Dosage Form Design Lec. 2 Dr. AA Yas Pharmaceutical and Formulation Considerations 10- Solubility and pH: •Another technique, if the drug is to be formulated into a liquid product, is adjustment of the pH of the solvent to enhance solubility. Weak acidic or basic drugs may require extremes in pH that are outside accepted physiologic limits or that may cause stability problems with formulation ingredients. •Adjustment of pH usually has little effect on the solubility of substances other than electrolytes. In many cases, it is desirable to use cosolvents or other techniques such as complexation, micronization, or solid dispersion to improve aqueous solubility. •Principles of pH – •The pH of a substance is a measure of its acidity, is defined in terms of the hydrogen ion activity: pH = -log 10 a H+ or 10 -pH = a H+ …..(Eq. 1) •pH equals the negative logarithm of the hydrogen ion activity, or the activity of the hydrogen ion is 10 raised to the exponent -pH. The activity is the effective concentration of the hydrogen ion in solution. The difference between effective and actual concentration decreases as one moves toward more dilute solutions, in which ionic interaction becomes progressively less important.
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Dosage Form Design Lec. 2 Dr. AA Yas
Pharmaceutical and Formulation Considerations
10- Solubility and pH:
•Another technique, if the drug is to be formulated into a liquid product, is adjustment
of the pH of the solvent to enhance solubility. Weak acidic or basic drugs may require
extremes in pH that are outside accepted physiologic limits or that may cause stability
problems with formulation ingredients.
•Adjustment of pH usually has little effect on the solubility of substances other than
electrolytes. In many cases, it is desirable to use cosolvents or other techniques such as
complexation, micronization, or solid dispersion to improve aqueous solubility.
•Principles of pH –
•The pH of a substance is a measure of its acidity, is defined in terms of the hydrogen
ion activity:
pH = -log10 aH+ or 10-pH = aH+ …..(Eq. 1)
•pH equals the negative logarithm of the hydrogen ion activity, or the activity of the
hydrogen ion is 10 raised to the exponent -pH. The activity is the effective
concentration of the hydrogen ion in solution. The difference between effective and
actual concentration decreases as one moves toward more dilute solutions, in which
ionic interaction becomes progressively less important.
•The hydrogen ion when reference should be made to the hydronium ion (H3O+), i.e.;
H+ + H2O = H3O+. The complexing of the hydrogen ion by water affects activity and
applies to other ions, which partially complex or establish an equilibrium with the
hydrogen ion. In other words, equilibrium such as: H2CO3 = H+ + HCO3- | HC2H3O2 =
H+ + C2H3O2-, complexes the hydrogen ion so that it is not sensed by the pH measuring
system.
•This is why an acid-base titration is performed if the total concentration of acid (H+) is
needed. These effects on hydrogen ion activity are obvious, but other more subtle
effects are involved in the correlation of activity and concentration. The activity of the
hydrogen ion can be defined by its relation to concentration (CH+, molality) and the
activity coefficient fH+: aH+ = fH + CH+.
•If the activity coefficient is unity, activity is equal to concentration, i.e.; dilute
solutions, whose ionic strength is low. Since the objective of most pH measurements is
to find a stable and reproducible reading that can be correlated to the results of some
process, it is important to know what influences the activity coefficient and therefore
the pH measurement.
•The factors that affect the activity coefficient are the temperature (T), the ionic strength
(µ), the dielectric constant (ε), the ion charge (Zi), the size of the ion in angstroms (Å),
and the density of the solvent (d).
•All of these factors are characteristics of the solution that relate the activity to the
concentration by two main effects: the salt effect and the medium effect; the latter
relates the influence that the solvent can have on the hydrogen ion activity.
•Thus, hydrogen activity is related to concentration through a salt effect and a solvent
effect. Because of these influences, a sample pH value cannot be extrapolated to
another temperature or dilution. If the pH value of a particular solution is known at
40°C, it is not automatically known at 25°C.
•The pH Scale –
•In pure water, hydrogen and hydroxyl ion concentrations are equal at 10-7 M at 25°C.
This is a neutral solution. Since most samples encountered have less than 1 M H+ or
OH-, the extremes of pH 0 for acids and pH 14 for bases are established. Of course,
with strong acids or bases, pH values below 0 and above 14 are possible but
infrequently measured.
