pH Buffers and Isotonic Solutions

Chapter 5

pH Buffers and Isotonic Solutions

Introduction

• Acids and bases contain ions of the element hydrogen. Acids are the substances that deliver hydrogen ion to the solution. The law of mass action can be applied to ionic reactions, such as dissociation of an acid into positively charged hydrogen ion and a negatively charged anion. The hydrogen ion concentration and hydroxyl ion concentrations are used to characterize solutions. The dissociation constant of weak acid is measure of an acid’s strength. Ions are atoms or molecules that have lost or gained electrons. If atoms lose one or more electrons, they become positively charged ions (cations). If they gain one or more electrons, they become negatively charged ions (anions). Hydrogen and hydroxyl ion concentrations found in aqueous solutions can be written in molar units, and denoted as [H+], and [OH− ], respectively. The concept of pH arose from a need to quantify the [H+] in aqueous solutions. Water has a nearly balanced concentration of positive (H+ ) and negative (OH-) ions.  

Sorensen’s pH Scale 

• The hydrogen ion concentration in pure water at room temperature is about 1.0 × 10−7 M. Since every water solution contains hydrogen ions, their concentration is one of the most important parameters describing solution properties. The pH scale was defined because the enormous range of hydrogen ion concentrations found in aqueous solutions make using H+ molarity awkward. For example, in a typical acid-base titration, [H+ ] may vary from about 0.01 M to 0.0000000000001 M. Such numbers are inconvenient to use but it is easier to write as “the pH varies from 2 to 13”

• To simplify things Danish biochemist Soren Sorensen in 1909 developed the pH scale and introduced pH definition as minus (−) logarithm of [H + ] to the base 10. A pH of 7 is considered as “neutral”, because the concentration of hydrogen ions is exactly equal to the concentration of hydroxide (OH− ) ions produced by dissociation of the water. Increasing the concentration of hydrogen ions above 1.0 × 10−7 M produces a solution with a pH of less than 7, and the solution is considered as “acidic”. On other hand decreasing the concentration of hydrogen ions below 1.0 × 10−7 M produces a solution with a pH above 7, and the solution is considered “alkaline” or “basic”

• The pH is an indication of the degree of acidity or basicity (alkalinity) relative to the ionization of water. The term pH is an abbreviation for “pondushydrogenii” (translated as potential hydrogen) meaning hydrogen power, as acidity is caused by a predominance of hydrogen ions. Initially pH was written as PH. According to the Compact Oxford English Dictionary, the modern notation “PH” was first adopted in 1920 by W. M. Clark. The letter “p” in the term “pH” stands for the German word “potenz” (power), so pH is an abbreviation for “power of hydrogen”. In simple terms pH is a logarithmic measure of hydrogen ion concentration. pH = − log [H+ ] … (5.1) where, log is a base −10 logarithm and [H+ ] is the concentration of hydrogen ions in moles per liter of solution.

• With the progress and development of theory of chemical reactions, the definition of pH was reexamined. As the role and behavior of electrical charge in chemical reactions became better understood, the definition of pH was changed to consider the active hydrogen ion concentration. Debey, Huckle and Lowry described a more detailed and theoretically more complete definition of pH. pH = − log Ah+ … (5.2) where, aH+ is the hydrogen ion activity meaning effective concentration of hydrogen ion. There is a difference between concentration and activity for acids, but the same holds true for bases.

1. In dilute solutions (0.001 molar = 1mM) all anions and all cations are so far apart that they are capable to produce the maximum of the chemical energy, i.e. [H+ ] = aH+ . 
2. At higher acid or base concentrations, the physical spacing between cations and anions decreases, such that they begin to obstruct each other, and shield each other’s charge. Therefore, the mobility of the any ion is impaired by interactions with other ions and their associated electrical fields. These local electric field interactions affect the extent to which the ions can participate in chemical reactions, and give an apparent concentration that is always smaller than the real concentration. In this case, the ion activity is “slowed down”; specifically, [H+ ] >aH+ 
3. The difference between ion activity and concentration increases with the acid concentration. Therefore, for acid concentrations greater than 1mM it is generally advisable to use activities instead of concentrations to accurately predict pH. 

The pOH

•  Not only H+ ions are present in every water solution but OH− ions are also always present, and their concentration can change in the very wide range. Thus, it is convenient to use similar definition to describe [OH− ]. pOH = − log [OH− ]  

• In real solutions ion activities rather than concentrations should be used for calculations. The definition of pH uses minus logarithm of activity and not the minus logarithm of concentration. In diluted solutions activity, for all practical purposes is identical to concentration. It means when the concentration goes higher activity starts first to be lower than the concentration and then once the concentration rises it becomes higher than the concentration. If the concentration of charged ions present in the solution is below 0.001M then don’t concerned about activities and use classic pH definition. The relationship between pH, [H+] and [OH+] in moles/L at 25 °C is given in Table 5.1.

• The presence of hydrogen ions in solutions allows us to measure the pH of a solution. The quantity of hydrogen ions (cations) or hydroxyl ions (anions) in a solution determines whether the solution is acidic or alkaline. The concentrations of hydrogen and hydroxyl ions in pure, acidic and alkaline aqueous solutions are used to find the following ionic concentrations: Pure water: [H+ ] = 1 × 10−7 moles/L and [OH− ] = 1 × 10−7 moles/L Acidic water (1 molar aqueous HCl): [H+ ] = 1 × 10° moles/L and [OH− ] = 1 × 10−14 moles/L Alkaline water (1 molar aqueous NaOH): [H+ ] = 1 × 10−14 moles/L and [OH− ] = 1 × 10° moles/L.

• Concentration of H+ ions have major effects on most of the chemical reactions. Depending on concentration hydrogen peroxide can behave as oxidizing or reducing agent, pepsin an enzyme used for digestion works best in strongly acidic conditions (which becomes inactive in neutral solutions) and tea changes its color on addition of a slice of lemon. Therefore, acidity of the solution is of such importance that it was convenient to create a pH scale for its measurements based upon use of Sorensen’s pH definition.

• On the pH scale, pure water has pH 7. Since air always contains small amounts of carbon dioxide, it dissolves in water to make it slightly acidic with pH of about 5.7. The lower the pH, the more acidic solution and solutions with pH above 7 are basic and hence higher the pH the more basic solution is. As the pH scale is logarithmic, it does not start at zero. The most acidic of liquids can have a pH as low as −5. The most alkaline solution has pH of 14. Measurement of extremely low pH values has various complications. 

• There are two important things about pH scale. 1. As pH scale is logarithmic, 
•  unit pH change means tenfold change in the H+ ion concentration. 
• Only solution with pH = 7 is strictly neutral and all solutions with pH in the range 4 to 10 have real concentration of H+ and OH− lower than 10−4 M which can be easily disturbed with small additions of acid and base.  

• The pH scale described earlier is sometimes called “concentration pH scale” because it considers H+ ion concentration. The another one is called “thermodynamic pH scale” which considers the H+ activity rather than the H+ ion concentration. Using pH electrodes we measure just activity and not the concentration in the solution and thus it is a thermodynamic pH scale. It describes real solutions but not the concentration. Concentration pH scale is defined for pure substance and not for water solution whereas thermodynamic pH scale can be defined not only for water solutions, but also for some other solvents, like methanol, ammonia, acetic acid etc. Range of pH for such solvents depends on their ion product for example, pH for acetic acid ranges from 0 to 15.2 while pH for methanol ranges from 0 to 16.7.  

