AMPHOTERIC MOLECULES, IONS, AND SALTS
0
DAVID DAVIDSON Brooklyn College, Brooklyn, New York S u s s T m m s which function both as acids and' bases are said t o be amphoteric or amphiprotic. For such substances the noun ampholyte is a convenient term. I t is the aim of this paper to call attention to the splendid opportunity ampholytes afford for the teaching of acid-base principles. A simplified method of approximating the pH's of aqueous solutions of ampholytes is included.
"hydrolysis constant" (in the case of cationic acids). It consists of the equilibrium constant for the reaction of the acid with water, the concentration of water itself being considered constant. Thus, for the two acids mentioned ahove the respective K.'s are: for acetic acid,
BACKGROUND
for ammonium ion,
Acids and bases are conveniently defined by means of the Brousted equation: Acid, G Base,
+ Hf
The basicity constant Kbis a measnre of the strength of a base. It is also known as the "ionization conThe acid and base connected by this equation are stant" (for uncharged bases) and the "hydrolysis known as conjugates but the reaction is only hypothetical, since actual acid-base reactions necessarily constant" (for anionic bases). It consists of the involve the interaction of two such systems. I n such equilibrium constant for the reaction of water with the reactions a proton is lost from an acid (which is thereby base, the concentration of water itself being conconverted to its conjugate base) and is transferred to a sidered constant. Thus, the Kblsfor the bases menbase (which is thereby converted t o its conjugate tioned above are: for acetate ion, acid). [ A ~ O H ][OH-] K* =
+ Basez* Acid* + Base,
Acid,
for ammonia,
The "ionization" of acetic acid, for example, involves the following proton transfer (protoly~is)~: AcOH
+ H2O
H80+
+ AcOFor many purposes the negative logarithms of K i s and K;s are convenient. The corresponding symbols are pK. and pKb. The pK, and pK, of conjugates are interdependent. This is readily demon~trated,~ using acetic acid as an example.
in which water functions as Base?. The "hydrolysis" of sodium acetate depends upon the transfer of protons from vater to acetate ion (water functions as Acid,). H20
+ AeO- e AcOH + OH-
I n the acetic acid-acetate ion system the acid is uncharged and its conjugate base anionic. I n a system such as ammonium ion-ammonia, on the other hand, the acid is cationio while its conjugate base is uncharged. I n this second case the protolysis ("hydrolysis") of ammonium ion involves the reaction: NH,+
AcOH H20
+ NHs
NH*+
Process HaO+ AeOH
++ AcO-= H20
Constant
++AcOOH-
adding: 2H10
+ HzO = H 3 0 f + NHa
e H20
+
+ OH-
K.&
therefore:
and the "ionization" of ammonia depends upon the reaction: HsO
[AcO-1
+ OH-
lHaO+l [OH-] = K.,KI,
but: [HaO+][OH-] = K,
The acidity constant K. is a measure of the strength of an acid. I t ~ i salso known as the "ionization constant" (in the case of uncharged acids) and as the I Some dictionaries use or rather than and. Or fails to imply that these substances function simuItaneously as acids and bases. 2 In this article, the acid-base equation. are written in conformity with the previous equation; that is, one set of conjugates h n k s the arrows while the other appears a t the extreme left and right.
=
lo-"
st 25'
hence: pK,,
+ pKa, = 14
Since the sum of the pK. and pKb for conjugates is 14, One constant is readily calculated from the other. It also follows from this relationship that an acid and DAYIDSON, D., AND K. GELLER,J. CREM.EDUC.,30, 238 (1953).
550
NOVEMBER, 1955
551
.
