QUALITY CONTROL: Refractive Index II: Osmolarity

Loyd V. Allen, Jr., PhD, RPh

This is the second in the series on the use of refractometry in quality determinations involving compounded preparations. This issue will cover the prediction followed by the confirmation of osmolarity values using refractive index (RI).

The Basics: Part II
Light travels quickly through a vacuum; it travels a little slower in air; and, still, it travels more slowly through gases, liquids, and solids. The speed of light through a transparent substance is dependent upon the interaction of the electrical properties of the light with the electronic density of the substances under question.

As light travels through air and enters a transparent substance, it slows down. Observing this phenomenon, the light appears to "bend." This bending of light waves is called refraction. The light entering from a less dense to a more dense substance bends toward the interface. If a pencil is placed at an angle in water, the image of the pencil appears to bend toward the interface; the position of the pencil in the water is actually below where it appears to be.

This refraction is due to an interaction between the electric component of the light and the bound electrons of the substance: the greater the interaction, the greater the refraction; the greater the electron density of the substance, the greater the refraction. The RI of a substance is defined as the ratio of the velocity of light in air to the velocity of light in the substance under like conditions. The RI, "n," is equal to the ratio of the sine of the angle of incidence of a ray of light in air to the sine of the angle of refraction of the ray in the substance under examination:

in which
    sin i is the sine of the angle of the incident ray of light, and
    sin r is the sine of the angle of the refracted ray

As a general convention, the numerator is the velocity of light in air and the denominator is the substance, or sample. By using this convention, the RI is greater than 1 for substances more dense than air, as they are in pharmacy. Actually, the reference should be light traveling through a vacuum, but this is technologically difficult to accomplish with inexpensive instrumentation that can be easily used; so air is used. This results in only a slight difference of 0.03% and is commonly used. The following adjustment can be made, if necessary, but is seldom required:

    n_vacc = 1.00027 _nD

The nD designates that the "D" line of sodium light was used for determining the RI.

As an example, the ratio of the velocities of light in air and in water is in the ratio of about 4 to 3. The index of refraction of water with respect to air is therefore about 1.3333.

Generally, values for RIs for the D line of sodium light are in the range of approximately 1.3 to 1.7.

Refractive Index and Density
There is a relationship between the RI of a substance and its density. This relationship has been known since the time of Newton, who observed that the relationship (n²-1)/d was approximately constant for a number of substances. Some refractometers, used in medical laboratories, actually have two or more adjacent scales so the technician can actually read the specific gravity of a body fluid, such as urine, directly off the scale of a handheld or clinical refractometer. In a study by Jirapinyo et al, they found a good correlation between osmolality and specific gravity of parenteral nutrition (PN) solutions containing various concentrations of amino acid and glucose, up to 1,000 mOsmol/kg water and 1.050, respectively.^1,

The Application
Let's look at a quick review of some definitions:
Osmol: The molecular weight of a solute, in grams, divided by the number of ions or particles into which it dissociates in solution
Osmolarity: The osmotic concentration of a solution expressed as osmoles of solute per liter of solution
Osmolality: The concentration of a solution expressed in osmoles of solute particles per kilogram of solvent
Degrees Brix (symbol °Bx): The sugar content of an aqueous solution. One degree Brix is 1 gram of sucrose in 100 grams of solution and represents the strength of the solution as percentage by weight (% w/w). If the solution contains dissolved solids other than pure sucrose, then the °Bx only approximates the dissolved solid content. The °Bx is traditionally used in the wine, sugar, fruit juice, and honey industries.¹ Since many refractometers use Brix, the following table is provided for conversion estimates.

Some earlier publications reported on the determination of osmolarities using different methods. Gatlin et al discussed four methods for determining the osmolarity of multicomponent i.v. solutions, including a vapor pressure osmometer, theoretically using osmotic coefficients of the solutes, using sodium chloride equivalents, and, finally, another theoretical method based on the sum of the solution components but not accounting for interionic forces. Of these, the first method based on actual measurements using an osmometer appeared to be the most reliable at the time in 1979.²

In 2011, Chang and Yeh published an article on the prediction of PN osmolarity using digital refractometry.³ In this study, to validate the predicted PN osmolarity equation, they measured 500 PN admixtures (Note: The refractometer in this study measured "Brix" values.). They concluded that the use of a refractometric method is simple, reproducible, and inexpensive, and only a 1-mL sample is required. The refractometric method of PN osmolarity prediction is a reasonable quality-assurance method before administration of the PN formulation.

References

1. Jirapinyo P, Muanqsri S, Komoltri J et al. The correlation between osmolality and specific gravity of parenteral nutrition solution. J Med Assoc Thai 1992; 75(3): 163-167.
2. Gatlin L, Kulkarni P, Hussain A et al. Determining Osmolarities: A practical approach for multicomponent intravenous and parenteral nutrient solutions. Am J Hosp Pharm 1979; 36(10): 1357-1361.
3. Chang WK, Yeh MK. Prediction of parenteral nutrition osmolarity by digital refractometry. JPEN 2011; 35(3): 412-418.

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