6 Key excerpts on "Finding Ka"

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  eBook - ePub

  Physicochemical and Biomimetic Properties in Drug Discovery

  Chromatographic Techniques for Lead Optimization

  • Klara Valko(Author)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Chapter 8

  Molecular Physicochemical Properties that Influence Absorption and Distribution—Acid Dissociation Constant—pKa

  Definition of pKa

  The presence of charge on the molecules dramatically influences many of their physicochemical properties, such as lipophilicity, solubility, and permeability. The presence of charge depends on the acid dissociation constant of the ionizable groups and the pH of the solution/environment. The pH is defined as the negative logarithm of the proton or, more precisely, the hydronium ion concentration in aqueous solutions. The product of the concentrations of hydronium and hydroxide ions in water is constant ; thus, the pH normally ranges from 1 to 14. The acid dissociation constant, or , is defined as the pH where an ionizable group is 50% in ionized form. In other words, the acid dissociation constant, , is the equilibrium constant for the reaction in which a weak acid is in equilibrium with its conjugate base in aqueous solution. For example, for acetic acid, the following equilibrium takes place:

  8.1

  8.2

  When the acetate ion concentration is equal to the acetic acid concentration, equals the concentration. The negative logarithm of the concentration is the pH. The smaller the value of , the stronger is the acid. For basic compounds, Equation 8.3 and Equation 8.4 can be used.

  8.3

  8.4

  Again, the negative logarithm of equals the pH of the aqueous environment, where 50% of the basic group is in a protonated charged form, while 50% is in a neutral, unionized form. The percentage of the ionized molecules depends on the proton concentration (pH) and can be calculated at any pH using the Henderson–Hasselbalch equation [1]. Equation 8.5 describes the relationship between the percentage of ionized molecules and pH for a given

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  eBook - ePub

  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  + log

  A –

  HA

  pH =  6.38 + log(0.5/0.10)  =  6.38 + log(5.0) =  6.38 + 0.70 = 7.08

  The Henderson-Hasselbalch equation can also be used to design a buffer with a specific pH. For example, if a buffer is required to maintain a pH value of 4.60, the most appropriate acid system would be acetic acid with a pK a of 4.74 (from Table 5.4 ). The required ratio of the concentrations of acid [CH3 CO2 H] and conjugate base [NaCH3 CO2 ] needed to give a pH value of 4.60 are given by;

  pH = p

  K a

  + log

  NaCH 3

  CO 2

  CH 3

  CO 2

  H

  pH – p

  K a

  = log

  NaCH 3

  CO 2

  CH 3

  CO 2

  H

  = 4.60 – 4.74 = – 0.14

  NaCH 3

  CO 2

  CH 3

  CO 2

  H

  =

  10

  – 0.14

  = 0.72

  The ratio of 0.72 can be obtained in several ways. If we choose a concentration of acetic acid to be 0.1 M, then the required concentration of sodium acetate would be;

  NaCH 3

  CO 2

  = 0.72 •

  0.10 M

  = 0.072 M

  5.6 The Titration

  A titration is a common laboratory method used to determine the unknown concentration of an analyte. A solution of known concentration, called the titrant , is added slowly to a known volume of the analyte until the reaction is complete. The added volume of titrant is accurately measured and the concentration of the analyte is determined from the concentration and volume of titrant added and the volume of the analyte. Since the measurement of volumes plays a key role, this type of analysis is known as a volumetric analysis .

  Titrations are most commonly associated with acid-base reactions, but they can also be used to determine the concentrations of reactants in other types of chemical reactions. An acid-base titration involves the determination of the concentration of an acid or base by exactly neutralizing the acid or base with an acid or base of known concentration. Neutralization

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  eBook - ePub

  Drug-Like Properties

  Concepts, Structure Design and Methods from ADME to Toxicity Optimization

  • Li Di, Edward H Kerns(Authors)
  • 2015(Publication Date)
  • Academic Press

    (Publisher)

  Table 24.1 ). The CE method separates components and, therefore, has low potential for interference from impurities in the sample.

  24.3.4 Definitive pK a Method: pH-Metric

  Various in-depth methods that have been used for definitive pK a determination have been discussed in an overview [13 ,14 ]. In pharmaceutical development, potentiometric titration is the most common method.

  24.3.5 Potentiometric Titration Method for pK a

  Potentiometric titration is a traditional and definitive method for pK a determination. A diagram of this approach is shown in Figure 24.6 . The compound is dissolved in water and titrated with an acidic or basic buffer of known molarity. In the classical potentiometric method, the pH of the test solution changes as the titrant is added. This change is monitored using a pH electrode. The change in pH with titrating equivalents is plotted versus solution pH. The pK a is the pH of the inflection point of the curve. A variation of this method measures the UV absorbance using a UV spectrophotometric probe in the solution of the test compound. As in the case of the UV methods above, the absorbance of a chromophore near the ionization center changes with ionization and may be monitored to determine the extent of ionization.

  Figure 24.6 In-depth potentiometric titration method for pK a determination: pH-metric method.

  This method has been studied in detail [15 ] and termed “pH-metric” method. It has been integrated as a commercial instrument that is available from Sirius Analytical (Table 24.1 ). This method is considered the “gold standard” for pK a and log P analysis in drug development laboratories. If the compound has low solubility, a co-solvent is added to the test compound solution. Titrations at three co-solvent concentrations allow extrapolation to zero co-solvent aqueous concentration. The throughput for pK a

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  eBook - ePub

  Aquatic Chemistry Concepts, Second Edition

  • James F. Pankow(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  5 Quantitative Acid/Base Calculations for Any Solution of Acids and Bases

  5.1 Introduction

  As discussed in Chapter 2 , the final equilibrium position that a given aqueous system will take is determined by: (1) the T - and P -dependent value(s) of the pertinent equilibrium constant(s); (2) the mass balance and other equation(s) governing the system; and (3) how the activity coefficients γ i depend on chemical composition. The γ i will be determined by the final equilibrium composition of the system, and so will not be exactly knowable a priori for use in the calculations. However, for dilute solutions, or when the reaction medium contains relatively large amount(s) of background dissolved salt(s) not participating in the reactions, then the γ i in the final equilibrium system may be estimated accurately.

