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0.2 g (hydromorphone HCl) × 0.22 (E-value) = 0.044 g (sodium chloride
equivalence)
20 mL − 4.89 mL = 15.11 mL 0.9% w/v sodium chloride solution
required
Other examples of calculated volumes of isotonic solutions that may be
prepared from 1 g of drug are given in Table 11.2 and available from other
references.3,
4
TABLE 11.2 EXAMPLES OF ISOTONIC SOLUTIONS
THAT MAY BE PREPARED FROM 1 g QUANTITIES OF
DRUGS
a
a
Calculated from the E-values in Table 11.1.
Use of freezing point data in isotonicity
calculations
Freezing point data (∆Tf) can be used in isotonicity calculations when the
agent has a tonicic effect and does not penetrate the biologic membranes in
question (e.g., red blood cells). As stated previously, the freezing point of
both blood and lacrimal fluid is −0.52°C. Thus, a pharmaceutical solution
that has a freezing point of −0.52°C is considered isotonic.
Representative data on freezing point depression by medicinal and
pharmaceutical substances are presented in Table 11.3. Although these data
are for solution strengths of 1%, data for other solution strengths and for
many additional agents may be found in physical pharmacy textbooks and
in the literature.
TABLE 11.3 FREEZING POINT DATA FOR SELECT
AGENTS
Freezing point depression data may be used in isotonicity calculations as
shown by the following.
Example calculations using freezing point data
How many milligrams each of sodium chloride and lidocaine hydrochloride
are required to prepare 30 mL of a 1% solution of lidocaine hydrochloride
isotonic with tears?
To make this solution isotonic, the freezing point must be lowered to
−0.52°C. From Table 11.3, it is determined that a 1% solution of lidocaine
hydrochloride has a freezing point lowering of 0.063°C. Thus, sufficient
sodium chloride must be added to lower the freezing point an additional
0.457°C (0.52°C − 0.063°C).
Also from Table 11.3, it is determined that a 1% solution of sodium
chloride lowers the freezing point by 0.58°C. By proportion:
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x = 0.79% sodium chloride needed to lower the freezing point by 0.457°C
and, therefore, required to make the solution isotonic.
Thus, to make 30 mL of solution,
NOTE: Should a prescription call for more than one medicinal and/or
pharmaceutic ingredient, the sum of the freezing points is subtracted from
the required value in determining the additional lowering required by the
agent used to provide isotonicity.
CALCULATIONS CAPSULE
Isotonicity
To calculate the “equivalent tonic effect” to sodium chloride represented
by an ingredient in a preparation, multiply its weight by its E-value:
To make a solution isotonic, calculate and ensure the quantity of sodium
chloride and/or the equivalent tonic effect of all other ingredients to total
0.9% w/v in the preparation:
To make an isotonic solution from a drug substance, add sufficient water
by the equation:
This solution may then be made to any volume with isotonic sodium
chloride solution to maintain its isotonicity.
The E-value can be derived from the same equation, given the grams
of drug substance and the milliliters of water required to make an isotonic
solution.
CASE IN POINT 11.1
A
A local ophthalmologist is treating one of his patients for a post-LASIK
eye infection that is not responding to topical ciprofloxacin. These
infections, although rare, can occur after laser in situ keratomileusis
(LASIK) surgery for vision correction.
Topical amikacin sulfate has been shown to be effective for the
treatment of eye infections due to ciprofloxacin-resistant
Pseudomonas,5,6 Burkholderia ambifaria,7 Mycobacterium chelonae, and
Mycobacterium fortuitum.8–
10
The ophthalmologist prescribes 60 mL of a 2.5% amikacin sulfate
isotonic solution, two drops in the affected eye every 2 hours.
Amikacin sulfate USP (C22H43N5O13·2H2SO4), m.w. 781.76, is an
aminoglycoside-type antibiotic containing three ions.
a. Determine the weight in grams of amikacin sulfate needed to
prepare the solution.
b. Calculate the sodium chloride equivalent (E-value) for amikacin
sulfate.
c. Calculate the amount of sodium chloride needed to make the
prepared solution isotonic.
d. How many milliliters of 23.5% sodium chloride injection should
be used to obtain the needed sodium chloride?
a
Case in Point courtesy of W. Beach, Athens, GA.