Electrometric pH Determination 

• The pH of the sample is determined electrometrically using either a glass electrode in combination with a reference potential or a combination electrode. The measuring device is calibrated using a series of standard solutions of known pH. A pH is commonly measured with a potentiometric glass electrode. A pH electrode consists of two half-cells; an indicating electrode and a reference electrode. This may, however, be combined into a single probe, called a “combination pH electrode”. A pH electrode contains a bulb at the end covered with a thin glass membrane, Fig. 5.3. This membrane becomes hydrated in the presence of water. Hydrogen ions can enter the silicon-oxygen structure of the glass and alter the charge. This creates a change in electrical potential with respect to the silver/silver chloride reference. The free energy change is related to the change in hydrogen ion activity by equation (5.5). G = −RT ln [H+ ]1 [H+ ]2 where [H+ ]1 and [H+ ]2 are hydrogen ion activities of unknown and reference.

• Glass pH electrodes respond to hydrogen ion activity rather than concentration. Activity may be expressed as product of an activity coefficient (γ) and the hydrogen ion concentration. [H+ ] = γ [H+ ] … (5.6)

• where, the activity coefficient is a function of ionic strength and it has a value close to 1 in dilute solution. Glass electrodes respond to sodium ions to a slight extent causing errors under conditions of low hydrogen ion activity (i.e., high pH) and high sodium concentrations. 

•  METER pH meter is a precise voltameter connected to the pH electrode which is very selective to ions. pH meter can read small millivolt changes from the pH electrode system. Voltage produced by the pH electrode is proportional to logartithm of the H+ activity. The pH meter display is scaled in such a way that the displayed results of measurement is just the pH of the solution.  

• pH measurement involves comparing the potential of solutions with unknown [H+ ] to a known reference potential. pH meters convert the voltage ratio between a reference half-cell and a sensing half-cell to pH values. The meter is seldom source of problems for pH measurements. A successful pH reading is dependent upon all components of the system being operational. Problems with any one of the three: electrode, meter or buffer yields poor readings. Over 90% of pH measurement problems are related to the improper use, storage or selection of electrodes. Most applications today use a combination electrode with both half cells in one body. Today pH meters have temperature compensation (either automatic or manual) to correct for variations in slope caused by changes in temperature. Microprocessor technology has created many new convenience features for pH measurement such as autobuffer recognition, calculated slope and % efficiency and log tables for concentration of ions etc.

• In acidic or alkaline solutions, the voltage on the outer membrane surface changes proportionally to changes in [H+]. The pH meter detects the change in potential and determines [H+ ] of the unknown by the equation (5.7). E = Eo + 2.303 RT n × F × log unknown [H+ ] internal [H+ ] …

• where, E is total potential difference (measured in mV), Eo is reference potential, R is gas constant, T is temperature in Kelvin, n is number of electrons, F is Faraday’s constant and [H+ ] is the hydrogen ion concentration.

Temperature Compensation 

•  The pH of any solution is a function of its temperature. Voltage output from the electrode changes linearly in relationship to changes in pH, and the temperature of the solution determines the slope of the graph. One pH unit corresponds to the standard voltage of 59.16 mV at 25 °C and temperature to which all calibrations are referenced. The electrode voltage decreases to 54.20 mV/pH units at 0 °C and increases to 74.04 mV/pH units at 100 °C. Since pH values are temperature dependent, pH applications require some form of temperature compensation to ensure standardized pH values. Meters and controllers with automatic temperature compensation (ATC) receive a continuous signal from a temperature element and automatically correct the pH value based on the temperature of the solution. Manual temperature compensation requires the user to enter the temperature of the solution to correct pH readings for temperature is more practical for most pH applications. Although there are some restrictions on the use of the electrodes and the way they are treated between measurements, pH meters are in most cases the best way to check pH of the solution, as they are much more precise than indicators and pH papers. Using properly calibrated pH meter with a good electrode one may measure pH with ± 0.01-unit accuracy without any problem.

Colorimetric pH Determination 

• Colorimetric means to measure color. The colorimetric (photometric) pH determination method is based on the property of acid-base indicator dyes, which produce color depending on the pH of the sample. In the colorimetric method, chemicals are added to the water sample and those chemicals react with the water to produce a color change. The color indicates the pH of the water. The color can be measured visually or electronically as an absorbance change spectrophotometrically. The colorimetric method does not work when the water is already colored because it contains dissolved organic matter or large amounts of algae. Colorimetric test kits are inexpensive and can cover a wide range of pH values.

Applications of Buffers 

• Buffers are used in chemical analysis and calibration of pH measurement system (an electrode and the meter). There can be small differences between the output of electrodes, as well as changes in the output over time. Therefore, the measurement system must be periodically calibrated. Most pH meters require calibration at several specific pH values. One calibration is usually performed near the isopotential point (the signal produced by an electrode at pH 7 is 0 mV at 25 °C), and a second is typically performed at either pH 4 or pH 10. It is best to select a buffer as close as possible to the actual pH value of the sample to be measured.

• Buffers resistance to changes in pH makes these solutions very useful for chemical manufacturing and essential for many biochemical processes. The ideal buffer for a pH has a pKa equal to the pH desired, since a solution of this buffer would contain equal amounts of acid and base and be in the middle of the range of buffer capacity.

• Buffer solutions are necessary to keep the correct pH for enzymes in many organisms to live. Many enzymes work only under very precise conditions; if the pH is too far, the enzymes slow or stop working and can denature, thus permanently disabling its catalytic activity. A buffer of carbonic acid (H2CO3) and bicarbonate (HCO− 3 ) present in blood plasma, help to maintain a pH between 7.35 and 7.45. Pepsin is another example which shows maximum activity at pH 1.5.

• Industrially, buffer solutions are used in fermentation processes. 

• Buffers can also be used to maintain the drug in its ionized as well as unionized form. The ionized form of a drug is more water soluble than the unionized form. Buffers can be used to maintain a drug in its ionized (salt) form for aqueous solutions. The unionized form of a drug is more lipid soluble than the ionized form. The unionized form therefore penetrates biological membranes much more efficiently than the ionized form.

• Amphoteric compounds are least soluble at isoelectric points. Substances such as proteins are purified based on this fact. Buffers are useful in maintaining the isoelectric pH. For example, insulin gets precipitated in the pH range of 5 to 6 and hence buffers are used for its purification.

• The pH can affect the stability of a drug in an aqueous solution. For example, ester drugs are very susceptible to hydrolytic reactions. Buffering formulations at low pH (pH 3-5) can reduce the rate of hydrolysis. Buffers also help to improve aspartame stability. Other examples are the alkaline instability of penicillin and ascorbic acid.

• High or low pH can cause tissue irritation. The pH of formulation must match the pH of body fluids otherwise it may cause discomfort. Buffering a formulation to near neutral pH can reduce tissue irritation for example, ophthalmic products are least irritating at pH 7 to 9. Other examples of discomfort are blood (hemolysis) and abraded surfaces (burning sensation). An extremely acid or alkaline pH must be avoided to reduce tissue damage. 

• Solubility of compounds can be controlled by providing a medium of suitable pH. For example, many organic salts such as Fe+3, phosphates, borates become soluble in acidic pH but precipitates in alkaline pH range.