  5.2 Solution of the Generic Acid HA, All γ i  = 1

  5.2.1 Introduction

  There are four species in a solution of HA (in addition to H2 O):

  H +   A −   OH −   HA .

  This means there are four unknowns [H+ ], [A− ], [OH− ], and [HA]. We will assume all γ i  = 1 so that concentrations may be used in the equilibrium K expressions rather than activities. How we can address cases when γ i  ≠ 1 will be considered in Section 5.7.

  With four unknowns, four independent equations are required to solve the problem:

  K w = [H + ][OH]       first chemical equilibrium equation

  (5.1)

  K a     =     [ H + ] [ A − ] [ HA ]     second chemical equilibrium equation

  (5.2)

  [HA] + [A − ] = A T = C     mass balance equation (MBE) on total A

  (5.3)

  [ H + ] = [A − ] + [OH − ]     electroneutrality equation (ENE) .

  (5.4)

  For our initial discussions in this chapter, the subscript “a” has been included in the K for the acid dissociation constant of HA. Later, we will drop this subscript. The variable C has been introduced as synonymous with AT . This is because C is commonly used in treatments of this problem by others. We will use C when we wish to emphasize prior treatments that the reader may have seen, and AT

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  eBook - ePub

  Intracellular pH and its Measurement

  • Arnost Kotyk, Jan Slavik(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  That is why, for instance, the dissociation constants shown here are actually apparent dissociation constants that may differ substantially from the true, thermodynamic dissociation constants based on activities. These apparent dissociation constants are often distinguished by a prime from the true ones (K ′ vs. K), but the simple notation will be used throughout. A weak monobasic acid, such as are mostly encountered in biological systems, dissociates in water according to HA + H 2 O ⇌ A − + H 3 O + (11) with the corresponding dissociation constant being defined as K A = c H 3 O + ⋅ c A − / c H 2 O = c T α 2 / (1 − α) (12) where c T = c A− + c HA and α, the degree of ionization, is equal. to c A -/ c T or c H 3 O + / c T. This This degree increases toward unity as c T approaches zero. (With strong acids α ≅ 1 even at moderate concentrations.) From the above equation c H 3 O + = c F α =1/2 (− K A + K A 2 + 4 c T K A) (13) For weak acids, at medium concentrations α ⪡ 1 so that C T = C HA and c H 3 O + ≅ c T K A (14a) or pH ≅ 1/2 (p K A − log c A) (14b) The use of this relatively simple formula is justified (i.e., the error of determination is less than 1%) only with certain limitations. The value of c H 3 O + defined by Equation 14a differs from that defined by Equation 13 in the expression 1 / 2 K A / c T as may be shown by the following consideration. It follows from Equation 12 that α 2 = K A (1 − α) / c T (15a) In the first approximation (for α very small), then, α 2 = K A / c T (15b) while in the second approximation α 2 = (K A / c T) (1 − K A / c T) (15c) For K A / c T to be less than 0.01 in the expression for α, it must be approximately less than 0.02 in the expression for α 2, so that K A /c T must be less than 4 · 10 −4. Hence, for an acid with a dissociation constant of 8.7 · 10 −4 mol dm −3, such as citric acid, a more than 2 M concentration would be required to justify the use of the simplified Equation 14a

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  eBook - ePub

  Biermann's Handbook of Pulp and Paper

  Volume 2: Paper and Board Making

  • Pratima Bajpai(Author)
  • 2018(Publication Date)
  • Elsevier

    (Publisher)

  − :

  [

  H +

  ]

  =

  K a

  [ A ]

  /

  [

  A −

  ]

  Taking the logarithm of each side gives

  pH = p

  K a

  − log

  (

  [ A ]

  /

  [

  A −

  ]

  )

  Using the properties of logarithms, this equation becomes

  pH = p

  K a

  + log

  (

  [

  A −

  ]

  /

  [ A ]

  )

  (21.2)

  Eq. (21.2) is called the Henderson–Hasselbalch equation . This equation should be used with some care if the ratio of the salt to acid is very high or very low. A 10

  − 3

    M solution of acetic acid without sodium acetate might be expected to have a very low pH as the ratio approaches 0 (and the log approaches − ∞). However, as shown in Example 7, Chapter 20 , Volume 2, the acid does ionize, and appreciable amounts of the conjugate base are present. Thus Eq. (21.2) cannot be used near equivalence points (endpoints) of titrations. Eq. (21.2) can be written in the form of a weak base as follows:

  pOH = p

  K b

  + log

  (

  [

  BH +

  ]

  /

  [ B ]

  )

  = p

  K b

  + log

  (

  [ salt ]

  /

  [ base ]

  )

  (21.3)

  The Henderson–Hasselbalch equation is very useful for describing the pH behaviors of mixtures of weak acids and their conjugate bases in solution. If equal molar concentrations of an acid and its conjugate base are in solution, the pH will be equal to the pK a of that acid, as − log(n /n )  =  0 and pH  =  pK a . This is a useful fact to remember because it gives a rough estimate of pH of a solution containing an acid and its conjugate base. Furthermore, even if this solution is diluted, the pH will not change. Also, this solution can absorb small amounts of acid or base without appreciably changing the ratio of acid and salt form. Therefore such a solution would be a good buffer

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