its coniuoale base .can be eoual i n strenoth onlu when mm-." " ' M Y L I is therefore a Strength Classifioation of Acids and Bases ( T e t r a ~ h o t o m ~ ) pK. = pKb = 7. The natural origin from which t o set out to designate acid Slrength designation Acidity scale Slraglh designation and base strengths. If PK. < 7, then PKB > 7, and q f c o j u g a t e acirl p ~ . p ~ a ofconjugale hose vice Rv . and 12. -~~ versa. - " choosinn two more ~ o i n t s 2 Sirang (A,) Feeble (B,) the system of strength classification given in Table 1 , , , , 2 . , , , .12. . . . . . . . . is obtained.' The tetrachotomv-strona, intermeIntermediate (Ai) Weak (U,) diate, weak, and feeble--servei to implement the Weak (A.) Intermediatc (Bi) mathematical relationship: pK, pKB = 14. At. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Feeble ( A 0 Strong (B,) tempts to express the strength relationships of conjugates in terms of the traditional dichotomy-strong and weak-have only led to inadequate or misleading in these simultaneous equilibria and to examine them statements? The difficulty is due t o the fact that, in from the standpoint of their dominant constants the dichotomy, weak acids have strong or weak con- (Table 2). The diprotic acid is dominated by the jugates, depending on how weak the acid is. The first acidity constant, K,,. Normally this is larger same is true for the conjugates of weak bases (see the than K,,. I n a symmetrical diprotic acid statistical diagram). considerations6 require that K., be a t least four times K.,. Usually this ratio is much larger owing t o elecAcid-Base Scale (Dichotomy) t.rostatic influence^.^ Since log 4 = 0.60, pK., ezceeds I pK., by a t least 0.60. (The inverted order of the pK,'s arises, of course, from their being negative logarithms.) The basicity constant of a simple ampholyte stems from the conjugate of the acidic group responsible for pK., in the diprotic acid. Siice pK., and pK,, refer to conjugates their sum is 14. Since, furthermore, We& Acids We& Buem pK., is larger than pK,, by a t least 0.6, it follows that: ~~~~~
-
+
1
strong B u r
AMPHOLYTES IN GENERAL
As has been said above, the loss of a proton from a monoprotic acid yields a base. The removal of one proton from a diprotic acid, however, yields an ampholyte, since this product of protolysis is not only the conjugate base of the original diprotic acid hut also the conjugate acid of the diprotic base which it yields on releasing the second proton. The process may be reversed by starting with a diprotic base and adding two ~ r o t o n sin succession. Such simple ampholytes with their conjugate are, therefore, in diprotic acids and diprotic bases as indicated below, ~
Diprotic acid e Hf Ampholyte e H f
+ + Ampholyte Diprotic base
This is the fundamental relationship which exists between the (nonconjugate) acidity and basicity constants of ampholytes. The inventory of species discussed above may often be useful in appraising the character of the several species involved in a polyprotic acid-base system. For example, given the two pK.'s of the carbonic acid system (Table 3), the remainder of the constants may pK,, = 14. be obtained by following the rule: pK., Thus, the species H&03 is characterized by pK,, (6.5): the first ~rotolvsismoduct. HCOn-, is an am-
+
6 GREENSPAN, J., Chem. Revs., 12, 339 (1933). In brief, the argument may be given as follows: A symmetrical diprotic acid has twice as many opportunities for losing one proton as does either acidic group alone; likewise, the diprotic base has twice as many opportunities for accepting a proton as does either basic group alone. Hence, the 6r8t protolysiis constant differs from the second by afactor of 2 X 2 = 4. 7 ~ T m ~ G.N W., ~ "Advanced , Organic Chemistry," 2nd ed., John Wiley & Sons, Inc., New York, 1949, Chap. 11.
,
It will be found convenient to tabulate the species 4 An earlier version of this olasmficrution scheme was given by DAVIDSON, D., J. CHEM.EDUC., 19,154 (1942). 6 Some examples of such statements are: (a) G ~ ~ ~ s., ~ z~ ~ ~ N e xEt b ,a of o kphysical chemistry? znd ed., D. Van Nostrand Co., Inc., New York, 1946, p. 984: "If the acid HA is we&, the conjugate base A- will be fairly strong, and interaction with the solvent, acting.as an acid, will take place to a definite extent."
.
TABLE 2
A&-B-
species ~~~~~t~~~ for --Speciess-----Dominant Type 1 Type Type
H,X HXX--
HzY+ HY Y-
%++
Z
Acldity P& PK,,
...
castantsBasicity
... pK6, pKa,
systems Character Dipratic acid Ampholyte Diprotic base
.......
