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FIGURE 5.2 Example of a glass pycnometer affixed with a
thermometer. Glass pycnometers are used to determine the
specific gravities of liquids at specific temperatures. See text
for additional discussion. (Courtesy of DWK Life Sciences.)
FIGURE 5.3 Example of an aluminum pycnometer used to
determine the specific gravity of highly viscous liquids and
semisolids.
In using a pycnometer, it is first weighed empty and then weighed again
when filled to capacity with water. The weight of the water is calculated
by difference. Because 1 g of water equals 1 mL, the exact volume of the
pycnometer becomes known. Then, when any other substance is placed in
the pycnometer, it is of equal volume to the water, and its specific gravity
may be determined.
1. 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.
2. An aluminum pycnometer weighs 24.84 g. When filled with water, it
weighs 35.05 g; when filled with an ointment, it weighs 35.52 g.
What is the specific gravity of the ointment?
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Use of Specific Gravity in Calculations of
Weight and Volume
It is important to remember that specific gravity is a factor that expresses
how much heavier or lighter a substance is than water, the standard with a
specific gravity of 1.0. For example, a liquid with a specific gravity of
1.25 is 1.25 times as heavy as water, and a liquid with a specific gravity
of 0.85 is 0.85 times as heavy as water.
Thus, if we had 50 mL of a liquid with a specific gravity of 1.2, it
would weigh 1.2 times as much as an equivalent volume of water. An
equivalent volume of water, 50 mL, would weigh 50 g, and therefore, the
liquid would weigh 1.2 times that, or 60 g.
Calculating Weight, Knowing the Volume and
Specific Gravity
Based on the explanation in the previous paragraphs, we can derive the
following equation:
Although it is both obvious and true that one cannot multiply milliliters
by specific gravity and have a product in grams, the equation “works”
because the volume of the liquid in question is assumed to be the same
volume as water for which milliliters equal grams. So, in essence, the true
equation would be:
Furthermore, because the specific gravity of water is 1 and is the standard
used in determining specific gravity, units of grams per milliliter (g/mL)
can be assumed in using specific gravity to convert from volume to
weight or vice versa. Volume must be expressed in milliliters for the
conversion to be used, however, which will give a resulting weight in
grams.
1. What is the weight, in grams, of 360 mL of alcohol with a specific
gravity of 0.82?
Using specific gravity as defined:
360 mL of water weigh 360 g
360 g × 0.82 = 295.2 g
Using specific gravity as a conversion:
2. Sevoflurane (ULTANE) is a volatile liquid for inhalation with a
specific gravity of 1.52. Calculate the weight of the contents of a
bottle of 250 mL of the product.
250 mL of water weigh 250 g
or
3. What is the weight, in grams, of 2 fl. oz. of a liquid having a specific
gravity of 1.118?
In this type of problem, it is best to convert the given volume to its
metric equivalent first and then solve the problem in the metric
or
Calculating Volume, Knowing the Weight and
Specific Gravity
By rearranging the previous equation, we can calculate the volume of a
liquid using the equation:
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As explained earlier, units of grams per milliliter (g/mL) can also be
assumed in using specific gravity to convert from weight to volume.
Similarly, weight must be expressed in grams for the conversion to be
used that will give a resulting volume in milliliters.
1. What is the volume, in milliliters, of 492 g of a liquid with a specific
gravity of 1.40?
Using specific gravity as defined:
492 g of water measure 492 mL
Using specific gravity as a conversion:
2. What is the volume, in milliliters, of 1 lb of a liquid with a specific
gravity of 1.185?
1 lb = 454 g
454 g of water measure 454 mL
or
3. What is the volume, in pints, of 50 lb of glycerin having a specific
gravity of 1.25?
Using Specific Gravity to Determine
Weight/Volume Costs
1. What is the cost of 1000 mL of glycerin, specific gravity 1.25, bought
at $5.43 per pound?
Using specific gravity as defined:
1000 mL of water weigh 1000 g
Weight of 1000 mL of glycerin = 1000 g × 1.25 = 1250 g
2. What is the cost of 1 pint of chloroform, specific gravity 1.475, bought
at $25.25 per pound?
Using specific gravity as a conversion:
Special Considerations of Specific Gravity
Pharmaceutical Applications
An interesting special application of specific gravity is in the use of
automated, computer-controlled pharmaceutical equipment, termed
automated compounders, in the preparation of multicomponent mixtures
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for parenteral nutrition (as described in Chapter 14). In such systems, the
measurement of the final volume of a mixture is determined by its weight
divided by the solution’s known specific gravity.2 A complete explanation
may be found in the indicated reference.
Clinical Application
Specific gravity is an important factor in urinalysis. In normal adults, the
specific gravity of urine is usually within the range of 1.020 and 1.028
with a normal fluid intake (this range may vary with the reference
source).