•Measurement of pH –
•The activity of the hydrogen ion in solution is measured with a glass electrode, a
reference electrode, and a pH meter.
•Combination Electrodes –
•A combination electrode is a combination of the glass and reference electrodes into a
single probe. The main advantage in using a combination electrode is with the
measurement of small volume samples or samples in limited-access containers.
•The total quantity of a monoprotic weak acid (HA) in solution at a specific pH is the
sum of the concentrations of both the free acid and salt (A-) forms. If excess drug is
present, the quantity of free acid in solution is maximized and constant because of its
saturation solubility. As the pH of the solution increases, the quantity of drug in solution
increases because the water-soluble ionizable salt is formed. The expression is:
HA H+ + A-…..(Eq. 2)
where Ka is the dissociation constant.
•There may be a certain pH level reached where the total solubility (ST) of the drug
solution is saturated with respect to both the salt and acid forms of the drug, that is, the
pHmax.
•The solution can be saturated with respect to the salt at pH values higher than this, but
not with respect to the acid. Also, at pH values less than this, the solution can be
saturated with respect to the acid but not to the salt. To calculate the total quantity of
drug that can be maintained in solution at a selected pH, either of two equations can be
used, depending on whether the product is to be in a pH region
-below the pHmax : ST = Sa [1 + ]…..(Eq. 3)
-above the pHmax: ST = S’a [1 + ]…..(Eq. 4)
where Sa is the saturation solubility of the free acid and S′a is the saturation solubility of
the salt form.
Example 1: A pharmacist prepares a 3.0% solution of an antibiotic as an ophthalmic
solution and dispenses it to a patient. A few days later the patient returns the eye drops
to the pharmacist because the product contains a precipitate. The pharmacist, checking
the pH of the solution and finding it to be 6.0, reasons that the problem may be pH
related. The physicochemical information of interest on the antibiotic includes the
following:
Molecular weight → 285 (salt) 263 (free acid)
3.0% solution of the drug → 0.1053 M solution
Acid form solubility (Sa) → 3.1 mg/mL (0.0118 M)
Ka → 5.86 × 10-6
•Using equation 3, the pharmacist calculates the quantity of the antibiotic in solution at
a pH of 6.0 (Note: pH of 6.0 = [H+] of 1 × 10-6) ST = 0.0118[1+] = 0.0809 molar.
•From this the pharmacist knows that at a pH of 6.0, a 0.0809-M solution can be
prepared. However, the concentration that was to be prepared was a 0.1053-M solution;
consequently, the drug will not be in solution at that pH. The pH may have been all
right initially but shifted to a lower pH over time, resulting in precipitation of the drug.
•The question is at what pH (hydrogen ion concentration) the drug will remain in
solution. This can be calculated using the same equation and information. The ST value
is 0.1053 M.
0.1053 = 0.0118 [1 + ]
[H+] = 7.333 X 10 – 7 or pH = 6.135
•The pharmacist prepares a solution of the antibiotic, adjusting the pH to above about
6.2, using a suitable buffer system, and dispenses the solution to the patient—with
positive results.
•An interesting phenomenon concerns the close relationship of pH to solubility. At a pH
of 6.0, only a 0.0809-M solution could be prepared, but at a pH of 6.13 a 0.1053-M
solution could be prepared. In other words, a difference of 0.13 pH units resulted in
more drug going into solution at the higher pH than at the lower pH, i.e.; a very small
change in pH resulted in about 30% more drug going into solution. According to the
figure, the slope of the curve would be very steep for this example drug, and a small
change in pH (x-axis) results in a large change in solubility (y-axis).
