Buffering index

Figure 4. Dispersion curve vs. cladding index for SPP-configuration at X=0.6(im, substrate s=1.45, waveguide thickness 4 rm, An=0.01, buffer index 1.40, buffer thickness O.Spm, Au thickness 50nm.

In principle, it would be logical to combine plots of the buffer index curves of each of the buffer components of milk and thus obtain a plot which could be compared with that actually found for milk. It is not difficult, of course, to conclude that the principal buffer components are phosphate, citrate, bicarbonate, and proteins, but quantitative assignment of the buffer capacity to these components proves to be rather difficult. This problem arises primarily from the presence of calcium and magnesium in the system. These alkaline earths are present as free ions as soluble, undissociated complexes with phosphates, citrate, and casein and as colloidal phosphates associated with casein. Thus precise definition of the ionic equilibria in milk becomes rather complicated. It is difficult to obtain ratios for the various physical states of some of the components, even in simple systems. Some concentrations must be calculated from the dissociation constants, whose... 

This quantity gives the capacity of an aqueous system to resist pH changes upon addition of an acid or a base. When one plots the amount of acid A (or base B) added per liter of solution (Ca, Cb) vs. pH change, the slope of the resulting curve (or titration curve) is the buffering index or buffer... 

Chiriac, V. Balea. G. Buffer Index and Buffer Capacity for a Simple Buffer Solution, /. Chem. Educ. 1997, 74, 937-939. 

Here we restrict ourselves to pH buffers. Van Slyke (1922) defined pH buffers as substances which by their presence in solution increase the amount of acid or alkali which must be added to cause a unit change in pH. In aqueous solutions pH buffering is especially due to the interaction of weak acids and bases and their salts with water. The quantification of this effect, the buffer capacity or buffer index, is by definition... 

To calculate the buffer index of an aqueous system we begin by deriving the equation for the acidity titration curve for that system. For pure water we will assume the litrant is NaOH. The charge-balance equation is then simply... 

To derive a function for the buffer index of a weak monoprotic acid, HA, we begin as before with equilibrium, mass-balance, and charge-balance equations, and first derive an equation for the titration curve. We are given the following expressions ... 

Remembering that for a monoprotic weak acid the buffer index equals... 

Where is the total concentration of acid species and A, and K2 are the first and second stepwise dissociation constants of the acids. This equation can be used to compute the buffer index of a polyprotic acid as long as successive dissociation constants differ by at least 20 times (this assures a calculation error of 5% or less). In other words, for a diprotic acid K2fK should be less than 0.05 (cf. Butler 1964). Thus, for example, Eq. (5.114) may be used to compute the buffer index due to species of carbonic acid, for which A = 10 and K2 = 10" °, or/ for species of silicic acid, for which a , = lO- and K, = 10... 

We can measure buffer action in terms of a definite unit called buffer capacity or buffer index x, where... 

If the B versus pH line is curved, we determine the buffer index at a given point by drawing a line tangent to the curve at this point and determining the slope of this straight line. 

In Fig. 4 is shown the buffer capacity of mixtures of 0.1 N and 0.2 N acetic acid solutions with a strong acid or with alkali. We see that between pH s of 2 and 3.5 the total buffer capacity is obtained by adding the ordinates of the two dotted lines which represent the buffer capacities of the strong and weak acid. Outside this pH-region, we have to deal only with the buffer index of the individual weak acid, strong acid, or base, without having to consider their mutual buffering action. 

A closely related measure is the buffer index or buffer capacity (3, which is the parameter originally introduced by Van Dyke. The two differ only by the factor ln( 10), i.e., the relation between Band (3 is... 

The amount of acid or base that can be added without causing a large change in pH is governed by the buffering capacity of the solution. This is determined by the concentrations of HA and A". The higher their concentrations, the more acid or base the solution can tolerate. The buffer capacity (buffer intensity, buffer index) of a solution is defined as... 

Figure 8.4 Titration Curve, Sharpness and Buffer Indexes for Na2C03 -HCl Titrations...

Treatment of buffer efficiency in general is not limited to examination of various monoprotic and polyprotic acids, but rather to the behavior of mixtures of acids. Further, from plots of buffer index vs. pH, it is easy to see that strong acids and bases are reasonable buffers for the extreme (low and high) Ph ranges. This leads to the definition of a buffer as a solution that has neutralization capacity, rather the more limited but commonly used definition as a mixture of a weak acid and its conjugate base (See Figure 8.5). 

The buffer index is a measure of the amount of acid or base that can be added to a solution before the pH changed by a given amount. If Equations 8-17 and 8-18 are rewritten as... 

This equation properly bears a striking resemblance to the analogous Equation 8-17 and can be very useful in describing the metal buffer index as well as for the sharpness index in complexometric titrations. 

B is called the buffer index and expresses the slope as the increment... 

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