Buffered solutions calculations involving

Buffer capacity is determined by the amounts of weak acid and conjugate base present in the solution. If enough H3 O is added to react completely with the conjugate base, the buffer is destroyed. Likewise, the buffer is destroyed if enough OH is added to consume all of the weak acid. Consequently, buffer capacity depends on the overall concentration as well as the volume of the buffer solution. A buffer solution whose overall concentration is 0.50 M has five times the capacity as an equal volume of a buffer solution whose overall concentration is 0.10 M. Two liters of 0.10 M buffer solution has twice the capacity as one liter of the same buffer solution. Example includes a calculation involving buffer capacity. 

Now let s consider what happens when we add H30+ or OH- to a buffer solution. First, suppose that we add 0.01 mol of solid NaOH to 1.00 L of the 0.10 M acetic acid-0.10 M sodium acetate solution. Because neutralization reactions involving strong acids or strong bases go essentially 100% to completion (Section 16.1), we must take account of neutralization before calculating [P130+]. Initially, we have (1.00 L)(0.10 mol/L) = 0.10 mol of acetic acid and an equal amount of acetate ion. When we add 0.01 mol of NaOH, the neutralization reaction will alter the numbers of moles ... 

The same procedures we have used for calculations involving weak acid and weak base equilibria can be used for calculations concerning buffer solutions. The major difference is that nonzero concentrations of both the weak acid or base and its conjugate are initially present. 

Equation 2-7 is more commonly called the Henderson-Ha.sselbalch equation and is the basis for most calculations involving weak acids and bases. It is used to calculate the pH of solutions of weak acids, weak ba.ses. and buffers consisting of weak acids and their conjugate bases or weak bases and their conjugate acids. Because the pK is a modified equilibrium constant, it corrects for the fact that weak acids do itnl completely react with water. 

Sections 15.4 and 15.5 outline methods for calculating equilibria involving weak acids, bases, and buffer solutions. There we assume that the amount of hydronium ion (or hydroxide ion) resulting from the ionization of water can be neglected in comparison with that produced by the ionization of dissolved acids or bases. In this section, we replace that approximation by a treatment of acid-base equilibria that is exact, within the limits of the mass-action law. This approach leads to somewhat more complicated equations, but it serves several purposes. It has great practical importance in cases in which the previous approximations no longer hold, such as very weak acids or bases or very dilute solutions. It includes as special cases the various aspects of acid-base equilibrium considered earlier. Finally, it provides a foundation for treating amphoteric equilibrium later in this section. 

When buffer solutions were not used and the pH was not reported, we calculated the pH using the solution concentration and pK values for all dissociation reactions and assuming that the pH was 7.0 prior to solute addition. A general treatment of simultaneous equilibrium involving equations for all linearly independent reactions, the water dissociation reaction (K = 1.0 x lO" " ), a molecular balance on the active species, and an equation requiring solution electroneutrafity is required to calculate the natural pH (Brescia et al., 1975). A more detailed discussion of the adjustment for ionization and associated calculations is presented in Vecchia and Bimge (2002b). 

Two assumptions are made to simplify calculations involving buffer solutions ... 

Example 16.3 and the For Practice Problems that follow it involve calculating pH changes in a buffer solution after small amounts of strong acid or strong base are added. 

We can make the numbers easier to deal with in calculations involving buffer solutions by using logarithms throughout. So instead of using the expression ... 

The arsenic oxidation state data and the calculated pH at 300°C (see Table H) allow an upper limit on the Eh of the solution in the basalt-water experiment to be estimated from Equation (2). Assuming aH,0 = 1 and As(V) = 15 pg/L, this upper limit Eh value is -400 100 mV. The basalt-fluid redox buffer mechanism of Jacobs and Apted (2) gives an Eh of about -600 mV at 300°C and pH 7.8 (19). This mechanism involves ferrous ironbearing basalt glass + water reacting to magnetite + silica. 

The method involves initial leaching of the soil with a solution of barium chloride-triethanolamine buffered at pH 8.1, followed by calcium saturation. The Ca-saturated soil is equilibrated with standard phosphoric acid solution and the quantity of phosphorus adsorbed is evaluated. From this adsorbed phosphorus plus phosphorus extracted initially the AEG of the soil is calculated using the formula. 

As stated earlier, the theoretical concentration profile is calculated on the assumption that the species of interest is not involved in a homogeneous reaction. With a pH probe such as the antimony-antimony oxide tip, this assumption is not valid because the buffer capacity of the solution significantly affects the concentration profile. For example, protons generated at the substrate react with the base form of the buffer and the concentration profile is no longer solely diffusion controlled. Similarly hydroxide anions produced by the substrate titrate the acid form of the buffer. A high-capacity buffer reestablishes the bulk conditions very close to the substrate, while a low-capacity buffer allows the concentration profile to extend far away from the substrate before returning to the bulk concentration. These effects were quantitatively predicted and theoretical pH profiles were found to agree with... 

We have seen earlier how calculations of pH in solutions with strong acid and strong base are relatively simple because strong acids and strong bases are completely dissociated. On the contrary, pH calculations in cases where the titrated acid is weak is not as simple. In order to be able to calculate the concentration of HsO ions after the addition of a given amount of strong base it is necessary to look at the weak acids dissociation equilibrium. Calculations of pH curves for titration of a weak acid with a strong base involve a series of buffer-related problems. 

The determination of formation constants may involve the photometric measurement of the complex formed in the presence of a large excess of one of the reagents, so that the formation of the complex may be considered to be essentially complete this is known as the method of mixtures of nonequimolar solutions. This method is based on Job s general equation [27, 28] for systems involving mixtures. The method has been applied to the determination of the dissociation constant of Fe(III)-sulfo-salicyclic acid mixtures in a pH 5.3 buffer, using sulfosalicyclic acid solutions 3, 5, and 8 times as concentrated as the ferric perchlorate. The best results were obtained by assuming that a 1 1 complex is formed, and was calculated to be 2 x 10" . 

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