552
JOURNAL OF CHEMICAL EDUCATION TABLE 3 species Inventory for the
Species
.-Dominant pK.'s
H&Oa HCOIC03--
( 1 ) 6.5 (2) 10.7
Acid
constantspKs's (1 j 7 . 5 (2) 3.3
...
system Chaharaele~
Diprotic acid Ampholyte Diprotic base
pholyte, characterized by pK., (10.7) and pKb, (14 - 6.5 = 7.5); the second protolysis product, COa--, is a diprotic base characterized by pKb, (14 - 10.7 = 3.3). The ampholyte, bicarbonate ion, is thus seen to be a weak base and a weak acid, its basicity being about a thousandfold stronger than its acidity. TABLE 4 Species Inventory for the Phosphoric Acid System Sueeies
-Dmninant constants-OK,% vK28
HsPO4 H?PO,-
( I ) 2.0 (2) 7.2
( i j ii.0
HP0,--
(3) 12.4
(2) 6.8
Triprotic acid Acidic amphdyte Basic ampho-
. ..
0)1.6
Triprotie base
P0.P
Chameter
tvtn .J ""
In conformity with the K,'s given above for acetic acid and ammonium ion, the concentration of water (as a base in ( 1 ) and as an acid in (2)) on theleft side of the chemical equations is included in the constant. STRENGTH TYPES OF AMPHOLYTES
It is apparent that the species H,O is both a feeble base and a feeble acid. If other acids or bases are t o manifest themselves at low concentrations in water, their pK.'s or pK;s must be sufficiently below 15.7 to compensate for their relatively low concentrations. For example, t o be merely as effective as water itself in producing hydronium ions, an acid of pK. 12 mould be required in a concentration of 0.01 M. Hence, the justification for considering a pK. of 12 the borderline between weak and feeble acids. I n qualitative organic analysis, feeble acids and bases are generally considered uonacidic and nonbasic, respecti~ely.~ From the relationship pK,, pKb, 7 14.6, it follows that if an ampholyte is a strong acid (pK,, < 2) it must necessarily be a feeble base (pK,, > 12.6). If, as may be desirable for many practical purposes, feeble acids and bases are disregarded, ampholytes may be limited to the three strength types B,A,, B,&, and B,A,. The relationship of these to their diprotic acids and bases is given in Table 6. A stable ampholyte of the type B,A* is impossible because, if, for euample, pK,, and pKo, were both five their sum would not be 7 14.6. Such a system would undergo a spontaneous protolysis in aqueous solution to form a tautomer of the type B,A,, both constants then being nine. -,-Aminobutyric acid is an example of such a case.
+
In the case of phosphoric acid (Table 4), two ampholytes occur between the triprotic acid and the triprotic base, one being preponderantly acidic and the other preponderantly basic. Note again that the pK. of one species plus the pK, of the next lower species totals 14, while the pK. plus the pKDof the am~hoteric suecies exceeds 14 by a considerable amount STRUCTURAL TYPES OF AMPHOLYTES It has been demonstrated above that simple, anionic TABLE 5 ampholytes are derived from uncharged, diprotic Species Inventory for the Water System acids. Among organic examples, the two acidic -Dominant constantsgroups may be identical in structure or different. PIG'S Character Snecies uK.'8 This opens the way for a large variety of structural HaOt (11-1.7 Diprotie acid types in which the acidic groups may be any of those HZO (2) 15.7 ( i j i5.7 Ampholyte given in Table 7. Uncharged or molecular ampholytes OH... (2) -1.7 Di~roticbase may contain one of each of the acidic and basic groups The system, water, is of interest (Tahle 5). The in Tahle 7, provided, as was indicated in the previous section, a t least one group is not intermediate in reactions and expressions involved are: strength. Simple, cationic ampholytes are derived HIOt + H 2 0 H 3 0 t + H 2 0 (1) from uncharged, diprotic bases. In dipolar ionic ampholytes, the acidic group is the cationic conjugate of one of the uncharged, basic groups in Table 7, and H?O + HzO HaOt OH(2) the basic group is the anionic conjugate of one of the . . uncharged, acidic groups in the table. Some examples of anionic ampholytes are found in potassium acid phthalate, sod~umbarbiturate, and sodium thioglycolate; of predominantly uncharged TABLE 6 Stranlrth (Restricted) ampholytes in sulfanilamide, adrenalin, 8-hydroxy- Tmes .- of Ampholytes quinoliie, p-aminophenol, and anthranilic acid; of Diprotic acid' Arnpholyte Diprotic base" predominantly dipolar ionic ampholytes in glycine AiAi B,Ai B~B, and c-aminocaproic acid; of cationic ampholytes in AiA, . BvAw BwBi procaine and p-phenylenediamine monohydrochloride. A,A, BiA, RiBi *Feeble acids and bases have hem omitted; consequently An interesting case of an ampholyte is found in im-
=
=
+
~
their conjugates, strong bases and aeids, also fail to appear.
