suspended solids.

To say that 200 mg/L equals 200 ppm would mean that one liter of sampled water weighs one million milligrams.  Then, 200 mg/L would be rewritten 200 mg per million milligrams of sampled water which is a parts per million weight to weight ratio.  The Weight-Volume Water Relationship indicates that one liter of water weighs 1000 grams which is equal to one million milligrams.  Therefore if one liter of water weighs one million milligrams then 200 ppm = 200 mg/L.  However, one liter of pure water weighs one million milligrams.  If the water contains pollutants, one liter will no longer by exactly equal to one million milligrams.  Then 200 mg/L will no longer be exactly equal to 200 ppm.  Another way of stating this is, if the specific gravity of a water sample is not equal to one, then ppm is not exactly equal to milligrams per liter.

Example 2:

One liter of raw sewage was found to weigh 1002 grams. (1,002,000 mg).  What is the specific gravity of this sample?

Solution:

We previously used 62.4 lb/ft3 as the density of water.  Density, however, may also be expressed in metric units, which the table indicates as 1000 grams/liter, so that,

In most cases, the specific gravity of sewage will be very close to 1,000 or 1 liter will weigh approximately 1000 grams and for this reason parts per million can be considered equivalent to milligrams per liter.  Because of this discrepancy, however, the use of milligrams per liter is now the more favorable expression of concentrations.  The use of just milligrams per liter eliminates any opportunity for confusion.

Expression of concentrations in terms of percent is generally used in cases where the concentrations of pollutants are high.  In sludge analyses, for example, results are expressed in terms of percent solids, percent moisture, percent volatile matter, and percent ash.  Percent is a weight to weight ratio.  A 5 percent sludge solids concentration indicates that there are 5 parts of solids per 100 parts of sludge, or 5 pounds of solids per 100 pounds of sludge.

Percent calculations are made by using the following equation:
Example 3:

A 56.3 g sludge sample contained 2.7 g of dry solids.  What is the percent concentration of solids?

Solution: