Henderson-Hasselbalch equation deriving

Although this qualitative view of buffering action is quite informative, both clinical and research activities involving buffered solutions, biologic fluids or laboratory made, require a quantitative approach. This can be achieved via the Henderson-Hasselbalch equation derived from Equation (3.5) as follows taking logs on both sides of Equation (3.5), we have... 

A buffer solution can be described by an equilibrium-constant expression. The equilibrium-constant expression for an acidic system can be rearranged and solved for [H3O+]. In that way, the pH of a buffer solution can be obtained, if the composition of the solution is known. Alternatively, the Henderson-Hasselbalch equation, derived from the equilibrium constant expression, may be used to calculate the pH of a buffer solution. 

Hemiketal (Section 17 8) A hemiacetal derived from a ketone Henderson-Hasselbalch equation (Section 19 4) An equa tion that relates degree of dissociation of an acid at a partic ular pH to its... 

The Henderson-Hasselbalch equation is derived below. A weak acid, HA, ionizes as follows ... 

The last part of Eq. (1) is derived from the pH dependence of permeability, given a pH gradient between the two sides of the intestinal barrier, based on the well known Henderson-Hasselbalch equation. Direct measurement of in situ intestinal perfusion absorption rates confirmed this pH dependence [14]. 

Dmw can be derived from the partition coefficients of the single species (equation 23) if the fractions of the species, a(W, under given conditions are known (Henderson-Hasselbalch equation). 

The Henderson-Hasselbalch equation is an equation expressing the relationship between pH, pK l, and the log of the ratio of the concentrations of the base to its conjugate acid or an acid to its conjugate base. It is derived from the K l or Kb expression. See Equations (5.26) to (5.30) in the text. They are each a form of this equation. 

B. The Henderson-Hasselbalch equation is derived from the rearrangement of the equilibrium equation for dissociation of a weak acid. 

Hasselbalch equation, which is important for understanding buffer action and acid-base balance in the blood and tissues of vertebrates. This equation is simply a useful way of restating the expression for the dissociation constant of an acid. For the dissociation of a weak acid HA into H+ and A-, the Henderson-Hasselbalch equation can be derived as follows ... 

Be able to derive the pH expression and the Henderson-Hasselbalch equation. 

An expression for instantaneous buffer capacity, jS, can be derived using calculus. Essentially, /S is the reciprocal of the slope of the titration curve at any point. Starting with the Henderson-Hasselbalch equation ... 

It is clear from equations (5.49) and (5.50) that there is a degree of empiricism about these equations which arises in their derivation from the fitting of data sets based on the independent variables. The ratio M /P can be obtained from the modified Henderson-Hasselbalch equation ... 

A buffer solution is a solution that resists changes in pH. If acid is added then, within reason, the pH does not fall if base is added, the pH does not rise. Buffers are usually composed of a mixture of weak acids or weak bases and their salts and function best at a pH equal to the pKa of the acid or base involved in the buffer. The equation that predicts the behaviour of buffers is known as the Henderson-Hasselbalch equation (named after chemists Lawrence Joseph Henderson and Karl Albert Hasselbalch), and is another vitally important equation worth committing to memory. It is derived as follows, by considering a weak acid that ionises in solution ... 

When a weakly acidic or basic drug is administered to the body, the drug will ionise to a greater or lesser extent depending on its piCa and the pH of the body fluid in which it is dissolved. The pH of the body varies widely, but the most important biological solution is the blood, which, as stated above, normally has a pH of 7.4. An equation can be derived that will predict the extent to which the drug ionises, and, as is often the case, the starting point for the derivation is the Henderson-Hasselbalch equation (1.7). 

Buffers are defined as substances that resist changes in the pH of a system. All weak acids or bases, in the presence of their salts, form buffer systems. The action of buffers and their role in maintaining the pH of a solution can best be explained with the aid of the Henderson-Hasselbalch equation, which may be derived as follows. 

The Henderson-Hasselbalch equation is described in detail in Chapter 27. However, it is important to review this equation here because it aids in understanding pH regulation of body fluids as it relates to the compensatory mechanisms of the body in acid-base disturbances. The equation derived in Chapter 27 can also be written as follows ... 

The buffer value (p) is defined as the amount of base required to cause a change in pH of one unit. The buffer value of the bicarbonate buffer in plasma is 55.6 mmol/L. Derivation of this value is obtained by taking partial differentials of the Henderson-Hasselbalch equation, which is presented in detail in the second edition of this textbook. ... 

If the assumptions leading to Equation 9-28 are not valid, the values for [HA] and [A ] are given by Equations 9-24 and 9-25, respectively. If we take the negative logarithms of these expressions, we derive extended Henderson-Hasselbalch equations. 

The Henderson-Hasselbalch equation was developed independently by the Ameriean biological chemist L. J. Henderson and the Swedish physiologist K. A. Hasselbaleh, for relating the pH to the bicarbonate buffer system of the blood (see below). In its general form, the Henderson-Hasselbalch equation is a useful expression for buffer caleulations. It can be derived from the equilibrium constant expression for a dissociation reaction of the general weak acid (HA) in Equation (1.3) ... 

Much of the beneht in solubihty enhancement from salt formation is attributable to the change in solution pH caused by the presence of the counterion. This occurs because the ionization and solubility of acidic drugs (such as barbiturates and non-steroidal anti-inflammatory drugs) increases in basic conditions but decreases in acidic conditions. This behavior is exemplified by derivations of the Henderson-Hasselbalch equations (37.2) and (37.3). The opposite situation occurs for basic drugs such as chlorpromazine, morphine and codeine, which are more soluble in acidic conditions. 

HENDERSON-HASSELBALCH EQUATION In choosing or making a buffer, the concepts of both pH and pKa are useful. The relationship between these two quantities is expressed in the Henderson-Hasselbalch equation, which is derived from the equilibrium expression below ... 

It is important to remember that the Henderson-Hasselbalch equation is derived from the equilibrium constant expression. It is valid regardless of the source of the conjugate base (that is, whether it comes from the acid alone or is supplied by both the acid and its salt). 

We can derive the Henderson-Hasselbalch equation for this system as follows. Rearranging the above equation we obtain... 

The degree of drug ionization depends upon both the pH of the solution in which it is presented to the biological membrane and on the pKa (dissociation constant) of the drug (whether it is an acid or base). The entire concept of pKa is derived from the Henderson-Hasselbalch equation for both acids and bases as follows ... 

Henderson-Hasselbalch equation cannot be used for thej rjt buffer region because the assumption in deriving that from the Kai expression was that the amount of [ or OH from dissociation or hydrolysis of H2A or HA was not appreciable compared to their concentrations. For a fairly strong acid, then, we can write... 

The Henderson-Hasselbalch equation gives a relationship for obtaining the pH of a buffer solution consisting of HA and A . Derive an analogous relationship f or obtaining the pOH of a buffer solution consisting of B and BH". ... 

The in silico models derived for solubility are based on intrinsic solubility as their experimental input data. The intrinsic solubility is the solubility value determined for the neutral (i.e., uncharged) species of the compound and is generally determined at 2 pH units above the pFCa value for bases and 2 pH units below the pKa value for acids. Ampholytes are determined at their isoelectric point. The solubility values used for the model development therefore seldom reflect the apparent solubility seen in the intestinal fluids. Hence, the predicted values obtained from the models need to be transferred to an in vivo situation, for instance, by use of the Henderson-Hasselbalch equation, which takes into account the pH dependency of solubility [16],... 

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