8
D~vrosou,D., J. CHEM.EDUC.,19, 221 (1942).
NOVEMBER, 1955
553 TABLE 7 Uncharged Groups Available for Ampholytas
-
- -
- A c i d i c groups Weak
Hydroxyl (phenols, ends of p-diketones, etc.) Oximino Imido 1' or 2' nitro Sulfhydryl (mercaptans or thioamides) Sulfonsmido
Intermediate Hydroxyl (enols of cyclic 6diketones, etc.) Sulfhydryl (thiophenols) Carboxyl
idazole in which both the basicity (BJ and acidity (A,) are enhanced through the operation of resonance. N
CH-NH\
I/
CH-NH Imidszole
CH
N
CH-NH
CH-N-
I 'CH CH-NHH
CH-NH\CH
+-
Its Conjugate Acid
1
-
Its Conjugste Base
Process
H9X HXHIX
+ H I O S HIO+ + HX-
+ H1O = H,O+ + X-+ 2H10 = 2H30+ + X--
At the isoprotic point: [H,Xl = [X--1
hence: IHaOC1r =
or:
d K X 2
Conslant
Ka, Km, K,,K.,
Amino (aromatic) Hydrazino (aromatio) Azamethino (RCH=NR')
Inlevmediate
-
Amino (aliphatic) Hpdrazino (aliphatic) Amidino Guanidino (aromatic)
+
pH, = '/z (6.5 10.7) = 8.6. The fact that this is greater than seven also indicates that the basicity of bicarbonate ion exceeds its acidity in strength. THE DISMUTATION EQUILIBRIUM
The proportions of the three species, diprotic acid, ampholgt.e, and diprotic base, present at the isoprotic point are determined as f o l l o ~ s . ~ Process H2X HnO HIOf HXHaOf X - HXH20 HIX X - - e 2HX-
THE ISOPROTIC POINT
It was seen earlier how the pK.'s of a polyprotic acid-base system could be employed to characterize the ampholytes in the system. Bicarbonate ion was found to be predominantly basic (pK., = 10.7; pKb, = 7.5) although both functions are weak. Another method of employing the pK.'s of a diprotic acid for this purpose is to determine the pH at which the ampholyte is in equilibrium with equivalent concentrations of the diprotic acid and base; that is, for example, the pH a t which [HzX]= [X--1. In the case of anionic and cationic ampholytes, this pH has been called the first equivalence point or half neutralization point. For uncharged or dipolar ionic ampholytes it has been termed the isoelectric point. A generic term to cover both of these is suggested; i. e., the isoprotic point. The derivation of the equation connecting the isoprotic point, pH,, with the pK.'s of a diprotic acid is given below.3
Basic groups
Weak
+ = + + = + +
Constant
Ks, &!l
K*,/Ka9
If: [HsX] = [X--1
then:
When K,,/K,, has the minimum value of four, [HX-I/[HPX] a t pH, equals two. Hence, [H,X] : [HX-1 : [X--1 = 1 : 2 : 1, and 50 per cent of the total specles is ampholyte. The greater the ratio of K,,/ K.,, the more stable is the ampholyte species relative to its two conjugates. Thus, in the case of the bicarbonate ion, the species HzC03,HC03-, and C03-occur in the ratio, 1 : 126 : 1 a t the isoprotlc point. In the case of higher polyprotic acids, the pH, of a given amphoteric species is equal to one-half the sum of its pK. plus the pK, corresponding to its pKD ( i . e., the pK, of the preceding species). Thus, the pH, of HzPOa- is equal to (2.0 7.2) = 4.6, while that of HPOa-- is eaual to '/. (7.2 12.4) = 9.8. Here again these figures reflect the character of the species, HzPOn- being predominantly acidic while HP04-- is predominantly basic. The method given in the preceding paragraph may be ~articularly useful, in calculating the isoelectric points of polyaminocarboxylic acids, aminopolycarboxylic acids, and polyaminopolycarboxylic acids, but before discussing these problems another questicn mnst be considered.