• Buffers help to maintain texture in gelled products by controlled gelling. Controlled gelling reduces reaction rates and minimizes variation in pH. They are also used to prevent color and flavour in food changes in the beverage systems. For example, red color of cherry and raspberry syrups has been maintained at acidic pH which becomes pale yellow to nearly colorless at alkaline pH.   

Buffer Equation 

• Buffers have properties that the pH of buffer solution remains constant, does not change with the dilution and on addition of small quantities of acids or bases as well as on storage for long period. In case of moderate pH solutions addition of small amounts of acids or bases leads to absorption by buffer with only slight pH change. For solutions having extreme pH values, small amounts of solutions of strong acids or bases for example, in case of pH 1, acid concentration is relatively high (0.1 M) and small addition of acid or base doesn’t change pH of such solution significantly. In most cases, we need to know the pKa of the weak acid to do these calculations. The pH of the buffer solution can be obtained by rearranging the equation (5.8) for dissociation constant:

• [H3O + ] = Ka [CH3COOH] [CH3COO− ] 

• Since acetic acid ionizes very slightly, the concentration of acetic acid can be considered as total concentration of acid in the solution. The term [CH3COOH] can be replaced by the term [Acid] and the term [CH3COO− ] can also be replaced by [Salt]. Thus, [H3O + ] = Ka [Acid] [Salt] … (5.9) To calculate pH of buffer solution containing both acid and its conjugated base the dissociation constant equation can be rearranged and rewritten as follows: [H+ ] = Ka [HA] [A− ] 

• where, [HA] is concentration of acid and [A− ] is concentration of its conjugate base. Expressing equation (5.10) in logarithmic form it becomes, pH = pKa + log [A− ] [HA] … (5.11) i.e. pH = pKa + log [Salt] [Acid] The equation (5.11) is called Henderson-Hasselbalch equation. It can be used for pH calculation of solutions containing pair of acid and conjugate base like HA/A− , HA− /A2− or B + /BOH. The buffer equation for weak bases and their corresponding salts can be obtained like that of weak acid buffers. Thus, [OH− ] = Kb [Base] [Salt] … (5.12) Since the ionic product of water (Kw) is H3O + × OH− OH− = Kw/H3O + … (5.13) On substituting value for OH− in equation (5.13) we get Kw/H3O + = Kb [Base] [Salt] … (5.14) In logarithmic form equation (5.14) can be expressed as, Kw/H3O + = pKb + log [B+ ] [BOH] … (5.15) i.e. = pKb + log Salt Base or pH = pKw − pKb + log Base Salt 

• where, [salt], [acid] and [base] are the molar concentrations of salt, acid and base. Henderson-Hasselbalch equation is used mostly to calculate pH of solution prepared by mixing known amount of acid and conjugate base. For example, the pH of a solution prepared by mixing reagents so that it contains 0.1 M of acetic acid and 0.05 M NaOH, the pH is calculated by using Henderson-Hasselbalch equation. If half of the acid is neutralized, then the concentrations of acid and its conjugate base are identical. Thus quotient under logarithm is 1 which is equal to 0 and therefore, pH = pKa. Henderson-Hasselbalch equation is valid when it contains equilibrium concentrations of acid and conjugate base. In case of solutions containing not so weak acids (or not so weak bases) equilibrium concentrations can be far from concentrations of components added into solution. If acetic acid is replaced with dichloroacetic acid (pKa = 1.5) then the proper pH value is 1.78 because dichloroacetic acid is strong enough to dissociate on its own. Therefore, the equilibrium concentration of conjugate base is not 0.05 M but it is 0.0334 M. 

• It is important to remember that acids with pKa less than 2.5 dissociate too easily and the use of Henderson-Hasselbalch equation for pH prediction can give wrong results, especially in case of diluted solutions. For solutions above 10 mM and acids weaker than pKa ≥ 2.5, Henderson-Hasselbalch equation gives results with acceptable error. The same holds for bases with pKb ≥ 2.5. However, the same equation works perfectly regardless of the pKa value in calculating ratio of acid to conjugated base in the solution with known pH. Henderson-Hasselbalch equation also can be used for pH calculation of polyprotic acids, if the consecutive pKa values differ by at least 2. Thus it can be safely used in case of phosphoric buffers but not in case of citric acid buffers. The Henderson-Hasselbalch equation (also known as buffer equation) is adapted to consider acids and their conjugate bases leading to solutions that are resistant to pH change. This equation can be used for the following purposes.

• 1. To calculate pH of a buffer solution when the HA/A− ratio is known. pH = pKa + log [Base] [Acid] … (5.17) 2. The pKa of various dugs can be determined from the pH of the solutions. pKa = pH + log [Acid] [Base] … (5.18) 3. To calculate A− /HA ratio to give a buffer of definite pH. pH − pKa = log [Base] [Acid] … (5.19) 4. To calculate the HA/A− ratio required to give a buffer of a definite pH. pKa − pH = log [Acid] [Base] … (5.20) 5. To calculate the pH changes due to addition of an acid or base to a buffer solution. 6. To calculate the percentage of the drug ionized or unionized in the solution. 7. It is useful in selection of suitable salt forming substance. 8. It helps to predict pH dependent solubility when intrinsic solubility and pKa are known.   

• Example 5.1: Calculate pH of a solution prepared by adding 25 mL of 0.1 M sodium hydroxide to 30 mL of 0.2 M of acetic acid. Dissociation constant of acetic acid is 1.8 × 10−5 .

•  Solution: pKa = − log Ka = − log 1.8 × 10−5 = − log 10−5 – log 1.8 = 5 log 10 − 0.225 = 5 − 0.225 = 4.76 Before reaction: Acetic acid = 2.5 M × 30 mL = 6 mM Sodium hydroxide = 0.1 M × 25 mL = 2.5 mM After reaction: Sodium acetate = 2.5 mM Acetic acid = (6 − 2.5) mM = 3.5 mM ∴ pH = 4.76 + log 2.5 3.5 pH = 4.61 Therefore, the pH of solution prepared by adding 25 mL of 0.1 M sodium hydroxide to 30 mL of 0.2 M of acetic acid is 4.61.  

Buffer Capacity 

• Buffer capacity is a quantitative measure of the efficiency of a buffer in resisting changes in pH. Buffer capacity may be defined as “maximum amount of either strong acid or strong base that can be added before a significant change in the pH occurs. In simple terms, it is the ability of a buffer system to resist pH changes. It is indicated by the term buffer index (β).

• Conventionally, the buffer capacity is expressed as the amount of strong acid or base, in gram-equivalents, that must be added to one liter of the solution to change its pH by one unit. Mathematically buffer capacity is expressed as: β = ∆B ∆pH 

• where, ∆B is gram equivalent of strong acid or base added to change pH of 1 liter of buffer solution and ∆pH is the pH change caused by the addition of strong acid or base. Practically it is possible to measure smaller pH changes. The buffer capacity is quantitatively expressed as the ratio of acid or base added to the change in pH produced.

• Buffer capacity must be large enough to maintain the product pH for a reasonably long shelf-life. Changes in product pH may be due to interaction of solution components with one another or with the type of product package for example, glass, plastic, rubber closures etc. On the other hand, the buffer capacity of ophthalmic and parenteral products must be low enough to allow rapid readjustment of the product to the physiological pH upon administration. The pH, chemical nature, and volume of the solution to be administered must all be considered. Buffer capacities ranging from 0.01 − 0.1 are usually adequate for most pharmaceutical solutions.

