Equilibrium constant Henderson-Hasselbalch

Suppose you need to prepare a buffer with a pH of 9.36. Using the Henderson-Hasselbalch equation, you calculate the amounts of acetic acid and sodium acetate needed and prepare the buffer. When you measure the pH, however, you find that it is 9.25. If you have been careful in your calculations and measurements, what can account for the difference between the obtained and expected pHs In this section, we will examine an important limitation to our use of equilibrium constants and learn how this limitation can be corrected. 

The common-ion effect is an application of Le Chatelicr s principle to equilibrium systems of slightly soluble salts. A buffer is a solution that resists a change in pH if we add an acid or base. We can calculate the pH of a buffer using the Henderson-Hasselbalch equation. We use titrations to determine the concentration of an acid or base solution. We can represent solubility equilibria by the solubility product constant expression, Ksp. We can use the concepts associated with weak acids and bases to calculate the pH at any point during a titration. 

With reference to a solvent, this term is usually restricted to Brpnsted acids. If the solvent is water, the pH value of the solution is a good measure of the proton-donating ability of the solvent, provided that the concentration of the solute is not too high. For concentrated solutions or for mixtures of solvents, the acidity of the solvent is best indicated by use of an acidity function. See Degree of Dissociation Henderson-Hasselbalch Equation Acid-Base Equilibrium Constants Bronsted Theory Lewis Acid Acidity Function Leveling Effect... 

ACYL-PHOSPHATE INTERMEDIATE ACID-BASE EQUILIBRIUM CONSTANTS DEGREE OF DISSOCIATION HENDERSON-HASSELBALCH EQUATION Acid/base groups in enzymes,... 

This equation essentially describes the relationship between pH and the degree of ionization of weak acids and bases. When applied to drugs, the equation tells us that when pH equals the apparent equilibrium dissociation constant of the drug (pKJ, 50 percent of the drug will be in the unionized form and 50 percent will be in the ionized form (i.e., log[base/acid] = 0 and antilog of 0 = 1, or unity). Application of the Henderson-Hasselbalch equation can, therefore, allow one to mathematically determine the exact proportion of ionized and nonionized species of a drug in a particular body compartment if the pKa of the drug and the pH of the local environment are known. 

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) ... 

The acidity or basicity of a drug substance is defined by the dissociation constant K, which is the equilibrium constant, more conveniently represented by its logarithmic parameter pK, reflecting the degree of ionization of a substance at a particular pH and described by the Henderson-Hasselbalch equations (37.2) and (37.3). ... 

Because the dissociation of acid-base pairs is an equilibrium reaction, the relationship between hydrogen ion concentration or pH and the relative concentrations of the acid and base can be described mathematically in terms of the dissociation constant for the acid-base buffer pair. When expressed as a logarithmic relationship, where pK is the negative logarithm of the dissociation constant this is known as the Henderson-Hasselbalch equation ... 

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). 

From this expression, commonly known as the Henderson-Hasselbalch equation, It can be seen that the pK of any acid Is equal to the pH at which half the molecules are dissociated and half are neutral (undissociated). This Is because when p/Q, = pH, then log ([A ]/[HA]) = 0, and therefore [A ] = [HA]. The Henderson-Hasselbalch equation allows us to calculate the degree of dissociation of an acid if both the pH of the solution and the p/Q, of the acid are known. Experimentally, by measuring the [A ] and [HA] as a function of the solution s pH, one can calculate the p/Q, of the acid and thus the equilibrium constant TC for the dissociation reaction. 

The solution of the equilibrium-constant expression and the pH are sometimes combined into one operation. The combined expression is termed the Henderson-Hasselbalch equation. 

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. 

The degree of dissociation can be calculated once the equilibrium constant, K, for the subspecies and the pH of the solution are known. For a restricted pH range, a very useful relationship has been given by the Henderson-Hasselbalch equation... 

Plan Solving this problem involves the two steps outlined in Figure 17.3. First we do a stoichiometry calculation to determine how the added OH affects the buffer composition. Then we use the resultant buffer composition and either the Henderson- Hasselbalch equation or the equilibrium-constant expression for the buffer to determine the pH. 

Think About It For each point in a titration, decide first what species are in solution and what type of problem it is. If the solution contains only a weak acid (or weak base), as is the case before any titiant is added, or if it contains only a conjugate base (or conjugate acid), as is the case at the equivalence point, when pH is determined by salt hydrolysis, it is an equilibrium problem that requires a concentration, an ionization constant, and an equilibrium table. If the solution contains comparable concentrations of both members of a conjugate pair, which is the case at points prior to the equivalence point, it is a buffer problem and is solved using the Henderson-Hasselbalch equation. If the solution contains excess titrant, either a strong base or strong acid, it is simply a pH problem requiring only a concentration. 

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