+
+
The isoprotic point (half-neutralimtion point or THE TAUTOMERIC EQUILIBRIUM A substance such as y-aminobutyric acid may be isoelectric point) is equal to one-half the sum of the two pK,,'s involved. For bicarbonate ion, for example, written in two different ways (I, 11). The difference
JOURNAL OF CHEMICAL EDUCATION -
-
of this system is given in Table 8. Quantitatively,g the ratio of [II]/[I] is given hy the ratio K., - K /K and amounts to 106.5. The proportions of diprotic -Dominant eonstanlsacid and diprotic base also present may be calculated Species" pK.'s pKb's Character as shown above in the case of bicarbonate ion (the +NH8CHnCH2CH&OOH (1) 4.2 Diprotic acid dismutation equilibrium). +NHCH.CH~CH~COO- (2) 10.4 (ij'(i.8 Ampholyte The method of comparing the first constant of the [NH.CHZCH.CH~COOH] NH2CH2CH2COO... (2) 3.6 Diprotic base amino acid hydrochloride with that of its ethyl ester a Minor species of the same net charge as the principal species hydrochloride is illuminating in the case of p-aminoare given in brackets. The principal and minor species are henzoic acid for which the pertinent constants are, tautomers. respectively, pK,, 2.3, and pK 2.4. Here the formation of the ampholyte from the diprotic acid does COOH (Ai) COO- (B,) COOH (Ai) COOCH. involve the ammono group and the predominant am1 I photeric species is the uncharged molecule (Table 9). CHz AH2 CH, AHp A species inventory of the polyprotic acid-base I I CHI system which includes 6,~-diaminobutyricacid yields the results given in Table 10. The ampholyte of zero net charge (to which the term isoeleclric point applies) has the acidity of pK., and the basicity of pK*,. Its between these two structures involves a proton transfer isoelectric point, therefore, equals (pK,, pK,,). from the carboxyl to the amino group so that equilih- .4ssuming the acidity constants to have the values 4, rium between these structures may be expected. To 10, and 11, pH, = 10.5. ~ r e d i c twhich of these structures predominates one AMPHOTERIC SALTS must refer to the acidity of monocarhoxylic acids and the basicity of aliphatic amines. The following sysA common type of ampholyte which has not received general recognition as such is neither a molecule nor a tematic procedure is recommended: (1) Add a proton to the ampholyte. Both struc- single ion but a salt consisting of two ions. The cation (the conjugate of an uncharged base) is responsible for tures (I) and (11) yield (111) . . which is the unamthe acidic properties of the salt, and the anion (the higuou$,' diprotic k i d . (2) Classify the acidic groups in (111) (use Table 7). conjugate of an uncharged acid) supplies the basic In the present case the carboxyl group is A,, the ali- properties. Ammonium acetate is an example of such an ampholyte. phatic ammonium ion, A,. Unlike the ampholytes previously discussed, these (3) Regenerate the ampholyte by removing a proton from the diprotic acid, taking the proton pre- salts are not related to diprotic acids and bases hut to dominantly from the stronger acidic group; in this two different monoprotic acids and bases. The algebra case, therefore, from the carboxyl group. This yields involved in their treatment, however, is much the (11) as the uredominant structure of the amino acid same provided that pK., refers to the related uncharged acid, and pKo, to the related uncharged base. (B,%). The conclusion reached concerning the dipolar ion Thus: structure of r-aminobutyric acid may be arrived at Pmeers Constant more directly by comparing the pK., of (111) (4.2) HA H 2 0 HIO+ + A K.1 with the pK. of the corresponding methyl ester hydroBH+ + H 2 0 = HIOf + B K, chloride (IV), (9.7). This discrepancy suggests that the pK., of (111) does not correspond to the protolysis Adding: of the ammono group and hence it must correspond to HA + BH+ + 2 H 1 0 = 2 H 3 0 t + A- f B K.,Ka, the protolysis of the carboxyl group (actually to their sum) resulting in the formation of the dipolar ion as the and : predominant amphoteric species. A species inventory
...,,. ,..,..
