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FIG 10.12. Control of preheat temperature is necessary for this reactor to be stable.
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While a discussion on end-point control in general might be in order, pH is used far more widely than any other measurement to sense the state of a react ion. So while pH has some peculiarities of its own, principally its logarithmic character, much of the following commentary applies to other end-point measurements. In several instances in earlier chapters, pH has been cited as a difficult control problem. It has, in addition to the usual properties of a composition loop, a severely nonlinear measurement. This very characteristic imposes exceptional demands in flow rangeability of the valves and control system.
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The outstanding property of each acid-base system is its pH curve; the The one shown in Fig. 2.12 is typical of a base neutralized by an acid. shape of the curve is related to the equilibrium constants for ionization of the acid and base, and the concentrations of each of the ions. But the basis of the coordinate system is logarithmic, in that pH is defined as the negative logarithm of the hydrogen-ion concentration, in gram-ions/ liter: pH = - log H+] or [Hf] = lo--* (10.25)
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Pure water ionizes into hydrogen and hydroxyl ions of equal concentration:
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The equilibrium constant for the ionization of water is 10-14:
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K = [H+l[oH-l [Hz01 = 10-M
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This is a useful relationship, because it defines the hydroxyl-ion concentration of any aqueous solution whose pH is known:
[ O H - ] = 10~=- 4
(10.26)
The neutral point for water is where hydrogen and hydroxyl ions are at equal strength, i.e., at pH 7. Each acid and base has its own ionization constant. Some acids (or 8 bases) have two or t,hree hydrogen (or hydroxyl) ions per atom, each of which has its own constant. The ionization constant determines the pH for a given strength of acid or base. Consider the example of an acid
1 Applications
HA Kth an ionization constant. KA and of a base BOH whose constant is Kn, in separate solutions. Ionization proceeds as follows: H A g A+ + ABOH eB+ + OHKB
The pH of each solution is readily derived: l(yPH = !$!&+I
l()pH- 4 = KB;tH]
(10.27)
Sotice that the pH is a function of the concentrat,ion of the companion ion in each solution. The pH of each solution mill be farthest from 7 when the companion ions are at a minimum: i.e., equal to the hydrogenor hydroxyl-ion concentration: (10.28) If some neutralization has already taken place, however, the concentration of the hydrogen or hydroxyl ion will be less than that of its companion, which could alter the pH vs. concentration relationship considerably. Because of the effect of the half-power in Eq. (10.28), the pH of pure acids and bases can be expected to change by 0.5 with every decade increase in concentration. This is true for weak acids and bases. Strong acids and bases, however, do not obey the rule, probably because their ionization is not affected by t,he presence of a companion ion, since every decade in concentration changes pH by about one unit, as Table 10.1 indicates. From the data in Table 10.1, the ionization constant for acetic acid is found to be 1.83 X lOA and for ammonium hydroxide, 3.47 X 10e5; ionization of the others is variable. When controlling to an end point, all of the acid (base) must be neutralized, both what, is already ionized and what is not. Let this total acid concentration be designated 54, and total base, 2~:
= [H+l + [HA]
xjj = [OH-] + [BOH]
(10.29)
TABLE 10.15
pH of Various Acids and Bases
Concentration,
1.0 01 0.01
HCl 0.10 1.07 2.02
CH,COOH 2.37 2.87
NaOH 14.05 13.07 12.12
NH,OH 11.77 11.27 10.77
* Normal concentration is defined as one gram-atom of replaceable hydrogen per liter of solution.
Controlling Chemical Reactions
FIG 10.13. A weak acid or base will require more reagent for neutralization from a given pII, but control is easier; buffering augments the effect.
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