• Buffer capacity is always positive. It is expressed as the normal concentration (equivalents per liter) of strong acid or base that changes pH by 1.0. The greater the buffer capacity the smaller is the change in pH upon addition of a given amount of strong acid or base. The buffer index number is generally experimentally determined by titration. For example, when 0.03 mole of sodium hydroxide is added to 0.1 M acetate buffer system the pH increases from 4.76 to 5.03 with a change of 0.27 pH units, Table 5.2. Therefore, by substituting values in the equation (5.21) we have; β = ∆B ∆pH (∴ ∆pH = 5.03 − 4.76 = 0.27) = 0.03 0.27 = 0.11 .

• It is important to remember that buffer capacity is highest when the smallest number of moles of NaOH is added. Buffer capacity is increased by increasing the concentration of the buffer system components. By doubling the total molar concentration of the buffer system will double the buffer capacity at a given pH. Buffer capacity can also be increased by using equimolar concentrations of the acid (HA) and its conjugate base (A− ). The buffer has its greatest capacity, when ratio [salt]/[acid] are equal to 1, i.e. [HA] = [A− ]. Therefore, the buffer equation (5.21) can be written as pH = pKa

Factors Affecting Capacity of Buffer 

Ratio of [A− ]/[HA]   

• The buffer capacity depends essentially on ratio of the salt to the acid or base. The actual concentrations of A− and HA influences the effectiveness of a buffer. The more is the A− and HA molecules available, the less of an effect of addition of a strong acid or base on the pH of a system. For example, consider the addition of a strong acid such as HCl. Initially, the HCl donates its proton to the weak base (A− ) through the reaction A− + HCl → HA + Cl− This changes the pH by lowering the ratio [A− ]/[HA], but if there is lot of A- present, the change in pH will be small. But if we keep adding HCl, the weak base A− will be removed. Once the A− is depleted, any addition of HCl will donate its proton to water as shown in reaction below. HCl + H2O → H3O + + Cl− This drastic increase in the [H+ ] leads to pH drop called as “breaking the buffer solution”. The amount of acid a buffer can absorb before it breaks is called the “buffer capacity for addition of strong acid”. A solution with weaker base, [A− ], has a higher buffer capacity for addition of strong acid. Similarly, a buffer can break when the amount of strong base added is so large that it consumes all the weak acid, through the reaction HA + OH− → A− + H2O A solution with more weak acid, [HA], has a higher buffer capacity for addition of strong base. The buffer capacity is optimal when the ratio is 1:1; that is, when pH = pKa.

Total Buffer Concentration:

• Buffer capacity depends upon the total buffer concentration. For example, it will take more acid or base to deplete a 0.5 M buffer than a 0.05 M buffer. The relationship between buffer capacity and buffer concentrations is given by the Van Slyke equation: β = 2.303 C      Ka [H  3O + ] (Ka + [H3O + ])2 … (5.23) where, C is the total buffer concentration (i.e. the sum of the molar concentrations of acid and salt). A buffer solution containing a weak acid and its salt has a maximum buffer capacity

• (βmax) when pH = pKa i.e. [H3O + ] = Ka. Therefore, by substituting [H3O + ] for Ka in equation (5.23), we get βmax = (2.303 × C) [H3O + ] 2 2[H3O + ] 2 … (5.24) βmax = 2.303 C (2)2 βmax = 0.576 C.

• Example 5.5: Calculate the buffer capacity for a mixture of 0.01 moles of acetic acid and 0.03 moles of CH3COONa in 100 mL of total solution. (Given: pKa= 4.76) Solution: pH = pKa + log [Acid] [Base] = 4.76 + log (0.03) (0.01) = 5.24 pH = − log [H+ ] 4.4 = − log [H+ ] − log [H+ ] = − 5.24 [H+ ] = antilog 5.24 ∴ [H+ ] = 5.75 × 10−6 Since, C = (0.01 + 0.03) moles/100 mL C = 0.4 moles/L We know, pKa = − log Ka Since, pKa = 4.76 4.76 = − log Ka log Ka = − 4.76 Ka = antilog (−4.76) ∴ Ka = 1.74 × 10−5 β = 2.303 × C Ka [H+ ] (Ka + [H+ ])2 = 2.303 × 0.4 1.74 × 10−5 × 5.75 × 10−6 (1.74 × 10−5 + 5.75 × 10−6) 2 = 9.20 × 10−11 7.49 × 10−10 = 0.172 The buffer capacity of a given mixture is 0.172.  

Temperature:

• Buffers are commercially available with a wide range of pH values, and they come in both premixed liquid form or as convenient dry powder, capsules or tablets (to be added to distilled water). These solutions contain acids and bases whose equilibrium is dependent on temperature. Thus, the precise pH is also a function of temperature. The buffers whose pH varies with temperature are shown in Table 5.3. Since the pH values are dependent on temperature, buffers are required to be maintained at constant temperature. Any change in temperature of the buffer results in reduction in effectiveness of the buffer. Buffer containing base and its salt found to show greater changes in buffer capacity with temperature.

Ionic Strength: 

• Ionic strength is reduced by dilution. Change in ionic strength changes the pH of buffer solution resulting in decreased buffer capacity. So, whenever pH of buffer solution is mentioned ionic strength should be specified.

• Example A buffer solution made by 0.1 M each of acetic acid and sodium acetate has a pH 4.76. If 0.02 moles of sodium hydroxide is added to this buffer the resultant pH was found to be 4.94. Calculate the buffer capacity. Solution: ∆pH = 4.94 − 4.76 = 0.18 Since, the amount of NaOH added (∆B) = 0.02 moles Therefore, β = ∆B ∆pH = 0.02 0.18 = 0.11 The buffer capacity of a given buffer is 0.11. 

Buffers in Pharmaceuticals 

Buffering Agents:

• Buffering agents are the substances that adjust the pH of a solution. Buffering agents can be either the weak acids or weak bases that make a buffer solution. These substances are usually added to water to form buffer solutions and are responsible for the buffering action seen in these solutions. The objective of a buffer is to keep the pH of a solution within a narrow range. The function of a buffering agent is to drive an acidic or basic solution to a certain pH state and prevent a change in pH. For example, buffered aspirin has a buffering agent magnesium oxide that maintains the pH of the aspirin as it passes through the stomach of the patient. The monopotassium phosphate also is an example of buffering agent. Buffering agents are primarily used to lower the acidity of the stomach for example, antacid tablets. These agents have variable properties that they have wide differences in solubility and acidity characteristics. As pH controllers, they are important in medicine. The buffering agents work similar to buffer solutions. As we know to avoid the little change in the concentration of the acid and base the solution is buffered. A buffering agent upon addition by providing the corresponding conjugate acid or base sets-up such a concentration ratio that stabilizes the pH of that solution. The resulting pH of this combination can be calculated using the Henderson-Hasselbalch equation. Buffering agents are the main and active components of buffer solutions. They both regulate the pH of a solution as well as resist changes in pH.

• Buffering agents (Buffer salts) and buffer solutions (buffer systems) have different applications that they improve stability (for example, aspartame), control gelling (for example, pectin-based products), reduce rate of reaction (for example, sucrose inversion) and reduce variation in pH. Therefore, the color, flavour (for example, foods and beverages) and texture (for example, gelled products) is maintained. A buffer can be made by partially neutralizing a weak acid like citric or malic acid with sodium hydroxide. However, sodium hydroxide, or caustic soda, is both hygroscopic and hazardous. Instead of using sodium hydroxide, salts of weak acids such as trisodium citrate, sodium lactate, trisodium phosphate, or sodium acetate are used to partially neutralize the acid. Since they contribute to the buffer capacity themselves, these salts are buffer salts. 