•pH Determination –
a- Solutions of Strong Acids and Bases:
Strong Acids –
…..(Eq. 5)
Strong Bases –
…..(Eq. 6)
b- Conjugated Acid – Base Pair –
…..(Eq. 7)
c- Solutions Containing Only A Weak Acid –
…..(Eq. 8)
…..(Eq. 9)
…..(Eq. 10)
d- Solutions Containing Only A Weak Base –
…..(Eq. 11)
…..(Eq. 12)
…..(Eq. 13)
…..(Eq. 14)
…..(Eq. 15)
e- Solutions Containing A Single Acid – Base Pair –
…..(Eq. 16)
f- Two Conjugated Acid – Base Pairs –
…..(Eq. 17)
g- Solutions Containing Only A Diprotic Acid –
…..(Eq. 18)
h- Solutions Containing Only An Ampholyte –
…..(Eq. 19)
…..(Eq. 20)
…..(Eq. 21)
i- Solutions Containing Only A Diacidic Base –
…..(Eq. 22)
…..(Eq. 23)
j- Two Independent Acid – Base Pairs –
…..(Eq. 24)
k- Solutions Containing Two Weak Acids –
…..(Eq. 25)
…..(Eq. 26)
l- Solutions Containing A Salt of A Weak Acid and A Weak Base –
…..(Eq. 27)
…..(Eq. 28)
…..(Eq. 29)
m- Solutions Containing A Weak Acid and A Weak Base –
11- Dissolution: •Variations in the biologic activity of a drug substance may be brought about by the rate at which it becomes available to the organism. Dissolution rate, the time it takes for the drug to dissolve in the fluids at the absorption site, is the rate-limiting step in absorption for drugs administered orally in solid forms (e.g.; tablets, capsules, or suspensions, and intramuscularly). •When the dissolution rate is the rate-limiting step, anything that affects it will also affect absorption and consequently, can affect the onset, intensity, and duration of response and control the overall bioavailability of the drug from the dosage form. •The dissolution rate of drugs may be increased by decreasing the drug's particle size and by increasing its solubility in the diffusion layer. The most effective means of obtaining higher dissolution rates is to use a highly water-soluble salt of the parent substance. Although a soluble salt of a weak acid will precipitate as the free acid in the bulk phase of an acidic solution, such as gastric fluid, it will do so in the form of fine particles with a large surface area. •The dissolution rates of chemical compounds are determined by: Constant-Surface Method - which provides intrinsic dissolution rate of the agent, and particulate dissolution, in which a suspension of the agent is added to a fixed amount of solvent without exact control of surface area, uses a compressed disc of known area.
Intrinsic Dissolution Rate - is characteristic of each solid compound and a given
solvent in the fixed experimental conditions. The value is expressed as mg/min/cm2,
value useful in predicting probable absorption problems due to dissolution rate. In
particulate dissolution, a weighed amount of powdered sample is added to the
dissolution medium in a constant agitation system. This method is frequently used to
study the influence of particle size, surface area, and excipients upon the active agent.
Occasionally, the surface properties of the drug produce an inverse relationship of
particle size to dissolution.
•Surface charge and/or agglomeration results in the reduced particle size form of the
drug presenting a lower effective surface area to the solvent due to incomplete wetting
or agglomeration.
•Fick's Laws of Diffusion and the Noyes-Whitney Equation –
•All drugs must diffuse through various barriers when administered to the body (e.g.;
skin, gastric mucosa) to gain access to the interior of the body.
•Parenteral drugs must diffuse through (e.g.; muscle, connective tissue) to get to the site
of action; even intravenous drugs must diffuse from the blood to the site of action.
•Drugs must also diffuse through various barriers for metabolism and excretion.
•Considering all the diffusion processes that occur in the body (passive, active, and
facilitated), it is not surprising that the laws governing diffusion are important to drug
delivery systems. In fact, diffusion is important not only in the body but also in some
quality control procedures used to determine batch-to-batch uniformity of products
(dissolution test for tablets based on the Noyes-Whitney equation, which can be derived
from Fick's law).
•When individual molecules move within a substance, diffusion is said to occur. This
may occur as the result of a concentration gradient or by random molecular motion.
Probably the most widely used laws of diffusion are:
Fick’s First Law - involving steady-state diffusion (where dc/dx does not change) is
derived from the following expression for the quantity of material (M) flowing through
a cross section of a barrier (S) in unit time (t) expressed as the flux (J):
J = dM/(Sdt)…..(Eq. 30)
•Under a concentration gradient (dc/dx), Fick's first law can be expressed thus:
J = D[(C1-C2)/h] or J = -D(dC/dx)…..(Eq. 31)
where J is the flux of a component across a plane of unit area, C1 and C2 are the
concentrations in the donor and receptor compartments, h is the membrane thickness,
and D is the diffusion coefficient (or diffusivity). The sign is -tive, denoting that the flux
is in the direction of decreasing concentration. The units of J are gm/cm2; C, gm/cm3;
M, gm or moles; S, cm2; x, cm; and D, cm2/sec.
