Density, Specific Gravity and Specific Volume

Why do we need this?

In the pharmacy some liquids are easier to measure than to weigh (oils, syrups, glycerol), but a formula may give the quantity in grams. Others are written in millilitres when you want to weigh them. Specific gravity lets you move between weight and volume.

Density

Density is the mass of a substance in one unit of its volume.

density = mass ÷ volume

In pharmacy it is usually written in grams per millilitre (g/mL). Water has a density of 1 g/mL.

Example. 50 mL of a liquid weighs 62.5 g. Density = 62.5 ÷ 50 = 1.25 g/mL.

Specific gravity

Specific gravity (SG), also called relative density, compares a substance with water.

SG = weight of a substance ÷ weight of an equal volume of water

• SG has no units, because it is a ratio of two weights.
• Because 1 mL of water weighs 1 g, the number for SG is the same as the density in g/mL.
• A liquid with SG greater than 1 is heavier than water and sinks in it. A liquid with SG less than 1 is lighter than water and floats on it.
• SG changes slightly with temperature, so it is measured at a stated temperature.

Some common values

Use the value given in the question or in your reference book. Values vary a little between sources.

Converting between weight and volume

weight = volume × SG
volume = weight ÷ SG

A quick check: for a liquid heavier than water (SG above 1), the weight in grams is bigger than the volume in millilitres. For a liquid lighter than water, the weight is smaller.

Example 1. What is the weight of 50 mL of glycerol (SG 1.25)?

• 50 × 1.25 = 62.5 g

Example 2. What is the weight of 200 mL of a liquid with SG 0.90?

• 200 × 0.90 = 180 g

Example 3. What volume does 150 g of syrup (SG 1.33) occupy?

• 150 ÷ 1.33 = 112.78 = 112.8 mL

Example 4. A formula needs 100 g of liquid paraffin (SG 0.87). What volume do you measure?

• 100 ÷ 0.87 = 114.94 = 114.9 mL

Example 5. A prescription needs 30 mL of glycerol (SG 1.25), but your formula is in grams. How many grams?

• 30 × 1.25 = 37.5 g

Specific volume

Specific volume is the volume (in mL) taken up by 1 gram of the substance.

specific volume = 1 ÷ SG

• Glycerol, SG 1.25: specific volume = 1 ÷ 1.25 = 0.8 mL/g
• Alcohol, SG 0.81: specific volume = 1 ÷ 0.81 = 1.23 mL/g

To find a volume: volume = weight × specific volume. For 50 g of alcohol: 50 × 1.2346 = 61.7 mL.

Measuring specific gravity

Specific gravity bottle (pycnometer)

A specific gravity bottle holds an exact volume. You weigh it three times:

1. empty,
2. full of water,
3. full of the liquid.

SG = (weight of liquid) ÷ (weight of water)

Example. Empty bottle 25.0 g. Filled with water 75.0 g. Filled with the liquid 87.5 g.

1. Weight of water = 75.0 − 25.0 = 50.0 g
2. Weight of liquid = 87.5 − 25.0 = 62.5 g
3. SG = 62.5 ÷ 50.0 = 1.25

Remember to subtract the empty bottle each time. Using 87.5 ÷ 75.0 = 1.17 would be a mistake.

Hydrometers

A hydrometer is a weighted glass float that sinks to a depth depending on the density of the liquid. You read the SG from the scale at the liquid surface. Special hydrometers have special names, such as the alcoholmeter (for alcohol), the lactometer (for milk) and the urinometer (for urine).