PREPARING BUFFER SOLUTIONS 

•  The simplest way of preparing a buffer solution is dissolving known quantity of the salt of the weak acid (or base) in a solution of weak acid (or base) of known concentration. Another way is to neutralize an excess of weak acid (or weak base) with some strong base (or strong acid). The neutralization produces the salt of the weak acid (or base) ‘in situ’. As the weak acid is in excess, there will still be some weak acid in the mixture. The resultant mixture contains both the salt of the weak acid and the weak acid itself.   

General considerations for preparing buffers:

• Determine the optimal pH for the product, based on physical and chemical stability, therapeutic activity and patient comfort and safety (must consider chemical and physical nature of the active and other ingredients and the route of administration).

• Select a weak acid with a pKa near the desired pH (must be non-toxic and physically/chemically compatible with other solution components).

• Calculate the ratio of salt to acid required to produce the desired pH (use Henderson-Hasselbalch equation). 

• Determine desired buffer capacity of the product (consider stability of product, route of administration, volume of dose and chemical nature of product).

• Calculate the total buffer concentration required to produce desired buffer capacity (Van Slyke equation).

• Determine the pH and the buffer capacity of the prepared buffer solution by using suitable method. 

 There are four commonly used methods to prepare buffer solutions:

 The Slow and Stupid Method:

• A buffer composed of an acid and its salt is prepared by dissolving the buffering agent (acid form) in about 60% of the water required for the final solution volume. The pH is adjusted using a strong base, such as NaOH. To prepare a buffer composed of a base and its salt, start with the base form and adjust the pH with strong acid, such as HCl. When the pH is correct, dilute the solution to just under the final volume of solution. Check the pH and correct if necessary, then add water to make the final volume. This method is easy to understand but is slow and may require lots of base (or acid). If the base (or acid) is concentrated, it is easy to increase the pH. If the base (or acid) is dilute, it is easy to increase the volume. Adding a strong acid or base can result in temperature changes, which make pH readings inaccurate (due to its temperature dependence) unless the solution is brought back to its initial temperature.

The Mentally Taxing Method:

• In this method using buffer pKa, the amounts (in moles) of acid/salt or base/salt present in the buffer at the desired pH is calculated. If both forms (i.e., the acid and the salt) are available, the amount required is converted from moles to grams, using the molecular weight of that component. The correct amounts of both forms are weighed and used. If only one form is available then the buffer is prepared by adding the entire buffer as one form, and then acid or base is added to convert some of the added buffer to the other form. Once the total concentration of buffer in the solution is decided, it is converted to amount (in moles) using the volume of solution, and then to grams, using the molecular weight of the buffer. The amounts (in moles) of each form that will be present in the final solution are calculated using the buffer pKa and the desired pH. Then the amount of strong acid or base that must be added to give the correct amounts of each form at the pH of the final solution  is calculated. The buffer and strong acid or base is dissolved in slightly less water than is required for the final solution volume. The pH is checked and corrected if necessary. Water is added to make-up the final volume. It is a fast method and easy to prepare. This method requires the buffer pKa value. Additional pH adjustment is rarely necessary, and when needed, the adjustment is small. 

The Two Solution Method: 

• The separate solutions of the acid form and base form of the buffer are prepared from solutions having the same buffer concentration. To obtain the desired pH, one solution is added to the other with continuous monitoring the pH. This method easy to do but requires both forms of buffer. The required solution volumes are proportional to the ratio of buffer components in the final solution at the desired final pH.

The Completely Mindless Method:

• The correct amounts of acid or its salt or base or its salt required for different pH values are selected from the standard data value tables and the same amounts of the components are dissolved in the slightly less water than is required to make the final volume of solution. The pH is checked and corrected if required followed by adjusting the final volume by adding water. This method is easy to do because of use of suitable reference table. It is convenient method for frequently prepared buffers but it may be difficult to find such table. This method requires both forms of buffer. Components amounts from table need to be adjusted to produce the required buffer concentration and volume.

 Alternative Method for Preparing Buffer Solutions: 

• This method is used rarely. In this method rather than mixing the weak acid with its salt a buffer solution is prepared by adding a limited amount of strong base to the weak acid to produce a solution of the weak acid (or base) and its conjugate base (or acid) which results in the weak acid and the salt of the weak acid. 

• Calculate pH of a solution containing 0.5 M acetic acid and 0.5 M sodium acetate; both before and after enough SO3 gas is dissolved to make the solution 0.1 M in sulfuric acid. The pKa of acetic acid is 4.75. Solution: Before the acid is added, using buffer equation pH is calculated as follows, pH = pKa + log [Base] [Acid] pH = pKa + log [0.5M] [0.5M] pH = 4.75 + log 1 pH = 4.75 + 0 pH = 4.75 To calculate the pH after the acid is added, we assume that the acid reacts with the base in solution and that the reaction has a 100% yield. Therefore, it can be said that 0.1 moles/L of acetate ions reacts with 0.1 moles/L of sulfuric acid to produce 0.1 moles/L of acetic acid nd hydrogen sulfate. The second dissociation of sulfuric acid is ignored as it is minor in comparison to the first. So the final concentration of acetic acid is 0.6 M and acetate is 0.4 M. Substituting those values into the buffer equation gives a pH of 4.75. It is important to remember that 0.1 M solution of strong acid give a pH 1 but the buffer gives a pH of 4.75.

Standard Buffer Solutions:

• The standard buffer solution of pH ranging from 1.2 to 10 are possible to prepare by appropriate combinations of 0.2 N HCl or 0.2 N NaOH or/and 0.2 M solutions of potassium hydrogen phthalate, potassium dihydrogen phosphate, boric acid-potassium chloride as given in pharmacopoeia. The pH range and the quantities of the ingredients used to make respective standard buffer at 25 °C are given in Table 5.5. Buffers have great use in biological research. Various criteria that can be applied while making buffers for this application are listed below.

• Buffers must possess enough buffer capacity in the required pH range.
• It must be available in highly purified form. 3. 
• It must be highly water soluble and impermeable to biological membranes. 
• It must be stable especially with respect to hydrolysis and enzymatic action.
• It must maintain pH which is influenced to a very small value by their concentration, temperature and ionic strength as well as salting out effect of the medium. 
• It must be non-toxic with no biological inhibition activity.
• Buffers must not form complexes. 8. 
• It must not absorb light in the visible or ultraviolet regions.
• It must not precipitate in redox reactions. 
• It must not alter solubility of active ingredients. 11. It must be safe to use in biological systems and do not alter the pharmacological responses of the active ingredients.