•D is appropriately called a diffusion coefficient, not a diffusion constant, as it is subject
to change. D may change in value with increased concentrations. Also, D can be
affected by temperature, pressure, solvent properties, and the chemical nature of the
drug itself.
Fick's Second Law - to study the rate of change of the drug in the system, one needs
an expression that relates the change in concentration with time at a definite location in
place of the mass of drug diffusing across a unit area of barrier in unit time. This law
can be summarized as stating that the change in concentration in a particular place with
time is proportional to the change in concentration gradient at that particular place in
the system.
•In summary, Fick's first law relates to a steady-state flow, whereas Fick's second law
relates to a change in concentration of drug with time, at any distance, or an unsteady
state of flow.
•The diffusion coefficients (D × 10-6) of various compounds in water (25°C) and other
media have been determined as follows: ethanol, 12.5 cm2 per second; glycine, 10.6
cm2 per second; sodium lauryl sulfate, 6.2 cm2 per second; glucose, 6.8 cm2 per second.
•The concentration of drug in the membrane can be calculated using the partition
coefficient (K) and the concentration in the donor and receptor compartments.
K = (C1/Cd) = (C2/Cr)…..(Eq. 32)
where C1 and Cd are the concentrations in the donor compartment (g/cm3) and C2 and Cr
are the concentrations in the receptor compartment (g/cm3).
•K is the partition coefficient of the drug between the solution and the membrane, and
by using drug oil solubility of versus water solubility, then, the higher the partition
coefficient, the more the drug will be soluble in a lipophilic substance and the
expression:
dM/dt = [DSK(Cd - Cr)]/h…..(Eq. 33)
or in sink conditions,
dM/dt = DSKCd/h = PSCd …..(Eq. 34)
•The permeability coefficient (centimeters per second) can be obtained by rearranging
to:
P = DK/h …..(Eq. 35)
Example 2: A drug passing through a 1-mm-thick membrane has a diffusion coefficient
of 4.23 × 10-7 cm2 per second and an oil-water partition coefficient of 2.03. The radius
of the area exposed to the solution is 2 cm, and the concentration of the drug in the
donor compartment is 0.5 mg/mL. Calculate the permeability and the diffusion rate of
the drug. h = 1 mm = 0.1 cm, D = 4.23 × 10-7 cm2/second, K = 2.03, r = 2 cm, S = π(2
cm)2 = 12.57 cm2, Cd = 0.5 mg/mL
P = [(4.23 × 10-7 cm2/second) (2.03)]/0.1 cm = 8.59 × 10-6 cm/second
type of data needed, |d| levels of specificity and |e| accuracy required.
Pharmaceutical Ingredients and Excipients:
•To produce a drug substance in a final dosage form requires pharmaceutical
ingredients. E.g., in the preparation of solutions; |a| one or more solvents, flavors and
sweeteners, colorants, preservatives, stabilizers and chelating agents.
Harmonization of Standards:
•There is great interest in the international harmonization of standards applicable to
pharmaceutical excipients. This is because the pharmaceutical industry is multinational.
•Standards for each drug substance and excipient used in pharmaceuticals are contained
in pharmacopeias.
•The four pharmacopeias with the largest international use are the USP-NF, BP, EP and
JP.
Fill in the Blanks: -
1- Oxidation involves ----------. [a gain of oxygen, a loss of hydrogen or a loss of
electrons]
2- ---------- is the most important reaction responsible for drug degradation in the solid
state. [solvolysis]
3- The Noyes-Whitney equation helps in understanding the effects on drug absorption
of particle size, solubility, saturation solubility and ---------- of diffusion layer.
[thickness]
4- In dilute solutions, whose ionic strength (µ) is low, the ---------- equal to the
concentration. [activities]
5- Weak bases, at pH > pKa, the predominant form present in solutions is the ----------
form. []
6-Weak bases, at pH > pKa, the total solubility equal to the ---------- solubility. []
7- Weak acids, the ---------- species concentrations will increase with pH increasing.
