Diprotic acids, equilibrium concentrations

The problem describes a weak diprotic acid and asks for ion concentrations. To determine concentrations of all ions, we need to consider more than one equilibrium. This is done in stages, starting with the dominant equilibrium. We apply the seven-step strategy. The problem asks us for the concentrations of the ions in carbonated water, in which the major species are H2 CO3 and H2 O. 

Part 1 From the deprotonation equilibrium of H3A (for a triprotic acid) or H2A (for a diprotic acid), determine the concentrations of the conjugate base, H2A- or HA-, respectively, and H30+, as illustrated in Example 10.12. 

Another constraint equation often used in equilibrium problems is the proton balance equation (PBE) (Pankow, 1991). It provides a means of keeping account of protons in the system. A PBE can be formulated by writing an MBE in which the concentration of each species in the EPM table is multiplied by the stoichiometric coefficient of H in the EPM table. For example, the PBE of a diprotic acid H2L where the components that define the species are H2L and H+ would be... 

In the following example we calculate the equilibrium concentrations of all the species of a diprotic acid in aqueous solution. 

Strategy Determining the equilibrium concentrations of the species of a diprotic acid in aqueous solution is more involved than for a monoprotic acid. We follow the same procedure as that used for a monoprotic acid for each stage, as in Example 15.8. Note that the conjugate base from the first stage of ionization becomes the acid for the second stage ionization. 

Several aspects of these equilibria are notable. First, although carbonic acid is a diprotic acid, the carbonate ion is unimportant in this system. Second, one of the components of this equilibrium, CO2, is a gas, which provides a mechanism for the body to adjust the equilibria. Removal of CO2 via exhalation shifts the equilibria to the right, consuming H ions. Third, the buffer system in blood operates at a pH of 7.4, which is fairly far removed from the pK i value of H2CO3 (6.1 at physiological temperatures). In order for the buffer to have a pH of 7.4, the ratio [base]/[acid] must have a value of about 20. In normal blood plasma the concentrations of HCOs and H2CO3 are about 0.024 M and 0.0012 M, respectively. As a consequence, the buffer has a high capacity to neutralize additional acid, but only a low capacity to neutralize additional base. 

Diprotic and polyprotic acids undergo successive ionizations, losing one proton at a time (W Section 4.3], and each ionization has a ATa associated with it Ionization constants fCT a diprotic acid are designated and We write a separate equUibrium exja ession for each ionization, and we may need two or more equilibrium expressions to calculate the concentrations of species in solution at equilibrium. For carbonic acid (H2CO3), for example, we write... 

Sample Problem 16.17 shows how to calculate equilibrium concentrations of all species in solution for an aqueous solution of a diprotic acid. 

Determination of the concentration of all species for a solution of a weak diprotic acid, H2A -> Solve the main equilibrium (ATai) as for any weak acid. 

Because sulfurous acid is diprotic, a second proton transfer equilibrium has an effect on the ion concentrations, and the water equilibrium also plays a secondaiy role ... 

Material balance Since H2A, HA-, and A-2 coexist at equilibrium, the sum of the concentrations of H2A, HA-, and A-2 should be equal to the amount of the diprotic weak acid initially added to the solution, Ca. 

There are six species present in equilibrium. Six equations are needed to solve for pH or for the concentration of H+. The same approach used for mono- and diprotic weak acids is employed here ... 

Any acid-base equilibrium can be described by a system of fundamental equations. The appropriate set of equations comprises the equilibrium constant (or mass law) relationships (which define the acidity constants and the ion product of water) and any two equations describing the constitution of the solution, for example, equations describing a concentration and an electroneutrality or proton condition. Table 3.6 gives the set of equations and their mathematical combination for pure solutions of acids, bases, or ampholytes in mono-protic or diprotic systems. 

The treatment of diprotic and polyprotic acids is more involved than that of mono-protic acids because these substances may yield more than one hydrogen ion per molecule. These acids ionize in a stepwise manner that is, they lose one proton at a time. An ionization constant expression can be written for each ionization stage. Consequently, two or more equilibrium constant expressions must often be used to calculate the concentrations of species in the acid solution. For example, for carbonic acid, H2CO3, we write... 

Example 3 Equilibrium investigation, concentration determination of a diprotic and a strong acid... 

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