Pharmaceutical Principles
Lec. 4
Density and Specific Gravity
Density: is mass per unit volume of a substance. It is usually expressed as grams per milliliter.
It is calculated as follows:
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
Thus, if 10 ml of sulfuric acid weighs 18 g, its density is:
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
18
10
= 1.8 g/mL.
Specific Gravity
Specific gravity (sp gr) is a ratio of the weight of a substance to the weight of an equal volume
of water, both substances at the same temperature.
Specific gravity is calculated by:
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 =
𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒 𝑤𝑒𝑖𝑔ℎ𝑡
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
Thus, if 10 mL of sulfuric acid weighs 18 g, and 10 mL of water, under similar conditions,
weighs 10g, the specific gravity of the acid is:
Sp gr = 18/10 = 1.8
Notes:
 Sp gr is unitless (why?).
 In practice, the calculations of the density and specific gravity are the same.
 Substances that have a specific gravity less than 1 are lighter than water.
 Substances that have a specific gravity greater than 1 are heavier than water (figure 1).
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Figure 1: Example of three liquids in a test tube. Mineral oil is lighter than water and
chloroform is heavier.
Pycnometer
Pycnometer is a special glass bottle used to determine specific gravity (Figure:2). In
using a pycnometer, it is first weighed empty and then weighed again when filled with
water. The weight of the water is calculated by the difference. Since 1 g of water equals 1
mL, the exact volume of the pycnometer becomes known. Then, when any other liquid
subsequently is placed in the pycnometer, it is of equal volume to the water, and its
specific gravity can be determined.
Figure 2: The pycnometer
Example: A 50 mL pycnometer is found to weigh 120 g when empty, 171 g when filled
with water, and 160 g when filled with an unknown liquid. Calculate the specific gravity
of the unknown liquid.
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Weight of water: 171 g – 120 g = 51 g
Weight of unknown liquid: 160 g – 120 g = 40 g
Sp gr = 40 g/51 g = 0.78, answer.
Example: A pycnometer weighs 23.66 g . When filled with water, it weighs 72.95 g;
when filled with another liquid, it weighs 73.56 g. What is the specific gravity of the
liquid?
Weight of water: 72.95 g - 23.66 g = 49.29 g
Weight of unknown liquid: 73.56 g - 23.66 g = 49.90 g
Sp gr =49.90 g/ 49.29 g = 1.012, answer.
Calculations Involving Specific Gravity
Example: If 54.96 mL of an oil weighs 52.78g, what is the specific gravity of the oil?
We should first weigh a volume of water equal to that of the oil, i.e. 54.96 mL. Since the
1 mL of water equals to 1 g, so 54.96 mL equals to 54.96 g. Thus:
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 =
𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒 𝑤𝑒𝑖𝑔ℎ𝑡
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
= 52.78(g)/ 54.96(g) = 0.96, answer.
Example: What is the weight, in grams, of 3620 mL of alcohol with a specific gravity of
0.820?
3620 mL of water weigh 3620 g, Then:
3620 g X 0.820 = 2968 g, answer.
Example: What is the volume, in milliliters, of 492 g of nitric acid with a specific gravity
of 1.40?
492 g of water measure 492 mL
492 mL/1.40 = 351 mL, answer.
Example: What is the volume, in milliliters, of one lb of methyl salicylate with a specific
gravity of 1.185?
1 lb = 454 g
454 mL/1.185 = 383.1 mL, answer.
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Example:
Rx
- Lactic Acid
1.5 g
- Salicylic Acid
1.5 g
- Flexible Collodion
ad
15 mL
Sig: Apply one drop to wart twice a day.
Label: Wart remover. For external use only.
Lactic acid is available as a liquid containing 85 g of the acid in 100 g of solution (sp.gr.
1.21). Calculate the quantity of this solution, in milliliters, needed to fill the prescription.
Answer: Quantity of lactic acid needed to fill the prescription is 1.5 g
Source of lactic acid: liquid containing 85 g/ 100 g; then:
85 g
100 g
1.5 g
X
--------------------X= 1.76 g of the liquid needed. Since we need mL and not g, then:
Sp gr = weight/volume
1.21 = 1.76 / volume
Volume = 1.46 mL, answer.
Example: If 250 mL of alcohol weighs 203 g, what is its density?
Density = 203/250 = 0.81 g/mL, answer.
Example: If 150 mL of sorbitol solution weighs 170 g, what is its specific gravity?
Sp gr = 170 g/ 150 mL = 1.13
Example: A Ringer’s solution has the following formula:
- Sodium chloride
8.6 g
- Potassium chloride
0.3 g
- Calcium chloride
0.33 g
- PEG
60 g
- Water for injection
ad
1000 mL
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Answer: Assuming that 980 mL of water is used in preparing the solution, calculate its
specific gravity.
980 mL of water = 980 g
Sp gr = weight/volume
= (8.6 + 0.3 + 0.33 +60 + 980)/1000
= 1.04
H.W: Solve the practice problems number 2, 3, 4, 17, 22, 23, 25, 27, 29 and 34 page 75 in
your textbook.
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