TABLE 8 Snecies Inventorv for the r-Aminobutvric Acid System
...,.,
+
+
TABLE 9 ~GeciesInventory for the p-Aminobenxoic Acid System Species"
-Dominant pK.'s
constantspKs's
Character
=
At the isoprotic point: [BH+] = [A-1
hence: [HA1 = [BI [HaOt1 = K.,K., PHI = 'ldpKo, pKaJ
+
Minor species of the name net charge as the principal species are given in brackets. The principal and minor species are tautomers. a
EDSALL,J. T., AND M. H. BUNCWRD,J. Am. Chem. Soc., 55, 2337 (1933); COHEN,E. J., AND J. T. EDSALL,"Proteins, Amino Acids and Peptides as Ions and Dipolar Ions," Reinhold, New York, 1943, p. 99. @
NOVEMBER, 1955
555
TABLE 10 Species Inventory for the B,y-Diaminobutyric Acid System -Dominant Acidzty
PK., PK., P K ~
constantsBasicity
.. .
Cationic acid Cationicampholyte Di~olaram~holvte (zero het chargej
PKS. PK~,
','Y"Z,"L12""".L,
a
Character
~.
CH2CH1NH,)CH,COO. .. Anionic base -D K ~ . Minor speeiea of the same net charge ss the principal species are given in brackets. The principal and minor ~peciesare tautomera.
The isoprotic point in this case is similar to the isoelectric point in that it is the pH a t which the number of cations in the system is equal to the number of anions, and the net charge of the species in the acid-base reaction under consideration is zero. Further information concerning the amphoteric salt may be obtained from the following derivation. Constant K.x l/G
Process
HA + H 1 O = H I O + + A BHf H70 HaOC B
+
+
(NH,+) COO-. In acidic solutions the following processes will occur.
+
H,Of HaOC
+
P~ocess HY (solid) HY (dslvd.) HY (dslvd.) H;Y+ H1O HY (solid) H Z + HpO
= = =
The observed solubility, S Hence:
Constant K, I/&, KdK.,
+ +
=
[HY],,,,,.
+
[H,YC].
Adding: HA
+B
e B H + +A-
In solutions of bases, on the other hand, the following relationships occur: At the isoprotic point:
+
The ratio KJK., is a measure of the stability of the pK,, = 14), salt. If K., = K., (that is, if pK., the salt will be half converted to its unchar~ed - urogenitors when dissolved in an aqueous solution having a pH = pH,. If KJK., is large (that is, if pK., pKb, > 14), the salt will be stable relative to its uncharged progenitors; while if K.,/K., is small (that is, if pK., pK,, < 14), the salt will be largely transformed into its uncharged progenitors in aqueous solution. In the case of ammonium acetate, for example, using the rounded values of 5 and 9 for the pK,'s of acetic acid and ammonium ion, respectively, one obtains a pH, of 7 and a ratio of [AcOH] : [Salt] : [NH,] a t the isoprotic point of 1 : 100 : 1. Furthermore, ammonium acetate is to be classified as a weak base (pK,: = 9) and a weak acid (pK., = 9). The close relationship of such salts to other ampholytes may be seen in the species inventory given in Table 11.