Pharmaceutical Buffers:

• Generally, buffers are used in the pharmaceutical products for two purposes viz. to adjust the pH of product for maximum stability and to maintain the pH within the optimum physiological pH range. Pharmaceutical solutions generally have a low buffer capacity in order to prevent overwhelming the body’s own buffer systems and significantly changing the pH of the body fluids. Buffers have concentrations in the range of 0.05 to 0.5 M and buffer capacities in the range of 0.01 to 0.1 which are usually sufficient for pharmaceutical solutions. The Table 5.6 gives some of the buffer systems used in the pharmaceutical formulations along with their pKa values. Most pharmaceutical buffers are composed of ingredients that are found in the body (for example, acetate, phosphate, citrate and borate). While selecting, the right pharmaceutical buffers choose a weak acid with pH > pKa. Carry out calculations using buffer equation to determination of acid/base needed to give required pH. Also, choose proper concentration needed to give suitable buffer capacity. The ingredients are selected from available ones considering their sterility, stability, cost, toxicity etc. 

 Solid dosage forms: 

• Buffers have been used widely in solid dosage forms such as tablets, capsules and powders for controlling the pH of the environment around the solid particles. This has practical application for the drugs that have dissolution rate limited absorption from unbuffered solutions. One of the special applications of buffers is to reduce the gastric irritation caused by the acidic drugs. For example, sodium bicarbonate, magnesium carbonate and sodium citrate antacids, used for reducing acidity. 

 Semisolid formulations:

• Semisolid preparations such as creams and ointments undergo pH changes upon storage for long time resulting in its reduced stability. Hence buffers such as citric acid and sodium citrate or phosphoric acid/sodium phosphate are included in these preparations to maintain their stability.

Parenteral products: 

• Use of buffers is common in the parenteral products. Since the pH of blood is 7.4 these products are required to be adjusted to this pH. Change in pH to higher side (more than 10) may cause tissue necrosis while on lower side (below 3) it may cause pain at the site of action. As blood, itself function like buffer, adjustment of pH for small volume parenteral preparations is not required. Commonly used buffers include citrate, glutamate, phthalate and acetate. The pH optimization is generally carried out to have better solubility, stability and reducing irritancy of the product. 

Ophthalmic products: 

• Many drugs, such as alkaloidal salts, are most effective at pH levels that favour the undissociated free bases. However, at such pH levels, the drug may be unstable Therefore such pH levels must be obtained by use of buffers. The purpose of buffering some ophthalmic solutions is to prevent an increase in pH caused by the slow release of hydroxyl ions by glass. Such a rise in pH can affect both the solubility and the stability of the drug. The decision whether buffering agents should be added in preparing an ophthalmic solution must be based on several considerations. Normal tears have a pH of about 7.4 and possess some buffer capacity.  

Buffers in Biological Systems 

• Biochemical reactions are specifically sensitive to pH. Most biological molecules contain groups of atoms that may be charged or neutral depending on pH, and whether these groups are charged or neutral has a significant effect on the biological activity of the molecule. In all multicellular organisms, the fluid within the cell and the fluids surrounding the cells have a characteristic and nearly constant pH. There is great variation in the pH of fluids in the body and small variation is found within each system. For example, the pH of body fluid can vary from 8 in the pancreatic fluid to 1 in the stomach. The average pH of blood is 7.4, and of cells is in the range of 7.3 to 7. This pH of body fluids is maintained through buffer systems. Body fluids contain buffering agents and buffer systems that maintain pH at or near 7.4. The kidneys and the lungs work together to help maintain a blood pH of 7.4 by affecting the components of the buffers in the blood. Proteins are the most important buffers in the body as their amino and carboxylic acid groups acts as proton donors or acceptors as H+ ions are either added or taken out from the environment. Important endogenous (natural) buffer systems include carbonic acid/sodium bicarbonate and sodium phosphate in the plasma and hemoglobin, and potassium phosphate in the cells. Two important biological buffer systems are the dihydrogen phosphate system and the carbonic acid system.

The Phosphate Buffer System:

• The phosphate buffer system operates in the internal fluid of all cells. This buffer system consists of dihydrogen phosphate ions (H2PO − 4 ) as hydrogen ion donor (acid) and hydrogen phosphate ions (HPO2− 4 ) as hydrogen-ion acceptor (base). These two ions are in equilibrium with each other as indicated by the chemical equation given below. H2PO − 4(aq) H + (aq) + HPO 2− 4(aqIf additional hydrogen ions enter the cellular fluid, they are consumed in the reaction with HPO2− 4 , and the equilibrium shifts to the left. If additional hydroxide ions enter the cellular fluid, they react with H2PO− 4, producing HPO2− 4 , and shifting the equilibrium to the right. The equilibrium expression for this equilibrium is expressed as given below. Ka = [H+ ] [HPO 2− 4 ] [H2PO − 4 ] 

• Buffer solutions are most effective in maintaining a pH near the value of the pKa. In mammals, cellular fluid has a pH in the range 6.9 to 7.4, and the phosphate buffer is effective in maintaining this pH range. The pKa for the phosphate buffer is 6.8, which allows this buffer to function within its optimal buffering range at physiological pH. The phosphate buffer only plays a minor role in the blood because H3PO4 and H2PO4 - are found in very low concentration in the blood. Hemoglobin also acts as a pH buffer in the blood. Hemoglobin protein can reversibly bind either H+ (to the protein) or O2 (to the Fe of the heme group), but that when one of these substances is bound, the other is released. During exercise, hemoglobin helps to control the pH of the blood by binding some of the excess protons that are generated in the muscles. At the same time, molecular oxygen is released for use by the muscles.

The Carbonic Acid System:

• Another biological fluid in which a buffer plays an important role in maintaining pH is blood plasma. In blood plasma, the carbonic acid and hydrogen carbonate ion equilibrium buffers the pH. In this buffer, carbonic acid (H2CO3) is the hydrogen ion donor (acid) and hydrogen carbonate ion (HCO− 3 ) is hydrogen-ion acceptor (base). The simultaneous equilibrium reaction is shown below. H2CO3(aq) H + (aq) + HCO − (3) (aq)

• This buffer functions in the same way as the phosphate buffer. Additional H+ is consumed by HCO− 3 and additional OH− is consumed by H2CO3. The value of Ka for this equilibrium is 7.9 × 10−7, and the pKa is 6.1 at body temperature. In blood plasma, the concentration of hydrogen carbonate ion is about twenty times the concentration of carbonic acid. The pH of arterial blood plasma is 7.4. If pH falls below this normal value, a condition called acidosis and when pH rises above the normal value, the condition is called alkalosis is observed.

• The concentrations of hydrogen carbonate ions and carbonic acid are controlled by two physiological systems. The concentration of hydrogen carbonate ions is controlled through the kidneys whereas excess hydrogen carbonate ions are excreted in the urine. The carbonic acid-hydrogen carbonate ion buffer works throughout the body to maintain the pH of blood plasma close to 7.4. Changes in hydrogen carbonate ion concentration, however, require hours through the relatively slow elimination through the kidneys. Carbonic acid concentration is controlled by respiration that is through the lungs. Carbonic acid is in equilibrium with dissolved carbon dioxide gas. An enzyme called carbonic anhydrase catalyzes the conversion of carbonic acid to dissolved carbon dioxide. In the lungs, excess dissolved carbon dioxide is exhaled as carbon dioxide gas. H2CO3(aq) CO2(aq) + H2O(l) CO2(aq) CO2(g) .

• The body maintains the buffer by eliminating either the acid (carbonic acid) or the base (hydrogen carbonate ions). Changes in carbonic acid concentration bring about within seconds through increased or decreased respiration.

Lysis Buffer: 

• A lysis buffer is used for lysing cells for use in experiments that analyze the compounds of the cells (for example, western blot). There are many kinds of lysis buffers that one can apply; depending on what analysis the cell lysate will be used for example, RBC lysis buffer. In studies like DNA finger printing the lysis buffer is used for DNA isolation. Dish soap can be used in a pinch to break down the cell and nuclear membranes, allowing the DNA to be released.  