[non – ionized]
8- ---------- salts have good oral bioavailability. [Weak bases ] 9-Fick’s first law relates concentration change with time at a definite location, whereas
Fick’s second law involving ----------. [steady – state diffusion]
10- When solute concentration doesn’t exceed half the drug solubility, then ----------
happen. [sink conditions]
11- The dissolution rate is ---------- proportional to the surface area exposed to the
dissolution medium. [inversely]
13- When the relative humidity exceeds a critical level, conversion from a hydrous to
anhydrous form happen. []
14-Moisture sorption used to quantitate the crystalline content of predominantly
amorphous material. []
15-The most efficient extraction results when a large number of extractions are carried
out with small portion of extracting liquid. []
16-The [H3O+] varies from 1 in a 1 M solution of a strong base to 1 X 10 – 14 in a 1 M
solution of a strong acid. []
17- LeChatelier’s principle; a system at equilibrium readjusts so as to increase the effect
of an external stress. []
18- Drug delivery point of view; a drug with an average potency of 1 mg/kg should
have a solubility of 1 gm/L. []
19- FDA; a drug is considered highly soluble when its highest dose strength is soluble
in < 250 ml water. []
20- The ∆Sf and K can be estimated from the ---------- of the compound. []
21- The effect of temperature on reaction rate is given by the equation ----------. []
22- The equation for determining the aqueous solubility of crystalline compounds is ----
------. []
23- Only ---------- water uptake is needed to form monolayer coverage of a crystalline
compound with an average particle size of 1 µm. []
24- The time for complete dissolution for initial particle radius to be reduced to zero is
----------. []
25- The logarithm form of weak base solubility equation is ----------. []
26- In dilute solutions, whose ionic strength is low, the activity coefficient is equal -----
-----. []
27- Yalkowsky and Valvani illustrate the importance of ---------- on solubility. []
28- As the length of a non – polar chain increases, the solubility of the compound in
water increases. []
29- The HLB value is calculated for emulsions and solutions. []
30- The term ―clarification‖ is applied when the solids do not exceed 1.5%. []
31- Water has a low dielectric constant with good buffering capacity. []
32- Any improvement in solubility obtained by using hydrated form of a drug will
translate into improvement in dissolution rate. []
33- The exponential form of weak base solubility equation is ----------. []
34- The dissolution rate from a solution depends on the drug ----------. []
35- The particle ---------- does not affect the saturation concentration of a solid drug. []
36- The three factors that influence the rate and extent of drug absorption for immediate
release oral dosage form are ----------. []
37- According to the FDA, a drug substance is considered highly soluble when the
highest dose strength is soluble in < ---------- ml water over a pH range of 1 – 7.5. []
38- A drug is considered highly permeable when the extent of absorption in humans is
determined to be > ---------- % of an administered dose, based on mass – balance or in
comparison to an IV reference dose. []
39- A 1 – log unit change in aqueous solubility can be expected for each log unit in --. []
40- It is termed as ----------, when the C does not exceed about 20 % of the drug
solubility. []
41- The dissolution rate of a drug is proportional to the ---------- exposed to the
dissolution medium. []
42-
12-For immediate release dosage form, if the drug particle diameter (µm) < solubility
(µg/ml), further particle size reduction is. [not essential]
Encircle the Correct Answer Only: -
1- Erythromycin undergoes acid-catalysed hydrolysis in gastric acid. Its stability in
gastric acid can be improved by: ----------. [1.Formulating it in enteric dosage form
2.Forming erythromycin estolate 3.Administering with meals].
a.1 b.2 c.3 [d. 1 and 2] e.1, 2 and 3
2- According to Fick’s law of diffusion, the rate of diffusion is directly proportional to
the: ----------. [1.Concentration difference between the two sides of the diffusion layer
2.Difference in concentration of solution at the solid surface (C1) and the bulk of the
solution (C2) 3.Difference in concentration of the saturated solution (Cs) in contact with
the solid at equilibrium and the bulk of the solution (C)].
a.1 b.1 and 2 c.1 and 3 d.2 and 3 [e.1, 2 and 3]
3- The solubility of an electrolyte is higher in a medium with ----------.
[a. a high dielectric constant] b. a low dielectric constant c. a high proportion of alcohol
d. a and c e. b and c
4- A drug solution (100 mg / ml) degrades to (90 mg / ml) in 1 day and to (50 mg / ml)
in 5 days. What is the order of the degradation reaction? ----------.
