Henderson formula

Although the Henderson formula depends on a number of simplifications and also employs ion concentrations rather than activities, it can nonetheless be used for estimation of the liquid junction potential up to moderate electrolyte concentrations, apparently as a result of compensation of errors. 

Equation (13-119) is the Henderson formula which is useful for order-of-magnitude estimates of 6. ... 

The measurement of membrane potentials is accomplished by use of cells of the type of Eq. (13-150). The measured emf of this system is given by Eq. (13-151). Usually, the assumption is made that = 8 = 0. The error involved in this approximation can be roughly determined by use of the Henderson formula [Eq. (13-119)]. In general, it is found that the sum is small compared... 

D. Henderson, L. Blum, J. L. Lebowitz. An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall. J Electroanal Chem 702 315-319, 1979. 

Taking for the diffusion potential the Henderson diffusion potential and adding the two Donnan potentials one gets the well-known formula of K. H. Meyer (97, 98), J. F. Sievers (97, 98) and T. Teorell (168). 

Blends of starch and konjac gum (Tye, 1991) and of some modified celluloses (Hercules, Inc., 1980) are synergistic. A ternary dispersion of 1% methylcellulose and 2.9% starch had almost 2.5 times the viscosity of a blend of 0.5% methylcellulose and 2.9% starch, and approximately 20 times the viscosity of 3.9% starch (Hegenbart, 1989). Methylcellulose-starch viscosity synergism was suggested as a formula to decrease caloric content (Henderson, 1989). Guar gum can increase starch paste viscosity tenfold (Christianson et al., 1981). 

One interesting consequence of these equations, which we will call the Henderson-Chan (HC) formulae, is that they predict phase separation when X2 is small [21]. Lebowitz and Rowlinson [22] showed that Eqs. (37) and (41) predicted that fluid hard sphere mixtures were miscible under all circumstances. This prediction has been unchallenged until recently. 

One other second-order integral equation calculation has been made. Henderson and Sokolowski [50] and Henderson et al. [51] have calculated the correlation functions of a hard sphere mixture, when X2 — 0, using the PY2 theory. They find excellent agreement with the HC formulae, Eqs. (42) and (43) with Eq. (41) for g (d ). In particular, the limit 2 = 0, the HNC/PY/PY approximation for 22( 22) is rather good. 

Equation 14.10 is known as the Henderson-Hasselbalch equation and is provided for you on the AP formula sheet. You can use it to calculate the pH of a buffer. There is a similar form of the equation that is rewritten to address the hydroxide ion concentration... 

In no case could Beilby and Henderson induce the nickel to combine with more than 7-5 per cent, of nitrogen Ni,N requires 7-36 per cent. NijN requires 10-6 per cent. If the latter formula is correct for the nitride, as analogy with iron and cobalt would lead one to anticipate, the substance obtainod by Beilby and Henderson was probably a solid solution of nickel in the nitride. 

The period of the oscillations is, in fact, always about the particle diameter. - In this aspect, the structural forces are appropriately called the volume exclusion forces by Henderson, who derived an explicit (although rather complex) formula for calculating these forces. 

Solution I Solution II Electrode P D Calculated by Nernst a Formula 1 1 Liquid Liquid Calculated by Henderson s Formula Sum of Total EMF of Cell Observed... 

D. Henderson, L. Blum, and J. L. Lebowitz, ]. Electroanal. Chem., 102, 315 (1979). An Exact Formula for the Contaa Value of the Density Profile of a System of Charged Hard Spheres Near a Charged Wall. 

At the beginning of the titration, [H" ] is equal to Vk HQA (cell E4 formula). The pH is calculated from this (cell H4 formula). Once the titration is begun and up to the equivalence point, we have a buffer of HOAc and OAc , and so we must calculate the concentrations of each. The former is the number of millimoles of remaining HOAc divided by the total volume (cell C5 formula). The [OAc ] is the number of millimoles NaOH added divided by the total volume (cell D5 formula). The pH is calculated frotn the Henderson-Hasselbach equation (cell H5 formula). At the equivalence point, [OH ] is determined by the concentration of OAc (cell F19 formula), and pOH (cell G19) and pH (cell H19) are calculated from this. The pH for the remainder of the titration is calculated from the excess millimoles NaOH and total volume (cell F20 formula), as was done for the titration of HCl. 

In the Henderson-Hasselbalch equation, the formula for the dissociation constant of a weak acid is converted to a convenient logarithmic equation (Equation 4.5). The term pK, represents the negative log of K. If the pK, for a weak acid is known, this... 

Strictly speaking, buffer capacity is obtained from the differential of the Henderson-Hasselbach expression, i.e. from the following derived formula ... 

Henderson-Hasselbalch equation n. A formula relating the pH value of a solution to the pK value of the acid in the solution and the ratio of the acid and the conjugate base concentrations pH = p-Ka+... 

Henderson-Hasselbalch equation is important for imderstanding buffer action and acid-base balance in the blood and tissues of the mammalian system. The equation is derived in the following way. Let us denote a weak acid by the general formula HA, and its salt by the general formula BA (B being the metal ion and A being the conjugate base). The sedt dissociates completely, while the weak acid dissociates only partly. We can write the equilibrium reactions for the dissociation of HA and BA in the buffer solution as follows ... 

Henderson-Hasselbalch Equation n A formula relating the pH value of a solution to the pK value of the acid in the solution and the ratio of the acid and the conjugate base concentrations pH = pIQ + log( [A—] / [HA]), where [A—] is the concentration of the conjugate base and [HA] is the concentration of the protonated acid. For the bicarbonate buffer system in blood,... 

Equation (3.9) is also known as the Lewis-Sargent formula [31]. This formula operates with equivalent conductivities of solutions A, not of the ions. The paper [31] published 1 year after Henderson s papers played a historical role. The cells of the same geometry as were used in [31] are still utilized for emf measurements. These cells with free diffusion boundary are sometimes called Lewis-Sargent cells. Another important note in ref. [31] concerns the search of conductivity values. 

An alternative form of distribution coefficient (Henderson and Kracek Formula) which has been comparatively little used in geochemistry, introduces the concept of carrier elements which can be thoiight of as the major elements for which the trace element... 

It would be useful to mention that other formulas given by Planck and Henderson for the liquid junction potential are similarly subject to... 

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] ... 

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