Laboratory Tutorials - Determination of Density

Density is defined by the equation: D = M/V

The density of a sample is usually found by determining the mass of a determined volume of the sample. Most often, the most complicated part of the procedure is determining the exact volume of an irregularly shaped solid. It is also difficult to determine the volume of liquids and gases becasue they have no specific shape.

Solids

Using displacement of a liquid to find volume:

If the sample is small enough to fit in a graduated cylinder, this method is a way to find the volume of an irregularly shaped solid. Water is the preferable liquid; however, if the sample is soluble in water, another liquid could be used as long as the sample is more dense than the liquid (i.e. it does not float in the liquid). If using a liquid other than water, you must account for the density of the liquid, since the density of the liquid will be less than or greater than 1 g/mL (the density of water).

The mass of the sample can be determined by weighing the sample on a toploader or analytical balance.
To find volume, start by filling a graduated cylinder with water and recording the volume. (see Figure 1. below)
- Figure 1. Before placing the solid in the graduated cylinder
- Figure 2. After placing the solid in the graduated cylinder
Place the sample into the graduated cylinder. The water level will rise (see Figure 2. above).
Record the new volume of the contents of the cylinder. The difference between this volume and the previous volume is the volume of the sample.

Example: If the mass of the object was 9 g, and the volume in the graduated cylinder changed from 63.0 mL to 67.5 mL, for a net volume of 4.5 mL, then the density would be: 9 g / 4.5 mL = 2 g/mL

Using specific gravity:

Specific gravity is defined as:

SG = M^a/(M^a - M^w)

where M^a is the mass in air and M^w is the mass in water. The density of a sample is equal to its specific gravity multiplied by the density of water. (As above, another liquid of known density can be used if the sample is soluble in water.)

Weigh the sample in air on a toploader or analytical balance and record the mass.
Using a fine wire, hang the sample from a bottom loader and suspend the sample in water and again record the mass.
Determine the specific gravity using the equation given above, then calculate density using the equation D = SG x D_liquid.

Example: If the mass of the object in air is 10 g, and the mass of the object in water is 5 g, the specific gravity would be 10/(10 - 5) = 2. Since the density of water is 1 g/mL, the density of the object is 2 g/mL.

Liquids

Using a pycnometer:

Figure 3. A 5 mL pycnometer
Note that the exact volume is unknown and the pycnometer must be calibrated before use.

The pycnometer that will be used in the density determination must first be calibrated:

Examine the pycnometer to be used. Unless the glassware is visibly dirty, do not clean it.
Place the pycnometer in a drying oven for fifteen to twenty minutes to insure that all residual moisture has been removed from the glass. Let cool before weighing.
Weigh the empty dry pycnometer on an analytical balance and record the mass. As you manipulate the pycnometer, be sure not to touch the glass with your hands as residue and oils from your hands will impact the accuracy of the measurement of the mass.
Fill the pycnometer with water of known temperature. Take the mass of the filled pycnometer. The difference between the mass of the empty pycnometer and the pycnometer when it is full yields the mass of the liquid that is within the pycnometer. The literature value for the density of water at the temperature observed can be used to determine the volume of the pycnometer using the equation:

V = M_H₂O/ D_H₂O

Knowing the exact volume of the pycnometer being used, the density of the unknown fluid can now be determined:

After emptying the pycnometer, place it in the drying oven again for at least an hour. When all the moisture has been removed, allow the glassware to cool in a desiccator.
Weigh the dried, cooled pycnometer on an analytical balance.
Fill the pycnometer with the unknown fluid. Weigh the pycnometer containing the fluid and again take the difference between this mass and the mass of the empty pycnometer.
Knowing the mass of the unknown fluid and the volume of the pycnometer, the density of the unknown fluid can be calculated using the equation:

D = M/V

Gases

Using a gas bulb with stopcock:

Weigh an empty bulb and record the mass.
Fill the bulb with the sample and close the stopcock.
Weigh the bulb again and record the mass. Also note the specific temperature and pressure at the time of weighing.
Find the difference in mass to get the mass of the gas.
Determine volume by filling the bulb with water.