Buffered Isotonic Solutions

• Tonicity is a measure of effective osmolarity or effective osmolality in cell biology. Osmolality and osmolarity are properties of a solution, independent of any membrane. Osmolality is a concentration scale to express total concentration of solute particles and is directly related to any of the four colligative properties. It is derived from molality by factoring in the dissociation of electrolytic solutes. Osmolality = Molecular weight × Number of particles/molecule.

• Tonicity is a property of a solution about a membrane, and is equal to the sum of the concentrations of the solutes which have the capacity to exert an osmotic force across that membrane. Tonicity depends on solute permeability. The permeable solutes do not affect tonicity but the impermeable solutes do affect tonicity. If a semi-permeable membrane is used to separate solutions of different solute concentrations, a phenomenon known as osmosis occurs to establish concentration equilibrium. The pressure driving this movement is called osmotic pressure and is governed by the number of particles of solute in solution. If solute is a non-electrolyte, then number of particles is determined solely by the solute concentration. If the solute is an electrolyte, the number of particles is governed by both the concentration and degree of dissociation of the substance.

• The distinction between the isosmotic and isotonic terms comes with the realization that red blood cell membranes are not perfect semipermeable membranes but allow passage of some solutes, such as alcohol, boric acid, ammonium chloride, glycerin, ascorbic acid, lactic acid, etc. A 2% solution of boric acid when physically measured found to be isosmotic (containing same number of particles) with blood and not isotonic (exerting equal pressure or tone) with blood but is isotonic with tears. This differentiation is not having any great significance and therefore isotonicity values are calculated based on the number of particles in solution is sufficient. The clinical significance of all this is to ensure that isotonic or isosmotic solutions do not damage tissue or produce pain when administered. 

• Tonicity is generally classified in three types; hypertonicity, hypotonicity and isotonicity. Hypertonic, isotonic and hypotonic solutions are defined in reference to a cell membrane by comparing the tonicity of the solution with the tonicity within the cell.

Hypertonicity: 

• A solution having higher osmotic pressure than the body fluids (or 0.9% NaCl solution) is known as hypertonic solution. These solutions draw water from the body tissues to dilute and establish equilibrium. An animal cell in a hypertonic environment is surrounded by a higher concentration of impermeable solute than exists in the inside of the cell. For example, if 2.0% NaCl solution is added to blood (defibrinated), osmotic pressure directs a net movement of water out of the cell causing it to shrink (the shape of the cell becomes distorted) and wrinkled (crenated), as water leaves the cell.. This movement is continued until the concentrations of salt on both sides of the membrane are identical. Hence, 2.0% NaCl solution is hypertonic with the blood, Fig. 5.6 (a).

Isotonicity: 

• The solution that have the same osmotic pressure as that of body fluids are said to be isotonic with the body fluid. Body fluids such as blood and tears have osmotic pressure corresponding to that of 0.9 % NaCl or 5% dextrose aqueous solution thus, a 0.9% NaCl or 5% dextrose solution is called as isosmotic or isotonic. The term isotonic means equal tone, and is used interchangeably with isosmotic regarding specific body fluids. Isosmotic is a physicochemical term that compares the osmotic pressure of two liquids that may or may not be body fluids. A cell in an isotonic environment is in a state of equilibrium with its surroundings with respect to osmotic pressure. When the amount of impermeable solute is same on the inside and outside of the cell, osmotic pressure becomes equal. When amount of impermeable solute is not same on the inside and outside of the cell, the force of water trying to exit or enter the cell to maintain the balance. This pressure drives hypertonic or hypotonic cells to become isotonic. For example, a 0.9% w/v solution of NaCl in water is isotonic in relation to RBC’s and their semi-permeable membranes.

• Requirements of isotonic solutions are that they must not cause any contraction or swelling of the tissues. The product must not produce discomfort when instilled in the eye, nasal tract, blood, or other body tissue for example, isotonic NaCl. On addition of 0.9 g NaCl/100 mL (0.9%) into blood (defibrinated), the cells retain their normal size. Isotonic solution should be restricted to solutions having equal osmotic pressures with respect to a particular membrane.

Hypotonicity: 

• A solution with low osmotic pressure than body fluids is known as hypotonic solution. Administration of a hypotonic solution produces shrinking of tissues (painful swelling) as water is pulled from the biological cells (tissues or blood cells) to dilute the hypertonic solution. The effects of administering a hypotonic solution are generally more severe than with hypertonic solutions, since ruptured cells can never be repaired. Hypotonic solutions show opposite effect compare to hypertonic solutions that the net movement of water is into the cell causing them to swell. If the cell contains more impermeable solute than its surroundings, water enters it. In the case of animal cells, they get swelled until burst; but this doesn’t happen to plant cells i.e. they do not burst due to the reinforcement their cell wall provides. If 0.2% NaCl solution is added to blood (defibrinated), the cells get swelled and burst. Therefore, 0.2% NaCl solution is hypotonic with respect to the blood, Fig. 5.6 (c). A 2.0% solution of boric acid has the same osmotic pressure with blood; but it is hypotonic because boric acid passes freely through cell membrane regardless of concentration. 

ISOTONICITY VALUE 

• Lachrymal fluid is isotonic with blood having an isotonicity value corresponding to that of a 0.9% NaCl solution. Ideally, an ophthalmic solution should have this isotonicity value; but the eye can tolerate isotonicity values as low as that of a 0.6 % NaCl solution and as high as that of a 2.0% NaCl solution without marked discomfort. Some ophthalmic solutions are necessarily hypertonic to enhance absorption and to provide a concentration of the active ingredient(s) strong enough to exert a prompt and effective action. The amount of such solutions used is small because on administration the dilution with lachrymal fluid takes place rapidly with minimal discomfort from the hypertonicity which is only temporary. However, any adjustment toward isotonicity by dilution with tears is negligible where large volumes of hypertonic solutions are used as collyria to wash the eyes; it is, therefore, important that solutions used for this purpose be approximately isotonic. 

Methods Used to Determine Tonicity Value:

• Many chemicals and drugs are used in the pharmaceutical formulations. These substances contribute to the tonicity of the solution. Hence methods are needed to verify the tonicity and adjust isotonicity. Two of the methods used to determine tonicity value are described below. 

 Hemolytic method: 

• Isotonicity value is calculated by using hemolytic method in which the effect of various solutions of drug is observed on the appearance of red blood cells suspended in solutions. In this method, RBC’s are suspended in various solutions and the appearance of RBC’s is observed for swelling, bursting, shrinking and wrinkling of the blood cells. In hypotonic solutions, oxyhemoglobin released is proportional to number of cells hemolyzed; in case of hypertonic solutions, the cells shrink and become wrinkled or crenated where as in case of isotonic solutions the cells do not change their morphology. 

Cryoscopic method:

• Isotonicity values can be determined from the colligative properties of the solutions. For this purpose, freezing point depression property is most extensively used. The freezing point of water is 0 ºC, and when any substance such as NaCl is added to it the freezing point of water decreases. The freezing point depression (∆Tf) of blood is – 0.52 ºC. Hence the ∆Tf value of the drug solution must be – 0.52 ºC. This solution shows osmotic pressure equal to the blood and hence the RBC’s morphology as well as functions found to be unchanged. 

