Acid-base monoprotic equations

Equations have been published [16] which relate pKa and p0Ka values to partition coefficient (P) values for monoprotic acids and bases, and diprotic acids, bases and ampholytes. For example, P1 for a monoprotic acid is calculated from... 

Obviously the buffer intensity can be expressed numerically by differentiating the equation defining the titration curve with respect to pH. For a monoprotic acid-base system (see equations 67 and 69). 

In an aqueous monoprotic acid-base system, [ANC] is defined by the right-hand side of equation 67 or 69 in Section 3.8. 

We often use HA as a general representation for a monoprotic acid and for its conjugate base. The equation for the ionization of a weak acid can be written as... 

Butanoic acid, CFf3CFf2CFf2C02ff, is a monoprotic weak acid that is responsible for the smell of rancid butter. Write the formula for the conjugate base of this acid. Write the equation for the reaction between this acid and water, and indicate the Bronsted-Lowry acid and base for the forward reaction. (The acidic hydrogen atom is on the right side of the formula.)... 

Figure 12 graphically presents the relation 0 =/(/protonation equation (7.14). It shows that the curves of different monoprotic acid-base pairs have the same form. They are simply shifted along the /tp axis. 

Method development in MLC can be largely potentiated by extending the modeling of the retention along the pH scale (Fig. 8.1). Arunyanart and Cline-Love [4], and Rodgers et al. [5,6], studied the effect of pH on the MLC retention of weak acids and bases. These authors combined the equations that describe the acid-base equilibrium for a monoprotic system in water ... 

Weak Monoprotic Acid-Bases. It has been traditional in elementary texts to use molarity equilibrium constant expressions and to make approximations for the numerical values of the concentrations of all species except the one to be calculated, usually H. This is a valid approach, but difficult for students because of the variety of assumptions used in making the approximations. Let us start by looking at the complete treatment and then showing under what conditions certain approximations will be justified. Until experience is achieved, the best method is to try the approximations and then check the result in the complete equation. 

The resemblance of this ratio to a monoprotic acid-base ratio can be seen by comparison of equation (12-7) with... 

Phenylamine, C5H5-NH2, is monoacidic. It reacts with only one molecule of a monobasic (monoprotic acid). Write an equation showing its dissociation or ionization in water. Identify the Br0nsted-Lowry acid and base. Explain your answer. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

When two immiscible solvents are placed in contact with each other and a non-ionizable compound is dissolved in one of the solvents, the compound distributes itself between the two solvents. This distribution is referred to as partitioning. The ratio of the concentrations of the compound in each phase is a constant for a specific set of solvents, pH, buffers, buffer concentrations, ionic strength and temperature. This ratio is referred to as a partition coefficient or distribution coefficient and is equal to the ratio of the solubilities in the two solvents. When the compound is a weak acid or base, the distribution of the compound can be shown to be given by the following equation for a monoprotic compound ... 

Strategy We use Eq. 23 to determine the pH of an amphiprotic salt. This equation is used for salts of the diprotic conjugate base (H2A-) of a triprotic acid (H3A) and the monoprotic conjugate base (HA-) of a diprotic acid (H2A). However, when the solute is a salt of an anion that has lost two protons, such as HP042-, we must adjust the expression to use the appropriate neighboring pKas ... 

The titration curve of a polyprotic acid can be obtained by using the same approach as for monoprotic weak acids or weak bases. The mass and charge balance equations... 

Figure 5.32 shows the pH-pseudo-ftrst-order rate constant profile of the degradation of aspartame (an ampholyte, pKal = 3.19 and pKa2 = 8.14). In the hydrolysis of aspartame, the protonated/undissociated form predominates at low pH (<3), while the deprotonated/dissociated form exists at high pH (>8). As demonstrated for monoprotic weak acids and weak bases, certain terms in the numerator of Equation (5.173) become negligible. For example, the hydrolysis of the protonated/undissociated form by OH-, of the protonated/dissociated form by H+ and OH-, and the deprotonated/dissociated form by H+ are not likely to occur. Then, Equation (5.173) for the ampholytic drug is written as ... 

Thevaluesof k2+ = 2.05xl0 5sec-1M-1 and k0 = 1.50 sec 1M 1 are estimated. Substituting these values into Equation (5.174) followed by nonlinear regression analysis gives other k values. Intuitively from the profile of pH 2 to 4, one can assume kj 0 = 0. As demonstrated for monoprotic and diprotic weak acids and weak bases, the pH-rate constant profile is dependent on the kinetic pathway of the hydrolysis. It can be seen from Figure 5.32 that at pH 3 to 4 and pH 4 to 9, k2>0 and k0 0 are the predominant processes of the hydrolysis of aspartame, respectively. 