Constant K, 1 /Ka, K./Kb,
Process HY (solid) e HY (dslvd.) HY (dslvd.) OH-= H 2 0 YHY (solid) OHH1O Y-
+
+
=
+ +
therefore:
+
+
INSOLUBLE AMPHOLYTES
+
The observedsolubility, S = [HY]d.,vd: [Y-1. Hence:
Thus, in the case of simple, slightly soluble ampholytes the solubility in acidic buffers will increase in proportion to the hydrogen-ion concentration (if [HaO+]/ K., is large compared with unity), the proportionality factor being K,/K.,. Likewise, the solubility in basic buffers will vary inversely as the hydrogen-ion concentration (if K.,/[H,O+] is large compared to unity), the proportionality factor being K.K,,. -
TABLE 11 Species Inventory of the Ammonium Acetate System
The occurrence of amphoteric properties in slightly soluble substances is evidenced by their increased ' -Dominant eonstanlsSpecies Acidity Basicity solubility in acidic and basic solutions. The simultaneous equilibria involved may be expressed as follows. AcOH; NH4+ pK, of AcOH NH*+ pK. of NH,+ pKa of'&& Let HY represent a simple, slightly soluble ampholyte AcO-; Acu-; .--IYHJ ... DKo ~f N H r of zero net charge, such a s phenylalanine, PhCH2CH-
Character
Monoprotie acids Amphoteric salt Mono~rotio bases
556
JOURNAL OF CHEMICAL EDUCATION
feeble acids of pK. > 15, a pH of 7. The intervening intermediate and weak acids form 0.1 M solutions having pH's between 1 and 7. As the concentration decremes, pH range for pH mnge for the pH range of solutions of acids becomes narrower; Concentration solutions of acids solutias of bases Concentration thus, at M it extends from 3 to 7, at M from lo-' . . . . . . . .. 7 7 . . . . . . . . .l3 lo-' 5 to 7, and so on (Table 12). The exact relationship 7 . . . . . . . .12 lo-' lo-' 2 . . . .7 7 . . . . 11 10-3 between [H30+l,C, the concentration of the acid-base lo-" 3 . . . .7 lo-' 4 . . . . . . .7 7 . . . . 10 lo-' system, and K. is given by the third-order equation:'O 5 . . . . . .7 7. . . . . .9 lo-" lo-' 6 . . . . .7 7 . . .8 10-0 [H80+I8 K.[H,O+ls - (CK. K , ) [H,Of1 - K.K, = 0 TABLE 12 pH Ranges of Solutions of Acids and Bases
10' 10-
6.79-7 7
7-7.21 7
+
10' 10-8
+
Since this equation cannot be solved directly, methods of approximation are desirable. The relationships given in Table 13 are useful for solutions of acids whose I n the discussion given above the concentration of are greaterthan 10-6 molar, similar the diprotic base has been neglected in acidic solution, relationships apply for solutious of bases if pH is that of the diprotic acid in basic solution. I n the pH replaced by p~~ and p ~ bya p ~ a the ; p~ is then ob. region where both of these concentrations are signifi- tained from the relationship, p~ = 14 - p ~ ~ . cant, the observed solubility is given by: The first of the expressions given in Table 13 is S = [HY1mVa. [FLY+] [Y-I derived from the approximate form of Ostwald's dilution law, a2C = KG. It neglects the ionization of The pH a t minimum solubility may be derived as water and considers [HA] = C. The second relationfollows. Substituting: ship is the logarithmic form of the expression [H,O+] K K.Koz= wC, and also neglects the ionization of water. The S = K , + 2 [H80+l ---Ka, [H3Oi1 third equation is derived from the expressions for Differentiating: K, and K, and the electrical balance, [HaO+]= [OH-] dS K, KX., [A-1. This does not neglect the ionization of water drao.1 = K,- [&O+]' but considers [HA] = C. Snhst'ituting in the equation for electrical balance: Setting the differential equal to zero and solving:
+
+
+
+
[H8Oi1 =
KaC Kw [H,Ot1 + IHJOi] [H30+lZ= Ky. K.C
[HaO+] =
d m
-
+
That is, the solubility of a slightly soluble ampholyte is a minimum in a buffer of pH equal to its isoelectric point.
[HaO+I =
d ~+ K.C , K,K,C
THE pH's OF AMPHOLYTE SOLUTIONS
An ampholyte which has acidic and basic properties of equal strength (pK., = pK0,; pH, = 7) forms solntions in pure water which have a pH of 7. Other ampholytes yield acidic or basic solutions depending upon which function of the ampholyte is stronger. The pH's of their solutions fall between 7 and the pH,, approaching the latter as the concentration increases. Before examining the pH's of ampholyte solutions further it may be useful to consider the pH's of solutions of simple acids or bases. At the 0.1 M level, for example, strong, monoprotic acids have a pH of 1,
pH
=
7 -log
4-
K,
The term p a which occurs in the'second of the approximate formulas given above may readily be calculated in the following way. Ost'wald's dilution law:
nC
I-ar
= K
may be transposed ": (;)u.+
a
- 1=0
Solving for m: TABLE 13 F o ~ m u l a sfor Calculating the pH's of Solutions of Acids pK.
+ PC
3 12 but