CASE IN POINT 11.2
11
A formula for a compounded ophthalmic solution is shown here:
This formula combines the antibacterial action of tobramycin sulfate with
the anti-inflammatory and analgesic properties of diclofenac sodium. It
should be prepared in an aseptic environment such as a laminar flow
hood and has a beyond-use date of up to 3 days if stored in the
refrigerator.
a. Tobramycin sulfate [(C18H37N5O9)2·5H2SO4] is a 7-ion electrolyte
and has a molecular weight of 1425.45. Assuming that it
dissociates 80% at a certain concentration, calculate the
dissociation factor (i) and sodium chloride equivalent (E-value)
for tobramycin sulfate.
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b. The potency of tobramycin sulfate is 634 to 739 mcg of
tobramycin activity per milligram. What is the amount range of
tobramycin activity in this formulation?
c. Diclofenac sodium (C14H10Cl2NNaO2) is a 2-ion electrolyte with
an average dissociation factor of 1.8 and a molecular weight of
318.13. Calculate the E-value for diclofenac sodium.
d. Is the amount of sodium chloride listed in the formulation correct
to make the solution isotonic?
e. How much of each ingredient would be needed to prepare 20 mL
of the compounded solution?
f. How much of a tobramycin sulfate injectable solution with a
concentration of 80 mg/2 mL would be needed to prepare 20 mL
of the compounded solution?
Buffers and Buffer Solutions
When a minute amount of hydrochloric acid is added to pure water, a
significant increase in hydrogen-ion concentration occurs immediately. In a
similar manner, when a minute amount of sodium hydroxide is added to
pure water, it causes a correspondingly large increase in the hydroxide-ion
concentration. These changes take place because water alone cannot
neutralize even traces of acid or base; that is, it has no ability to resist
changes in hydrogen-ion concentration or pH. A solution of a neutral salt,
such as sodium chloride, also lacks this ability. Therefore, it is said to be
unbuffered.
The presence of certain substances or combinations of substances in
aqueous solution imparts to the system the ability to maintain a desired pH
at a relatively constant level, even with the addition of materials that may be
expected to change the hydrogen-ion concentration. These substances or
combinations of substances are called buffers, and solutions of them are
called buffer solutions. By definition, then, a buffer solution is a system,
usually an aqueous solution, that possesses the property of resisting changes
in pH with the addition of small amounts of an acid or base.
Buffers are used to establish and maintain an ion activity within rather
narrow limits. In pharmacy, the most common buffer systems are used in (i)
the preparation of such dosage forms as injections and ophthalmic solutions,
which are placed directly into pH-sensitive body fluids; (ii) the manufacture
of formulations in which the pH must be maintained at a relatively constant
level to ensure maximum product stability; and (iii) pharmaceutical tests
and assays requiring adjustment to or maintenance of a specific pH for
analytic purposes.
A buffer solution is usually composed of a weak acid and a salt of the
acid, such as acetic acid and sodium acetate, or a weak base and a salt of the
base, such as ammonium hydroxide and ammonium chloride. Typical buffer
systems that may be used in pharmaceutical formulations include the
following pairs: acetic acid and sodium acetate, boric acid and sodium
borate, and sodium phosphate monobasic and sodium phosphate dibasic.
Formulas for standard buffer solutions for pharmaceutical analysis are given
in the United States Pharmacopeia.
12
In the selection of a buffer system, due consideration must be given to
the dissociation constant of the weak acid or base to ensure maximum buffer
capacity. This dissociation constant, in the case of an acid, is a measure of
the strength of the acid; the more readily the acid dissociates, the higher its
dissociation constant and the stronger the acid. Selected dissociation
constants, or Ka values, are given in Table 11.4.
TABLE 11.4 DISSOCIATION CONSTANTS OF SOME
WEAK ACIDS AT 25°C
The dissociation constant, or Ka value, of a weak acid is given by the
equation:
Because the numeric values of most dissociation constants are small
numbers and may vary over many powers of 10, it is more convenient to
express them as negative logarithms:
When equation is expressed in logarithmic form, it is
written:
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and because pH = −log [H+]:
Buffer equation
The equation just derived is the Henderson-Hasselbalch equation for weak
acids, commonly known as the buffer equation.
