Buffer solutions equilibrium concentrations

Figure 18.4 The hanging-drop method of protein crystallization, (a) About 10 pi of a 10 mg/ml protein solution in a buffer with added precipitant—such as ammonium sulfate, at a concentration below that at which it causes the protein to precipitate—is put on a thin glass plate that is sealed upside down on the top of a small container. In the container there is about 1 ml of concentrated precipitant solution. Equilibrium between the drop and the container is slowly reached through vapor diffusion, the precipitant concentration in the drop is increased by loss of water to the reservoir, and once the saturation point is reached the protein slowly comes out of solution. If other conditions such as pH and temperature are right, protein crystals will occur in the drop, (b) Crystals of recombinant enzyme RuBisCo from Anacystis nidulans formed by the hanging-drop method. (Courtesy of Janet Newman, Uppsala, who produced these crystals.)...

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 ... 

The analysis carried out in Example reveals one of the key features of buffer solutions The equilibrium concentrations of both the weak acid and its conjugate base are essentially the same as their initial concentrations. 

The pH of a buffer solution depends on the weak acid equilibrium constant and the concentrations of the weak acid and its conjugate base. To show this, we begin by taking the logarithm of the acid equilibrium constant ... 

This equation is exact, but it can be simplified by applying one of the key features of buffer solutions. Any buffer solution contains both members of a conjugate acid-base pair as major species. In other words, both the weak acid and its conjugate base are present in relatively large amounts. As a result, the change to equilibrium, x, is small relative to each initial concentration, and the equilibrium concentrations are virtually the same as the initial leq linitial " = linitial... 

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. 

Solubility measurement at a single pH [37-39] under equilibrium conditions is largely a labor-intensive procedure, requiring long equilibration times (12h-7 days). It s a simple procedure. The drug is added to a standard buffer solution (in a flask) until saturation occurs, indicated by undissolved excess dmg. The thermostated saturated solution is shaken as equilibration between the two phases is established. After microfiltration or centrifugation, the concentration of the substance in the supernatant solution is then determined using HPLC, usually with UV detection. If a solubility-pH profile is required, then the measurement needs to be performed in parallel in several different pH buffers. 

Acid-base reactions of buffers act either to add or to remove hydrogen ions to or from the solution so as to maintain a nearly constant equilibrium concentration of H+. For example, carbon dioxide acts as a buffer when it dissolves in water to form carbonic acid, which dissociates to carbonate and bicarbonate ions ... 

At equilibrium, the concentration of H+ will remain constant. When a strong acid (represented by H+ or HA) is introduced into solution, the concentration of H+ is increased. The buffer compensates by reacting with the excess H ions, moving the direction of the above reaction to the left. By combining with bicarbonate and carbonate ions to form the nonionic carbonic acid, equilibrium is reestablished at a pH nearly the same as that existing before. The buffer capacity in this case is determined by the total concentration of carbonate and bicarbonate ions. When no more carbonate or bicarbonate ions are available to combine with excess H+ ions, the buffer capacity has been exceeded and pH will change dramatically upon addition of further acid. 

We know the initial concentration of NH3 in the buffer solution and can use the pH to find the equilibrium [OH ]. The rest of the solution is organized around the balanced chemical equation. Our first goal is to determine the initial concentration of NH/. 

Unless standards are prepared in buffered media, positive or negative deviations may result from measurements made at 348 nm or 372 nm respectively Alternatively, measurements can be made at the isosbesticpoint, i.e. where the absorbance curves of each form intersect, and where absorbance is not a function of equilibrium concentrations but only of the overall concentration. Solutions of weak acids and bases should also be measured at their isosbestic points for the same reason. 

The kinetics of the ionic hydrogenation of isobutyraldehyde were studied using [CpMo(CO)3H] as the hydride and CF3C02H as the acid [41]. The apparent rate decreases as the reaction proceeds, since the acid is consumed. However, when the acidity is held constant by a buffered solution in the presence of excess metal hydride, the reaction is first-order in acid. The reaction is also first-order in metal hydride concentration. A mechanism consistent with these kinetics results is shown in Scheme 7.8. Pre-equilibrium protonation of the aldehyde is followed by rate-determining hydride transfer. 

Now imagine adding some acid to the solution - either by mistake or deliberately. Clearly, the concentration of H+ will increase. To prevent the value of Ka changing, some of the hydrogen phosphate ions combine with the additional protons to form dihydrogen phosphate (i.e. Equation (6.48) in reverse). The position of the equilibrium adjusts quickly and efficiently to mop up the extra protons in the buffer solution. In summary, the pH is prevented from changing because protons are consumed. 

We can now use these two values for the equilibrium portion of the problem. There are two options for this buffer solution. We can use these concentrations in a Ka calculation, or we can use the Henderson-Hasselbalch equation. Either method will give you the same answer however, the Henderson-Hasselbalch equation is faster. 

In a perfectly-buffered solution the SO2 vapor pressure will be directly proportional to the total concentration of SO2 and bisulfite, giving a linear equilibrium relationship. In simple alkali sulfite solution without added buffer, the equilibrium relationship is highly nonlinear, because H-1" accumulates as SO2 is absorbed. Under these conditions is it not possible to carry out reversible SO2 absorption/stripping in a simple system, resulting in greater steam requirements than expected with a linear equilibrium relationship. Weak acid buffers such as sodium citrate have been proposed to "straighten" the equilibrium relationship and thereby reduce ultimate steam requirements (Jl, 2, 7). Citrate buffer is attractive because it is effective over a wide range, from pH 2.5 to pH 5.5 in concentrated solutions. 