[a. zero order] b. first order c. second order d. third order
e. can not be determined with the information provided
5- A drug solution (100 mg / ml) degrades to (90 mg / ml) in 1 day and to (50 mg / ml)
in 5 days. What is the likely value of the degradation reaction constant? ----------.
a. 5 b. 10 c. 20 d. 30
6- A drug solution (100 mg / ml) undergoes a first – order degradation reaction. If the
half – life of the degradation reaction is equal to 30 days, what is the shelf – life of the
solution? ----------.
a. 10 days b. 6 days [c. 4.5 days] d. 3 days e. 1.5 days
7-A drug solution (100 mg / ml) undergoes a first – order degradation reaction. If the
half – life of the degradation reaction is equal to 30 days, what is the number of days
required to degrade to 25% of its initial concentration? ----------.
a. 45 b. 70 c. 90 d. 60
8- Which of the following is not a ―derived‖ property of a drug compound? ----------.
[a. bulk density] b. solubility c. flow behavior d. microscopy e. compression
9- Which of the following would not be tested in a typical preformulation programme? -
---------.
a. solubility b. pKa c. toxicology d. partition coefficient
10- A high degree of hygroscopicity can cause ----------.
a. stability (physical and chemical) – related problems on storage
b. physical changes such as cake formation and colour changes
c. processing – related problems such as poor flow and sticking d. a, b & c
11- In Noyes – Whitney equation, dC / dt = DA (Cs - C) / h, A refers to ----------.
[a. effective surface area of drug particles in contact with G.I.T. fluid]
b. surface area of suspended particles in a suspension
c. angle of repose d. area of emulsion droplets
e. combined area of a powder mix
12- The partition coefficient (log P) of a given compound is a ratio of its solubility -----.
a. in water and oil [b. in oil and water] c. in water and an oily formulation d. in pure form and in emulsion form
e. of its tablet and cream formulations
13- A form of Fick’s law describes steady – state transport through the skin: J=
which of the following statement is incorrect? ----------.
a. drug flux involving bidirectional movement of the drug at the membrane or surface is
possible
b. the smaller the drug partition coefficient between the vehicle and the skin, the greater
the drug flux into the skin
c. the greater the thickness of the stratum corneum, the lower the drug flux
[d. the larger the drug diffusion coefficient, the greater the drug flux into the skin]
14- Which of the following approaches would not be suitable for improving drug
solubility with an aim of increasing the dissolution rate? ----------.
a. hydrate form b. complexation c. micellar solubilization d. salt form
15- Which of the following statements about the Noyes – Whitney dissolution
mechanism is incorrect? ----------.
a. dissolution rate is directly proportional to the drug particle surface area
b. drug concentration in the diffusion layer is higher than in the unstirred layer
c. dissolution rate is not equal to the intrinsic dissolution rate
d. dissolution rate is dependent on the drug concentration in the bulk solution
16- The solubility of an electrolyte is higher in a medium with ----------.
a. a high dielectric constant b. a low dielectric constant
c. a high proportion of alcohol d. a low proportion of alcohol
17- The saturation solubility of the drug in solution in the diffusion layer surrounding
the dissolving particle can be increased by ----------.
a. increasing the agitation rate b. increasing the particle size
c. increasing the bulk fluid volume d. increasing the temperature
18- The hygroscopic growth on the steroid drugs is ----------.
a. due to water condensation b. due to increased solution vapor pressure
c. due to a decrease in particle size d. negligible since it is lipohpilic drugs
19- Surfactants can function as solubilizing agents for certain poorly soluble drugs
because they can ----------.
a. form more soluble ionized salts with the drugs
b. alter the dielectric constant of the medium
c. form more soluble complex with the drugs
d. increase the viscosity of the medium
20- The configuration of a molecule and the type of arrangement in the crystal will
affect the solubility; therefore ---------- increase the solubility.
a. hydrate particle b. anhydrous particle
c. a symmetric particle d. an unsymmetrical particle
21- According to the FDA, a drug substance is considered to be rapidly dissolving when
> 85 % of the labeled amount of drug substance dissolves within using USP I or II in a
volume of ≤ 900 ml.
a. 1 hour b. 30 minutes c. 15 minutes d. 3 hours
22- The drug saturation solubility in the diffusion layer surrounding the dissolving
particle can be increased by ----------.