Similarly, the dissociation constant, or Kb value, of a weak base is given
by the equation:
and the buffer equation for weak bases, which is derived from this
relationship, may be expressed as:
The buffer equation is useful for calculating (1) the pH of a buffer system if
its composition is known and (2) the molar ratio of the components of a
buffer system required to give a solution of a desired pH. The equation can
also be used to calculate the change in pH of a buffered solution with the
addition of a given amount of acid or base.
pKa Value of a Weak Acid with Known Dissociation Constant
Calculating the pKa value of a weak acid, given its dissociation constant,
Ka:
The dissociation constant of acetic acid is 1.75 × 10−5 at 25°C.
Calculate its pKa value.
pH Value of a Salt/Acid Buffer System
Calculating the pH value:
What is the pH of a buffer solution prepared with 0.05 M sodium borate
and 0.005 M boric acid? The pKa value of boric acid is 9.24 at 25°C.
Note that the ratio of the components of the buffer solution is given in
molar concentrations.
Using the buffer equation for weak acids:
pH Value of a Base/Salt Buffer System
Calculating the pH value:
What is the pH of a buffer solution prepared with 0.05 M ammonia and
0.05 M ammonium chloride? The Kb value of ammonia is 1.80 × 10−5 at
25°C.
Using the buffer equation for weak bases:
Because the Kw value for water is 1014 at 25°C, pKw = 14.
Molar Ratio of Salt/Acid for a Buffer System of Desired pH
Calculating the molar ratio of salt/acid required to prepare a buffer system
with a desired pH value:
What molar ratio of salt/acid is required to prepare a sodium acetate–
acetic acid buffer solution with a pH of 5.76? The pKa value of acetic acid
is 4.76 at 25°C.
Using the buffer equation:
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Quantity of Components in a Buffer Solution to Yield a Specific Volume
Calculating the amounts of the components of a buffer solution required to
prepare a desired volume, given the molar ratio of the components and the
total buffer concentration:
The molar ratio of sodium acetate to acetic acid in a buffer solution
with a pH of 5.76 is 10:1. Assuming the total buffer concentration is 0.022
mol/L, how many grams of sodium acetate (m.w. 82) and how many grams
of acetic acid (m.w. 60) should be used in preparing a liter of the solution?
Because the molar ratio of sodium acetate to acetic acid is 10:1,
If the total buffer concentration = 0.022 mol/L,
The efficiency of buffer solutions—that is, their specific ability to resist
changes in pH—is measured in terms of buffer capacity: the smaller the pH
change with the addition of a given amount of acid or base, the greater the
buffer capacity of the system. Among other factors, the buffer capacity of a
system depends on (1) the relative concentration of the buffer components
and (2) the ratio of the components. For example, a 0.5-M acetate buffer at a
pH of 4.76 would have a higher buffer capacity than a 0.05-M buffer.
If a strong base such as sodium hydroxide is added to a buffer system
consisting of sodium acetate and acetic acid, the base is neutralized by the
acetic acid forming more sodium acetate, and the resulting increase in pH is
slight. Actually, the addition of the base increases the concentration of
sodium acetate and decreases by an equal amount the concentration of
acetic acid. In a similar manner, the addition of a strong acid to a buffer
1.
system consisting of a weak base and its salt would produce only a small
decrease in pH.
Change in pH with Addition of an Acid or Base
Calculating the change in pH of a buffer solution with the addition of a
given amount of acid or base:
Calculate the change in pH after adding 0.04 mol of sodium hydroxide
to a liter of a buffer solution containing 0.2 M concentrations each of
sodium acetate and acetic acid. The pKa value of acetic acid is 4.76 at
25°C.
The pH of the buffer solution is calculated by using the buffer equation
as follows:
The addition of 0.04 mol of sodium hydroxide converts 0.04 mol of acetic
acid to 0.04 mol of sodium acetate. Consequently, the concentration of
acetic acid is decreased and the concentration of sodium acetate is increased
by equal amounts, according to the following equation:
Because the pH before the addition of the sodium hydroxide was 4.76, the
change in pH = 4.94 − 4.76 = 0.18 unit.
PRACTICE PROBLEMS
Calculations of Tonicity
Isotonic sodium chloride solution contains 0.9% w/v sodium chloride.
If the E-value of boric acid is 0.52, calculate the percentage strength
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