In this section, you compared strong and weak acids and bases using your understanding of chemical equilibrium, and you solved problems involving their concentrations and pH. Then you considered the effect on pH of buffer solutions solutions that contain a mixture of acid ions and base ions. In the next section, you will compare pH changes that occur when solutions of acids and bases with different strengths react together. 

The dynamic features of each of the thiols were subsequently evaluated in transthiolesterification reactions in buffered D O solution (NaOD/D PO, pD 7.0) with the ACh analog acetylthiocholine [ASCh (14), Table 6.1]. Formation/thiolysis of each thiolester was carefully followed by H-NMR spectroscopy at different time intervals, and exchange rate and equilibrium composition were determined for each combination. The rate of exchange was directly correlated to the p/f of the thiols the lower the pK, the faster the exchange reaction (Table 6.1). Thiols having pK values lower than 8.5 reached equilibrium very rapidly. The results also showed that the majority of thiols produce equilibrium concentrations that are close to... 

All membrane exposures were carried out by soak testing under equilibrium conditions at fixed concentrations and constant pH. Pretreatment chemicals were added to buffer solutions at pH 3.0, 5.8 and 8.6. These buffers, representing an arbitrary pH range were prepared according to directions given by Perrin and Dempsey... 

The total free chlorine in wastewaters as measured by colorimetric techniques constitutes both the dissolved molecular chlorine, hypochlorite ion, OCl, and hypochlorous acid. An equilibrium exists between these species, the concentrations of which depend on the temperature and pH of the waste-water. Concentration of the hypochlorous acid may be estimated from the K value or from the ratio (33% of the measured concentration of free chlorine). The free chlorine may be measured by amperometric titration after the addition of a phosphate buffer solution to produce a pH between 6.5 and 7.5. The sample is titrated against a standard solution of phenylarsine oxide. Alternatively, the syringaldazine (3,5-dimethoxy-4-hydroxybenzaldazine) colorimetric test may be performed. This color-forming reagent in 2-propanol yields a colored product with free chlorine, the absorbance of which may be... 

The pH of pure (and also not so pure) water is very sensitive to small concentrations of acids and bases. One drop of concentrated sulphuric acid added to a liter of water will change the pH by 4 pH nnits (from 7 to ca. 3). Solntion pH can be stabilized by a buffer (although there may be cases where a stable pH is not desirable) addition of (not too large) quantities of acid or base to a buffered solution will not affect the pH mnch. Buffers are usually mixtures of weak acids or bases and their salts. A common example in CD is the nse of an ammoninm salt (NH4X ) to control the pH of an ammonia solntion. The equilibrium of ammonia in water is given by... 

Pseudo-first-order kinetics are observed whenever the concentration of one of the reactants is maintained constant, either by a substantial excess in initial concentration or by rapid replenishment of one of the reactants. If one of the reactants is the hydrogen ion or the hydroxide ion, its concentration, though probably small when compared with that of the drug, can be kept constant throughout the reaction by using buffers in the solution. The concentration of an unstable drug in solution can be maintained invariant by utilization of a suspension, which provides excess solid in equilibrium with the drug in solution. 

A more comprehensive analysis of the influences on the ozone solubility was made by Sotelo et al., (1989). The Henry s Law constant H was measured in the presence of several salts, i. e. buffer solutions frequently used in ozonation experiments. Based on an ozone mass balance in a stirred tank reactor and employing the two film theory of gas absorption followed by an irreversible chemical reaction (Charpentier, 1981), equations for the Henry s Law constant as a function of temperature, pH and ionic strength, which agreed with the experimental values within 15 % were developed (Table 3-2). In this study, much care was taken to correctly analyse the ozone decomposition due to changes in the pH as well as to achieve the steady state experimental concentration at every temperature in the range considered (0°C [Pg.86]

To see how a buffer solution works, let s return to the 0.10 M acetic acid-0.10 M sodium acetate solution discussed in Section 16.2. The principal reaction and the equilibrium concentrations for the solution are... 

Note that in calculating this result we have set the equilibrium concentrations, (0.10 - x) and (0.10 + x), equal to the initial concentrations, 0.10, because x is negligible compared with the initial concentrations. For commonly used buffer solutions, Ka is small and the initial concentrations are relatively large. As a result, x is generally negligible compared with the initial concentrations, and we can use initial concentrations in the calculations. 

In buffered solutions, the term k2KsKi [S]/[SH+] is constant, so the expected overall rate law is again second order (i.e. pseudo first order in [Y ]) but the correspondence of fcQbs with mechanistic rate constants is different. Of course, if the equilibrium constant Ki is appreciable, the phenolate concentration must be taken into account in the mass balance for the total phenol, i.e. [ArOH]T [ArOH]free + [ArOH- -S] + [ArO-], whereupon the mechanistic rate equation becomes more complicated. 

If 0.00200mol of citric acid is dissolved in 1 L of a solution buffered at pH 5.00 (without changing the volume), what will be the equilibrium concentrations of citric acid, its singly charged anion, the doubly charged anion, and the triply charged anion Use the pK values from Problem 17.101. 

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