[a. increasing the temperature] b. increasing the agitation rate
c. decreasing the particle size d. increasing the bulk fluid volume
23- In Noyes – Whitney equation, = DA , A refers to: ----------.
a. area of emulsion droplets b. combined area of a powder mix
[c. effective surface area of drug particles in contact with G.I.T. fluid]
d. angle of repose e. surface area of drug particles in a suspension
24- In order for dissolution to occur spontaneously, the change in free energy must be: -
---------.
a. negative first and then zero at equilibrium
b. positive first and then zero at equilibrium
c. positive first and then negative at equilibrium
d. negative first and then positive at equilibrium
25-
Briefly Answer Each of the Followings: -
1- Write an equation to predict the effect of temperature on solubility.
2- Write a modified form for Noyes – Whitney equation that takes into account the
changing surface area during the dissolution process.
3- Write an equation to predict the effect of temperature on the specific rate constant for
a reaction.
4- Write an equation to predict the maximum buffer capacity.
5- How Noyes – Whitney equation will include the effect of drug particle size / surface
area on the dissolution rate?
6- How the medium pH will affect weak electrolytes solubility?
7- What are the laws that govern the drug diffusion?
8- What are the types of stability that concern pharmacists? …..etc. Slide 24 within lec.
2
9- pH – solubility profile.
10- Fick’s laws of diffusion.
11- Sink conditions.
12- Methods determining chemical compounds dissolution rates.
13- Sink condition expression.
14-
Calculate Answers for Each of the Followings: -
1- The pH of a 1:500 aqueous solution of ephedrine is 10.7, calculate the pKb. (Hint:
M.Wt. = 165.23).
2- A new drug is under development and the pharmaceutical scientist responsible for
designing the first clinical formulation must identify the particle size necessary to
achieve an acceptable rate of dissolution. The drug has a constant aqueous solubility of
10 µg/ml in the physiological pH range 1 – 7, the density of the crystalline drug (ρ =
1.52 gm/cm3) and the aqueous diffusion coefficient (D = 9X10-6 cm2/sec). Estimate the
time it would take for particles of 1, 10, and 100 µm in diameter to dissolve.
3- The lag time for the diffusion of medroxyprogesterone acetate at 25°C through a
patch of rat skin was calculated to be 45 sec. The surface area and the thickness of the
skin were 18.5 cm2 and 15 µm, respectively. Calculate the permeability coefficient of
the drug through the skin if the partition coefficient was 2.05.
4- To study the oral absorption of cyclosporine from an o/w emulsion formulation, an
inverted closed – loop intestinal model was used. The drug was instilled in the intestine,
and the system was maintained at 37°C in an O2 rich buffer medium. The lag time for
the permeation of cyclosporine through the intestinal wall of 75 µm thickness was 7.85
min. The surface area available for diffusion was 28.4 cm2, and the concentration of
cyclosporine in the intestine was 1.35X10-3 gm/cm3. a. Calculate the partition
coefficient of cyclosporine in this system if the permeability coefficient was 4.25X10-6
cm/sec. b. Determine the cumulative amount of cyclosporine in mg that permeated
through the intestinal wall in 6 hr. of the study. c. What is the release order from a
diffusional delivery system? Explain.
5- Calculate the pH of a 1 gm / 100 ml solution of ephedrine sulfate. The M.Wt. of the
salt is 428.5, and Kb for ephedrine base is 2.3 X 10 – 5.
6- The distribution coefficient for iodine between water and carbon tetrachloride at 25 ºC is 0.012. How many grams of iodine are extracted from a solution in water
containing 0.1 gm in 50 ml by one extraction with 10 ml of CCl4? How many grams are
extracted by two 5 ml portions of CCl4?
7- Prepare a buffer solution of pH 5 having a capacity of 0.02. Chose acetic acid, pKa
of 4.76 and .
8- Calculate the pH of a 1 X 10 – 3 M solution of Na2Co3. The acidity constants for
carbonic acid are Ka1 = 4.31 X 10 – 7 and Ka2 = 4.7 X 10 – 11.
9- A solid is to be comminuted so as to increase its solubility by 10%. What must be the
final particle size, assuming that the surface tension of the solid is 100 dynes / cm and
the volume per mole is 50 cm 3? The temperature is 27 ºC.
10- Below what pH will free Phenobarbital begin to separate from a solution having an
initial concentration of 1 gm of sodium Phenobarbital per 100 ml at 25 ºC? The molar
solubility of Phenobarbital is 0.005 and the pKa is 7.41 at 25 ºC. The molecular weight
of sodium Phenobarbital is 254.
