Henderson solution

In the derivation of the formula for calculating the liquid junction potential, the electric work done in separating the charges is set equal to the work of diffusion that is, the change in chemical potential arising from the diffusion of the ions. Only after making certain approximations can one arrive at the so-called Henderson solution [56] of the Nernst-Planck equation [57] ... 

Henderson-Hasselbach equation A simplified version of the relationships used in calculations on buffer solutions. 

This relationship is one form of the Henderson-Hasselbalch equation It is a useful relationship m chemistry and biochemistry One rarely needs to cal culate the pH of a solution—pH is more often mea sured than calculated It is much more common that one needs to know the degree of ionization of an acid at a particular pH and the Henderson-Hasselbalch equation gives that ratio... 

Although this treatment of buffers was based on acid-base chemistry, the idea of a buffer is general and can be extended to equilibria involving complexation or redox reactions. For example, the Nernst equation for a solution containing Fe + and Fe + is similar in form to the Henderson-Hasselbalch equation. 

Any solution containing comparable amounts of a weak acid, HA, and its conjugate weak base, A-, is a buffer. As we learned in Chapter 6, we can calculate the pH of a buffer using the Henderson-Hasselbalch equation. 

This relationship is known as the Henderson-Hasselbalch equation. Thus, the pH of a solution can be calculated, provided and the concentrations of the weak acid HA and its conjugate base A are known. Note particularly that when [HA] = [A ], pH = pAl,. For example, if equal volumes of 0.1 MHAc and 0.1 M sodium acetate are mixed, then... 

The Henderson-Hasselbalch equation provides a general solution to the quantitative treatment of acid-base equilibria in biological systems. Table 2.4 gives the acid dissociation constants and values for some weak electrolytes of biochemical interest. 

Introduction to the Study of Physical Chemistry Physical Organic Chemistry Solutions of Electrolytes Henderson and Fernelius—... 

As an example of how to use the Henderson-Hasselbalch equation, let s find out what species are present in a 0.0010 M solution of acetic acid at pH = 7.3. According to Table 20.3, the pKa of acetic acid is 4.76. From the Henderson-Hasselbalch equation, we have... 

We saw in Section 20.3 that the extent of dissociation of a carboxylic acid HA in an aqueous solution buffered to a given pH can be calculated with the Henderson-Hasselbalch equation. Furthermore, we concluded that at the physiological... 

To apply the Henderson-Hasselbalch equation to an amino acid, let s find out what species are present in a 1.00 M solution of alanine at pH = 9.00. According to Table 26.1, protonated alanine [ NCHfCH CC H] has p/Cal =2.34, and neutral zwitteTionlc alanine [+ll3NCH(CH3)C02-] has pK52 = 9.69 ... 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

The values of [HA] and [A ] in this expression are the equilibrium concentrations of acid and base in the solution, not the concentrations added initially. However, a weak acid HA typically loses only a tiny fraction of its protons, and so [HA] is negligibly different from the concentration of the acid used to prepare the buffer, [HA]initia. Likewise, only a tiny fraction of the weakly basic anions A- accept protons, and so [A-] is negligibly different from the initial concentration of the base used to prepare the buffer. With the approximations A ] [base]initia and [HA] [acid]initia, we obtain the Henderson-Hasselbalch equation ... 

In practice, the Henderson-Hasselbalch equation is used to make rapid estimates of the pH of a mixed solution intended to be used as a buffer, and then the pH is adjusted to the precise value required by adding more acid or base and monitoring the solution with a pH meter. 

We can use these numbers to express the range of buffer action in terms of the pH of the solution. The Henderson-Hasselbalch equation shows us that,... 

Heisenberg uncertainty principle If the location of a particle is known to within an uncertainty Ax, then the linear momentum parallel to the x-axis can he known only to within an uncertainty Ap, where ApAx > till. Henderson-Hasselbalch equation An approximate equation for estimating the pH of a solution containing a conjugate acid and base. See also Section 11.2. Henry s constant The constant kH that appears in Henry s law. 

The buffer equation, which is often called the Henderson-Hasselbalch equation, is used to calculate the equilibrium pH of a buffer solution directly from initial concentrations. The approximation is valid as long as the difference between initial concentrations and equilibrium concentrations is negligibly small. As a rule of thumb, the buffer equation can be applied when initial concentrations of H j4 and A differ by less than a factor of 10. Example provides an illustration of the use of the buffer equation. 

When both solutions are binary and identical in nature and differ only by their concentration and the component E of the held strength is given by Eq. (4.18), the diffusion potential 9 can be expressed by Eq. (4.19). An equation of this type was derived by Walther Nemst in 1888. Like other equations resting on Eick s law (4.1), this equation, is approximate and becomes less exact with increasing concentration. For the more general case of multicomponent solutions, the Henderson equation (1907),... 

For binary solutions of symmetric z z electrolytes having a common ion and the same concentration c a = Cma general Henderson equation changes to... 

Although Fig. 3.2 properly conveys the shapes of solubility-pH curves in saturated solutions of uncharged species, according to the Henderson-Hasselbalch equation, the indefinite ascendancy of the dashed curves in the plots can be misleading. When pH changes elevate the solubihty, at some value of pH, the solubihty product of the salt wiU be reached, causing the shape of the solubihty-pH curve to level off, as indicated in Fig. 3.2(a) for pH >8.38. 

Fig. 3.2 Solubility profiles log S-pH. The dashed curves, representing uncharged precipitate in equilibrium with solution of the drugs, were calculated by Henderson-Hasselbalch equations. The dotted horizontal lines are estimates of the solubility of the charged form of the drugs, using either actual data (naproxen) or estimates based on the sdiff 3-4 approximation (atenolol and...

When a compound forms a dimer or a higher-order oligomer in aqueous solution, the characteristic solubility-pH profile takes on a shape not predicted by the Henderson-Hasselbalch equation and often indicates an apparent pJCj that is different from the true piQ. Figure 3.3 shows several examples of sparingly-soluble... 

Fig. 3.3 Solubility profiles of sparingly soluble drugs, based on data taken from Avdeef et al. [20]. The solutions consisted of robotically adjusted universal buffers, based on a mixture of Good buffers (see text), and contained 0.2 M KCl. The dashed lines were calculated by the Henderson-Hasselbalch equation and, as can be seen, did not accurately describe the solubility profiles. The solid curves were...

Gnillanmont R, Bouissieres G, Muxart R (1968) Chimie du Protactinium. I. Solutions aqueuses de protactinium penta- et tetravalent. Actinides Rev 1 135-163 Harvey BG (1962) Introduction to Nuclear Physics and Chemistiy. Prentice Hall Inc, New Jersey Henderson GM, Anderson RF (2003) The U-series toolbox for paleoceanography. Rev Mineral Geochem... 

Here, x is the coordinate normal to the diaphragm, so that d — q—p. The liquid junction potential A0L is the diffusion potential difference between solutions 2 and 1. The liquid junction potential can be calculated for more complex systems than that leading to Eq. (2.5.31) by several methods. A general calculation of the integral in Eq. (2.5.30) is not possible and thus assumptions must be made for the dependence of the ion concentration on x in the liquid junction. The approximate calculation of L. J. Henderson is... 

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

For formic acid, pATa = - log(1.8 x 10 4) = 3.74. The Henderson-Hasselbalch equation provides the pH of the original buffer solution ... 

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