Acids solution equilibrium calculations

Acid solutions are often analyzed by titration with a solution of a strong base of known concentration similarly, solutions of bases are analyzed by titration with a strong acid. In either case, the measured pH is plotted as a function of the titrant volume. Calculation of a pH titration curve is a particularly good introduction to acid-base equilibrium calculations since a variety of calculations are involved. 

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 acidity or basicity of a solution is frequently an important factor in chemical reactions. The use of buffers of a given pH to maintain the solution pH at a desired level is very important. In addition, fundamental acid-base equihbria are important in understanding acid-base titrations and the effects of acids on chemical species and reactions, for example, the effects of complexation or precipitation. In Chapter 6, we described the fundamental concept of equilibrium constants. In this chapter, we consider in more detail various acid-base equilibrium calculations, including weak acids and bases, hydrolysis, of salts of weak acids and bases, buffers, polyprotic acids and their salts, and physiological buffers. Acid-base theories and the basic pH concept are reviewed first. 

Because acid-base reactions in solution generally are so rapid, we can concern ourselves primarily with the determination of species concentrations at equilibrium. Usually, we desire to know [H+], [OH ], and the concentration of the acid and its conjugate base that result when an acid or a base is added to water. As we shall see later in this text, acid-base equilibrium calculations are of central importance in the chemistry of natural waters and in water and wastewater treatment processes. The purpose of this section is to develop a general approach to the solution of acid-base equilibrium problems and to apply this approach to a variety of situations involving strong and weak acids and bases. 

In aqueous solutions, two ions have dominant roles. These ions, the hydronium ion, H30 (or hydrogen ion, H" ), and the hydroxide ion, (OH ), are available in any aqueous solution as a result of the self-ionization of water, a reaction of water with itself, which we will describe in the next section. This will also give us some background to acid-base equilibrium calculations, which we will discuss in Chapter 17. 

Solutions of Salts of Polyprotic Acids 17-6 Acid-Base Equilibrium Calculations A Summary... 

Acid-Base Equilibrium Calculations A Summary— As a general summary of acid-base equilibrium calculations, the essential factors are identifying all the species in solution, their concentrations, the possible reactions between them, and the stoichiometry and equilibrium constants of those reactions. 

Balance the following redox reactions, and calculate the standard-state potential and the equilibrium constant for each. Assume that the [H3O+] is 1 M for acidic solutions, and that the [OH ] is 1 M for basic solutions. 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

The starting pH of the solution is calculated using i and the initial molarity of the diprotic acid. We use the standard approach to a weak acid equilibrium ... 

New NH3/NH4+ buffer When 0.142 mol per liter of HC1 is added to the original buffer presented in (a), it reacts with the base component of the buffer, NH3, to form more of the acid component, NH4+ (the conjugate acid of NH3). Since HC1 is in the gaseous phase, there is no total volume change. A new buffer solution is created with a slightly more acidic pH. In this type of problem, always perform the acid-base limiting reactant problem first, then the equilibrium calculation. 

Fig. 15.10. Calculated effects on pH of reacting sodium hydroxide into an initially acidic solution that is either closed to mass transfer (fine line) or in equilibrium with atmospheric C02 (bold line).

The reaction between ethyl alcohol and formic acid in acid solution to give ethyl formate and water, C2H5OH + HCOOH HCOOC2H5 + H20, is first-order with respect to formic acid in the forward direction and first-order with respect to ethyl formate in the reverse direction, when the alcohol and water are present in such large amounts that their concentrations do not change appreciably. At 25°C, the rate constants are kf = 1.85 xlO-3 min 1and kr = 1.76 xlO-3 min-1. If the initial concentration of formic acid is 0.07 mol L-1 (no formate present initially), calculate the time required for the reaction to reach 90% of the equilibrium concentration of formate in a batch reactor. 

The data indicate that in strong acidic solution H2C03 may be in equilibrium with protonated carbonic acid. The structures of carbamic acid and its O- and N-proto-nated forms 111 and 112 were calculated at the MP2/6-31G(d) level.140... 

PROFILE is a biogeochemical model developed specially to calculate the influence of acid depositions on soil as a part of an ecosystem. The sets of chemical and biogeochemical reactions implemented in this model are (1) soil solution equilibrium, (2) mineral weathering, (3) nitrification and (4) nutrient uptake. Other biogeochemical processes affect soil chemistry via boundary conditions. However, there are many important physical soil processes and site conditions such as convective transport of solutes through the soil profile, the almost total absence of radial water flux (down through the soil profile) in mountain soils, the absence of radial runoff from the profile in soils with permafrost, etc., which are not implemented in the model and have to be taken into account in other ways. 

In the titration of a weak acid with a strong base, we must consider the acid dissociation equilibrium of a weak acid (Kg) to calculate [H30 ], after the addition of a strong base. Let us consider the titration of 100 mL of a 0.1 M solution of acetic acid (CH3COOH) with 0.1 M NaOH solution. 