11- Calculate the rate of dissolution of relatively hydrophobic drug particles with a
surface area of 2.5 x 10 3 cm 2 and a saturated solubility of 0.35 mg / ml at 25 ºC in
water. The diffusion coefficient is 1.75 x 10 – 7 cm 2 / sec. and the thickness of the
diffusion layer is 1.25 µm. The concentration of drug in the bulk solution is 2.1 x 10 – 4
mg / ml.
12- The initial concentration of a drug decomposing according to first – order kinetics is
94 units / ml. The specific decomposition rate obtained from an Arrhenius plot is 2.09 x
10 – 5 hr – 1 at room temperature. What is the time required for 45 units / ml of the drug
to remain.
13- Calculate the pH of precipitation for 1 % lidocaine HCl. The lidocaine solubility is
1 x 10 – 4 gm / ml and molecular weight of 234.33 whereas lidocaine HCl molecular
weight of 270.79 and the pKa is 7.87.
14- The release of fluocinolone acetonide with a concentration of 4.5 x 10 – 5 gm / cm 3
inside a patch with a cross – sectional area of 12.5 cm 2 and a membrane thickness of 75
µm was investigated. By knowing that the lag time of diffusion is (tL = 8.45 min) and
the partition coefficient is (K = 2.43), calculate the fluocinolone acetonide permeability
coefficient in (cm / sec) and the total amount released in 24 hr in (mg). (Hint: D = h 2 / 6
tL)
15- At 25 °C the distribution partition constant for a second generation cephalosporin
between fermentation broth and butanol is 0.7. If the 50 ml broth phase contains 0.1 gm
drug, how many gm will be extracted using 50 ml and four 12.5 ml successive portions
of butanol?
16- Calculate the pH of the following solution of a monocarboxylic acid and its sodium
salt, which was intended to serve as a medium for an ophthalmic drug. The Ka of the
acid is 6.3 x 10 – 5.
Acid (m.wt. = 122) 0.3 gm
Na salt (m.wt. = 144) 1.7 gm
D.W. qs ad 100 ml
17- For a reaction between diethyl acetate and potassium hydroxide were at a
concentration of 0.05 M.
C2H5COOC2H5 + KOH → C2H5COOK + C2H5OH
Potassium hydroxide concentration was observed to change by 0.0088 mole / L over a
period of 35 min. Calculate the rate constant for the reaction and the half – life.
18- Prepare a pharmaceutical acetate buffer of pH 4.76, having a capacity of 0.05,
knowing that the pKa is 4.76.
19- During accelerated stability testing, a medicine was analyzed to have 3.2 mg / ml of
active drug and its stability constant was found to be 0.05 mg / ml / hr. How long will it
take before the drug decomposes by 10 %?
20- An analgesic formulation is found to degrade at 110 °C with a rate constant of 2 h – 1
and 3.8 h – 1 at 150 °C. Calculate the activation energy.
21- If sorbic acid is distributed between equal volumes of a vegetable oil and water,
what must be the original concentration in the aqueous phase so that 0.5 mg / ml of
associated sorbic acid remains in the aqueous buffered at pH 4.5? Kd = 10.8 and Ka =
1.7 x 10 – 5. (Hint: C = [HA]w (Kd + )) (i.e. =?)
22- What is the theophylline particles rate of dissolution (mg / min)? Knowing that Cs =
7.5 µg / ml, S = 3.75 x 10 3 cm 2, D = 1.75 x 10 – 8 cm 2 / sec, h = 25 µm and Cb = 0.13
µg / ml.
23- The rate constant K1 for the decomposition of 5 – hydroxymethylfurfural at 120 °C
is 1.173 hr – 1 and K2 at 140 °C is 4.86 hr – 1. What is the activation energy, Ea, in Kcal /
mole and the frequency factor, A, in sec – 1 for the breakdown of 5 – HMF within this
temperature range? [Hint: K = Ae – Ea / RT]
24- Calculate the pH of a 0.165 M solution of sodium sulfathiazole. The acidity
constant for sulfathiazole is 7.6 X 10 – 8.
25- Reconstituted ampicillin suspension is stable for 14 days when stored in the
refrigerator (5 °C). If the product is left at room temperature for 12 hr, what is the