3
Specific gravity is an indicator of both the concentration of particles
in the urine and a patient’s degree of hydration. A higher-than-normal
specific gravity indicates that the urine is concentrated. This may be due
to the presence of excess waste products or electrolytes in the urine, the
presence of glucose (glucosuria) or protein (proteinuria), excessive water
loss, decreased fluid intake, or other factors. A low specific gravity
indicates that the urine is dilute, which may be a result of diabetes
insipidus, renal disease (by virtue of the kidney’s reduced ability to
concentrate urine), increased fluid intake, intravenous hydration, or other
factors.
4
CASE IN POINT 5.1
5
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.
CALCULATIONS CAPSULE
Specific Gravity
The specific gravity (sp gr) of a substance or a pharmaceutical
preparation may be determined by the following equation:
1.
2.
3.
4.
5.
6.
7.
The following equation may be used to convert the volume of a
substance or pharmaceutical preparation to its weight:
a
Or simply,
The following equation may be used to convert the weight of a
substance or pharmaceutical preparation to its volumea:
Or simply,
In addition, units of grams per milliliter (g/mL) can be assigned to
specific gravity, then used as a conversion between weight and volume.
a
The full explanation of why these equations or conversions work may be found in the
section “Use of Specific Gravity in Calculations of Weight and Volume.”
PRACTICE PROBLEMS
Calculations of Density
If 250 mL of alcohol weigh 203 g, what is its density?
A metal substance weighs 53.6 g and has a volume of 6 mL.
Calculate its density.
Calculations of Specific Gravity
If 150 mL of a sorbitol solution weigh 170 g, what is its specific
gravity?
If a liter of a cough syrup weighs 1285 g, what is its specific
gravity?
If 500 mL of a solution weigh 650 g, what is its specific gravity?
If 2 fl. oz. of glycerol weigh 74.1 g, what is its specific gravity?
An empty aluminum pycnometer weighs 24.91 g and 30.08 g when
filled with water. Filled with a compounded lotion, the pycnometer
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8.
9.
10.
11.
12.
13.
14.
15.
16.
weighs 29.94 g. What is the specific gravity of the lotion?
A glass pycnometer weighs 21.62 g. Filled with water, it weighs
46.71 g; filled with another liquid, it weighs 43.28 g. Calculate the
specific gravity of the liquid.
A modified Ringer’s Irrigation has the following formula:
Assuming that 980 mL of water is used, calculate the specific
gravity of the irrigation.
α-Tocopherol is a form of vitamin E that is a yellow-brown viscous
liquid with a density of 0.950 g/cm3. Calculate its specific gravity.
A patient added a 17-g measured dose of polyethylene glycol 3350
(MIRALAX) to 180 mL of water to use as a laxative. If the volume
of the resultant mixture was 195.6 mL, calculate the specific
gravity of the mixture.
If 1 fl. oz. of a liquid weigh 1 oz., what will be the specific gravity
of the liquid calculated to three decimal places?
Calculations of Weight or Volume Using Specific Gravity
NOTE: Use the information in Table 5.1 as necessary.
Concentrated hydrochloric acid solution has a specific gravity of
1.096. What would be the weight of 75 mL of this solution?
A pharmacist needs to prepare 30 capsules, each containing 850 mg
of fish oil (sp gr = 0.907). How many milliliters of fish oil would
be needed to prepare the total quantity of capsules?
A topical analgesic formulation requires 8 g of methyl salicylate
(sp gr = 1.174). Convert this quantity to milliliters.
Calculate the weight, in grams, of 100 mL of each of the following:
a. Acetone
b. Liquid petrolatum
c. Syrup
d. Nitroglycerin
e. Mercury
17.
18.
19.
20.
21.
22.
23.
24.
What is the weight, in kilograms, of 5 liters of a liquid with a
specific gravity of 1.84?
What is the weight, in kilograms, of 1 gallon of sorbitol solution
having a specific gravity of 1.285?
If 500 mL of mineral oil are used to prepare a liter of mineral oil
emulsion, how many grams of the oil, having a specific gravity of
0.87, would be used in the preparation of 1 gallon of the emulsion?
Calculate the volume, in milliliters, of 100 g of each of the
following:
a. Peanut oil
b. Castor oil
c. Polysorbate 80
d. Phosphoric acid
e. Mercury
What is the volume, in milliliters, of 1 lb of benzyl benzoate having
a specific gravity of 1.12?
Calculate the corresponding weights of liquefied phenol and
propylene glycol needed to prepare 24 15-mL bottles of the
following formula:
Calculate the total weight of the following formula for a pediatric
chewable gummy gel base for medication.
Calculate the number of milliliters of polysorbate 80 required to
prepare 48 100-g tubes of the following formula for a progesterone
vaginal cream.
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