For a solution of two weak acids with comparable values of Ka, there is no single principal reaction. The two acid-dissociation equilibrium equations must therefore be solved simultaneously. Calculate the pH in a solution that is 0.10 M in acetic acid (CH3C02H, Ka = 1.8 X 10 5) and 0.10 M in benzoic acid (C6H5C02H, Ka = 6.5 X 10 5). (Hint Letx = [CH3C02H] that dissociates and y = [C HsCCAH] that dissociates then [H30+] =x + y.)... 

All stereocenters in 1,6-anhydrohexopyranoses are of inverted orientation compared to those in the parent 4Ci(d) or 1C4(l) conformations of the corresponding hexopyranoses for example, see 21, 23, and l,6-anhydro-/J-D-glucopyranose (22). In chemical properties, these compounds resemble to a certain degree the methyl /f-D-hexopyranosides. They are relatively stable in alkaline media, but are readily hydrolyzed by acids. In aqueous acid solution, an equilibrium is established between the 1,6-anhydrohexo-pyranose and the corresponding aldohexose, whose composition correlates with expectations from conformational analysis and calculations from thermodynamic data.121 Extreme values, 0.2 and 86%, are observed respectively with 1,6-anhydro-/f-D-glucopyranose (22) and l,6-anhydro-/f-D-idopyranose (the latter has all hydroxyl groups in equatorial disposition). 

These calculations (Fig. 5.8) assumed chemical equilibria at each temperature. It is well known that atmospheric liquid aerosols are often supercooled (Carslaw et al. 1997 Sattler et al. 2001 Buseck and Schwartz, 2004). If these simulations were run without water ice as a solid phase in the minerals database (in essence, supercooling), then the predicted pH values up to 12 km would be just an extension of the lower data points (temperature = 0 to 25 °C) in Fig. 5.8. Given that stratospheric aerosols are concentrated acidic solutions (Carslaw et al. 1997), clearly the equilibrium calculations... 

Hydrolysis of cyclohexane-1,2,3-trione-l,3-dioxime (23, X = O) and its 2-imine (X = NH) has been studied in perchloric acid solution.91 The mechanism is proposed to involve a protonation pre-equilibrium, followed by slow water addition to protonated and non-protonated forms. Oxime protonation pXas have been calculated. 

Let a = fraction ionized. For every mole of acid added to the solution, there will be (1 — a) moles of un-ionized acid at equilibrium, a moles of H+, and a moles of anion base conjugate to the acid. This gives us a total of (1 + a) moles of dissolved particles. Then, the molality with respect to all dissolved particles is (1 + a) times the molality calculated without regard to ionization. 

In this problem, we have made the assumption that the contribution of water to [OH-] (equal to [H+], or 2.4 x 10-11 M) is negligible compared with that of NH3. Kw is used to calculate [H+], since water is the only supplier of H+. In general, [H+] for acidic solutions can be calculated without regard to the water equilibrium then Kw is used to calculate [OH-]. Conversely, [OH-] for basic solutions can usually be calculated without regard to the water equilibrium then, Kw is used to calculate [H+]. 

Calculating the pH of weak acids and bases is more challenging, because they do not ionize completely. So, in a 0.10 M solution of acetic acid, the [H+] concentration is not 0.10 M. We must use the equilibrium constant expression to find the pH of weak acid solutions. So, what is the pH of a 0.10 M solution of acetic acid The K of acetic acid is 1.8 x 10"5. 

Just like sodium ions, chloride ions are spectator ions in acid-base chemistry. Their job is to provide a charge balance to the cations in solution. So, in calculating the pH of lidocaine hydrochloride we ignore the chloride ion. Now we could draw out the structure or write the molecular formula of lidocaine and its conjugate acid, but it is tedious to do so. Let s do what most chemists do, and postulate a temporary abbreviation for these species. How about using L for lidocaine, and HL+ for its conjugate acid Now, we can write an equation for the acid ionization equilibrium reaction. 

Many commercially available and investigational drugs are anionic or cationic salt forms of weak acids or weak bases (undissociated). Their properties (solubility, partition coefficient, bioavailability, etc.) are strongly dependent upon the degree of ionization, the pH of the solution, and other constituents in the solutions of the drugs. In this chapter, ionic equilibrium calculations will be demonstrated in order to facilitate study of their properties. 

Four species are present in the solution of the weak acid at equilibrium HA, A, H+, and OH-. To calculate the concentrations of the four species in the solution, four equations are needed ... 

This shows that the ionic equilibrium calculation for the salt formed between the weak base and the strong acid is identical for the undissociated acid. Therefore, one may use Equation (2.15), Equation (2.17), and Equation (2.19) for the calculation of H+ in the solution of a salt between a weak base and a strong acid. Equation (2.21a), Equation (2.21b), and Equation (2.21c) may be used for the calculation of OH- in the solution of the salt between a weak acid and a strong base along with Equation (2.20). 

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