Methods of Adjusting Tonicity And pH:

• Several methods are used to adjust isotonicity of pharmaceutical solutions. Isotonicity can also be calculated from the colligative properties of the drug solutions. If solutions are injected or introduced into the eyes and nose, these are to be made isotonic to avoid hemolysis of RBC’s and to avoid pain and discomfort. This is possible for either manufactured or extemporaneously prepared solutions. By using the appropriate calculations based on colligative properties of solutions, it is easy to determine the amount of adjusting agents to be added. It helps to overcome the side effects caused from administering solutions which contain adjusting agents less or more than isotonic solutions. The three frequently used methods to calculate isotonicity of the solutions are described below. If carried out correctly, these methods give closely comparable results with a little deviation. 

Class I: 

• NaCl or some other substance is added to the solution of the drug to lower the freezing point of the solution to − 0.52 °C and thus make the solution isotonic. Cryoscopic method and Sodium chloride equivalent method are the examples of this class.

 Class II: 

• Water is added to the drug in sufficient amount to make it isotonic and then the preparation is brought to its final volume with an isotonic or buffered isotonic solution. White –Vincent method is example of this type. 

 Class III: 

• A freezing point depressions and Liso values for number of drugs are estimated theoretically from the molecular weight of the drug and can be used to calculate the amount of adjusting substance to be added to make the solution isotonic for example, using reference tables for ∆Tf and Liso values from different books.      

Cryoscopic method:

• In this method, the quantity of each substance required for an isotonic solution can be calculated from the freezing point depression values. A solution which is isotonic with blood has a ∆Tf of 0.52 °C. Therefore, the freezing point of drug solution must be adjusted to this value. Many pharmaceutical textbooks usually list the freezing point depression of many compounds and it is then easy to calculate the concentration needed to achieve isotonicity from these values. In case of drug solutions if it is not possible to adjust tonicity by altering the drug concentration then an adjusting substance is added to achieve desired tonicity. The weight (in grams) of adjusting substance can be calculated as described below. For example, the drug concentration in 100 mL solution is ‘a’ grams, then: ∆Tf (for drug solution) = a × ∆Tf of 1 % drug solution = x If w are the grams of the adjusting substance to be added to 100 mL of drug solution to make it isotonic then: ∆Tf (for adjusting solution) = w × ∆Tf of 1 % adjusting substance = w × b For making a solution isotonic: x + wb = 0.52 or w = (0.52 − x) b … (5.27) If sodium chloride is used as adjusting substance whose ∆Tf of 1 % solution is 0.58 °C (≈ 0.576 °C), then w = (0.52 − x) 0.58 … (5.28).

• Addition of any buffering agent to a solution affects its isotonicity leading to change in osmotic pressure of a solution. It happens not only by drug but also by any buffer compounds that are added in the formulation. But on addition of these buffering agents the solution will not be isotonic and hence it is necessary to add additional NaCl to bring the solution to isotonicity. The most widely used method is the sodium chloride equivalent method. This method uses the NaCl equivalent to calculate the amount of an adjusting agent  needed to be added to a solution to bring it to isotonicity. The NaCl equivalent is the weight of the NaCl (in grams) that produces the same colligative properties (osmotic effect; based on number of particles) as that of 1 g of a drug. For example, if the ENaCl of a drug is 0.20 this means that 0.20 g of NaCl will have identical osmotic pressure and freezing point depression as 1 g of the drug. 

• In this method, the amount of the drug is multiplied by the (ENaCl) to obtain the amount of NaCl that will produce similar osmotic conditions to those of the drug in the solution. This value is then subtracted from the amount of NaCl needed to make an isotonic solution. If the adjusting solute is not NaCl, the amount of calculated NaCl is divided by the ENaCl of the adjusting solute. This then represents the weight of the adjusting agent to be added to bring the solution to tonicity. The ENaCl for many drugs.

• The ENaCl value of tonicity adjusting substances also can be calculated from the Liso value of the substances. The Liso values of the tonicity adjusting substances are given in Table 5.8 and mentioned as constants in many references. In this method freezing point depression equation is used to calculate the amount of the isotonicity adjusting substance that must be added to hypotonic solution of drug to bring to tonicity. As the freezing point depression for solutions of electrolytes are greater than those calculated by the equation, ∆Tf = Kfm, a new constant Liso (= iKf) is introduced to account for this deviation. The equation then becomes ∆Tf = Liso C

• where, ∆Tf = Liso is molal freezing point depression of water considering the ionization of electrolyte (i.e. iKf) and C is the concentration of the solution in molarity. In dilute solution, the molal concentrations are not much different from the molar concentration and can be used interchangeably. The following equations help to calculate the ENaCl value from Liso value of these substances. The ∆Tf of 1 g of drug per 1000 mL of solution is equal to LisoC. Therefore, ∆Tf = Liso 1 g M = Liso M … (5.30) where, M is molecular weight of the solute. Since, the Liso value of NaCl is 3.4. ∆Tf = 3.4 × ENaCl 58.45 … (where, ENaCl is the weight of NaCl with the same freezing point as 1 g of drug. Thus Liso = 3.4 × ENaCl 58.45 … (5.32) ENaCl = 17 × Liso M 

• In some cases instead of NaCl another isotonic agent such as mannitol, propylene glycol, or glycerin is used. Using ENaCl values, isotonic solutions are prepared by just multiplying quantity of each drug in the formulation by its ENaCl values and subtracting them from the 0.9 g/100 mL. Thus for ‘x’ grams of drug the amount of NaCl required to obtain 100 mL solution isotonic is obtained as Amount of NaCl (Y) = 0.9 – [x × ENaCl] … (5.34) For using another isotonic agent its amount (X) required to make solution isotonic is obtained by

D. White-Vincent method:

• This method involves use of addition of water to drug to make isotonic solution followed by final volume adjustment with addition of isotonic or isotonic buffered solution. White Vincent from their study of need of pH adjustment in addition to tonicity of ophthalmic solution developed an equation as given below. For example, to make 40 mL of 1% solution of procaine hydrochloride isotonic with body fluid first the weight of drug (x) is multiplied by ENaCl X = x × ENaCl … (5.36) = 0.4 × 0.21 = 0.084 g The quantity 0.084 is amount of NaCl equivalent to 0.4 g of procaine hydrochloride. We know 0.9 g/100 mL solution is isotonic; therefore, the volume (V) of isotonic solution that can be prepared from (X) g of NaCl is obtained as 0.9 100 = 0.084 V … (5.37) ∴ V = 0.084 100 0.9 … (5.38) = 9.33 mIn equation (5.38) the 0.084 is equal to weight of drug (x) multiplied by ENaCl as shown in equation (5.36). The ratio (100/0.9) can be written as 111.1. Therefore, the equation (5.38) can be written as V = x × ENaCl × 111.1 … (5.40) where, V is volume in mL of isotonic solution prepared by mixing drug in water, x is grams of drug and ENaCl is sodium chloride equivalent from Table 5.7. The constant 111.1 is volume in mL of isotonic solution prepared by dissolving 1 gram of sodium chloride in water. The volume of isotonic solution prepared by dissolving drug in water is calculated as V = 0.4 × 0.21 × 111.1 = 9.33 mL To make an isotonic solution sufficient sodium chloride solution or an isotonic buffered diluting solution is added to make 40 mL of final solution.