In calculating titration curves, separate equations for different regions of the curve ("before the equivalence point", "at the equivalence point", "after the equivalence point", etc.) are often employed. This section illustrates how to use a single "master" equation to calculate points on a titration curve. Instead of calculating pH as a function of the independent variable V, it is convenient to use pH as the independent variable and V as the dependent variable. The species distribution at a particular pH value is calculated from the [H ], and the volume of titrant required to produce that amount of each species is calculated. For example, in the titration of a weak monoprotic acid HA, we can calculate the concentration of A at a particular pH and then calculate the number of moles of base required to produce that amount of A . In general (J -j) moles of base per mole of acid are required to produce the species HjA from the original acid species HjA. 

To correct capacity factors for ionization, the same equations are used as for the corresponding correction of the apparent partition coefficients. Thus for monoprotic acids and bases, Eqs. 13 and 14 are suggested for extrapolated, as well as isocratic, capacity factors derived froiUg HPLC and RP-TLC I... 

Prolonged exercise can temporarily overload the body s capacity for ehrnination of this substance, and the resulting increase in lactic acid concentration in the muscles causes pain and stiffness, (a) Lactic acid has six H atoms, yet it acts as a monoprotic acid in an aqueous environment. Which of the H atoms is ionizable (b) Draw the structural formula of the conjugate base, (c) Write a net ionic equation that illustrates the ionization of lactic acid... 

We can derive a relationship for [OH-] in a solution containing a weak base, B, plus a salt that contains the cation, BH+, of the weak base, just as we did for weak acids. In general terms the equation for the ionization of a monoprotic weak base and its expression are... 

In a complex mixture of monoprotic acids, the overall degree of ionization of acidic functional groups (a) can be calculated from the electroneutrality equation at any point in the titration of the acid mixture with strong base. 

PAMPA-pKa fiux optimized design (pOD)-permeabiiity Iso-pH mapping unstirred PAMPA was used to measure the effective permeability, Pe, as a function of pH from 3 to 10, of five weak monoprotic acids (ibuprofen, naproxen, ketoprofen, salicylic acid, benzoic acid), an ampholyte (piroxicam), five monoprotic weak bases (imipramine, verapamil, propranolol, phenazopyridine, metoprolol), and a diprotic weak base (quinine). The intrinsic permeability, Po, the UWL permeability, Pu, and the apparent pKa (pKa.fiux) were determined from the pH dependence of log Pg. The underlying permeability-pH equations were derived for multiprotic weak acids, weak bases, and ampholytes. The average thickness of the UWL on each side of the membrane was estimated to be nearly 2000 p, somewhat larger than that found in Caco-2 permeability assays (unstirred). As the UWL thickness in the human intestine is believed to be about forty times smaller, it is critical to correct the in vitro permeability data for the effect of the UWL. Without such correction, the in vitro permeability coefficient of lipophilic molecules would be indicative only of the property of water. In single-pH PAMPA (e.g., pH 7.4), the uncertainty of the UWL contribution can be minimized if a specially selected pH (possibly different from 7.4) were used in the assay. From the analysis of the shapes of the log Pe-pH plots, a method to improve the selection of the assay pH, called pOD-PAMPA, was described and tested. From an optimally selected assay pH, it is possible to estimate Pg, as well as the entire membrane permeability-pH profile. 

The constant Kaz is very small, and so the equilibrium lies significantly to the right. Because Kai, hydrolysis of HP04 is suppressed by the OH from the first step, and the pH of P04 can be calculated just as for a salt of a monoprotic weak acid. However, because Kaz is so small, Kf, is relatively large, and the amount of OH- is not negligible compared with the jnitial concentration of P04 - (Cb-), and the quadratic equation must be solved, that is, P04 is quite a strong base. 

We will hot constract a diprotic titration curve here, but if you want a good mental exercise, try it You just can t make the simplifying assumptions that we can usually use with monoprotic acids that are sufficiently weak or not too dilute. See your CD, Chapter 8, for auxiliary data for the spreadsheet calculation of the titration curve for 50.00 mL 0.1000 M H2C1O4 versus 0.1000 M NaOH. You can download that and enter the Kai and Kai values for other diprotic acids and see what their titration curves look like. Try, for example, maleic acid. For the calculations, we used the more exact equations mentioned above for the initial pH, the first buffet zone, and the first equivalence point. We did not use the quadratic equation for the second equivalence point since Cr04 is a quite weak base (Kbi = 3.12 X 10 ). See Ref. 8 for other examples of calculated titration curves. 

Titration. Polyelectrolytes that dissociate as polyvalent weak acids or bases in an aqueous medium can be titrated with strong acid or base for the purpose of characterizing or varying the charge density. For a low molecular weight monoprotic acid, the degree of dissociation a closely follows the classic Henderson-Hasselbalch equation... 

If a single reaction is quantitative within certain pH regions, the equations derived above apply. We treated glycine as a monoprotic acid for the purpose of titration by a strong base. As shown in Figure 5-5, the pH of phosphate systems can be quantitatively described by Ki alone up to pH 4, by K2 from about pH 5 to 9, and by K 3 above pH 10. Linearizing equations tike (7-5), (7-7), and (7-8) can be derived using, and for the volumes of titrant added to reach the... 

---