The Conjugate Acid-Base Chart Richard S. Treptow Chicago State University, Chicago, IL 60628 Beginning students are often confused by the many suhtleties of acid-base chemistry. In my classroom, I find that conjugate acid-base charts are effective teaching tools for overcoming their problems. The charts provide a framework for visualizing the conjugate relationship and depicting the strength of acids and bases. Students readily learn to use them to predict the direction and extent of proton transfer reactions. Although brief versions of the chart appear in advanced texts (1-3),their use in general chemistry has not been previously advocated. Our discussion begins with the Br6nsted definition of an acid as a proton donor. In aqueous solution an acid, HX, transfers its proton to H20, the reference hase, HX + HzO e H30t + XAcid strength is measured by the dissociation constant,
from which we define pK. = -log K,. If the reaction above is viewed in the reverse direction, Xis seen to be a Brflnsted hase. X- is called the conjugate hase of HX. Base strength is measured by the ability of the species to accept a proton from water, which now serves as the reference acid, The strength of the hase is expressed by the constant,
which leads to the definition pKb = -log Kh. For a given acid and conjugate hase, the productof K, and Kb reduces to
the pKb scale is fixed by the relationship derived above. This second scale appears on the right. As one proceeds down the chart, pKb increases and hase strength decreases. Placing a conjugate pair on the chart requires knowledge of either its acid pK, or hase pKh. The charts in this paper were cnnstructed using data from standard literature sources ( 4 6 ) . Special mention should he made of the appearance and location of Hz0 in both columns of the chart. Water is amphoteric, as illustrated by the proton transfer it undergoes with itself, Hz0 + Hz0 e H30C+ OHThis reaction, autoprotolysis, can he used in conjunction with the definitions above to calculate pK, and pKb of water. Both values turn out to he 14.0. Hz0 can thus he positioned in both columns.~ Students with some understanding of how molecular structure affects acid or base strength will be able to identify trends on the chart. For example, Figure 1shows a decrease in acid strength among the hydrides: Hz0 > NH3 > CH4. This trend is predictable from central atom electronegativities. The decreasing acidity in the series H30+ > Hz0 > OHresults from the effect of charge on proton donating ability. Polyprotic acids become progressively weaker as they dissociate protons; pK, values typically increase by several units with each proton lost. In general, any correlation between molecular structure and acidity or basicity can be depicted on the chart simply by displaying the relevant species.
ACIDS
BASES
Theexpression on the right, the ion product of water, has the value 1.0 X 10-l4 a t 25 "C. Substituting and taking logarithms yields Thus, the pK, of an acid and the pKb of its conjugate hase are not independent. As pK, decreases, pKb must increase. In other words, as acids become stronger their conjugate bases become weaker. Chart Construction and Features For comparative purposes acids are frequently listed according to their strengths. In the conjugate acid-base chart, acids are positioned on a vertical pK, scale. As illustrated in Figure 1, the scale appears on the left side of the chart. Since pK, decreases from top to bottom, acids become stronger as we descend the chart. Once an acid is positioned, its conjngate base is entered beside it. With the pK, scale already set, HCI
' The K, and K, of water are both 1.0 X lo-"
not by coincidence but because their expressions both reduce to [H30+] [OH-]. in deriving these expressions we employ the convention. as elsewhere. that H20has unit activity as the solvent. 938
Journal of Chemical Education
HCIOL
CI CIO;
Figure 1. A simple conjugate acid-base chart. The diagonal arrow illustrates the rule that an acid tends to donate protoffi to a base higher on the chart.
An important use of acid-base charts is for predicting the extent of reaction between any acid and base. The general reaction has an equilibrium constant IHyl [X-I Keq = [HXI WI By definition, proton transfer from H X to Y- is favored if K, > 1.In order to evaluate K., it can be expressed in terms of K.(HX) and K.(HY), thedissociation constantsof the two acids involved,
Taking the logarithms of both sides gives log Kq = pKa(HY)- pK.(HX) Proton transfer is favored if log K, > 0. This requires that pKJHY) > pK.(HX). In terms of the acid-base chart, proton transfer tends to occur if Y- appears higher on the base side than HX is on the acid side. In other words: Proton transfer is favored if a line drawn from the acid to the base slopes upward. Figure 1exemplifies thisrule with a diagonal arrow pointing in the favored direction of transfer. Let us apply the above rule to predict the fate of various acids in aqueous solution. A strong acid, such as HCI, appears near the chart bottom; it is lower on the acid side than the Hz0 on the base side. HCl can be expected t o donate its
ACIDS
protons nearly quantitatively to HzO. The result is the formation of H30+. Strong acids are said to be "leveled" to H30+ in aqueous solution. A weaker acid, such as HC2H302, donates protons to water t o only a limited extent since it is higher than the base H20. At the top of the acid column are species such as CHI, NH3, and OH-, which ordinarily are not classified as acids. They are so much above HzO that for practical purposes they do not donate protons to it. The fact that protons are most easily donated up the chart can also be used to predict the fate of bases in aqueous solution. Very strong bases, such as CH3-, NH2-, and 02-, readily accept a proton from HzO, an acid below them. In the process, these bases are leveled to OH-. A weak base, such as NH3, accepts protons from water only to slight extent since the acid H20 is above it. Finally, C1-and CIOa-are so weak that for practical purposes they are not bases a t all in water. Figure 2 summarizes these principles. Labels classify chart reaions as strong. moderate. weak.. verv" weak. and negligibik. Arrows showfavored directions of reaction. Thus, single-direction arrows a t the tor, and bottom remind us that string acids and bases react with the solvent irreversibly. Bidirectional arrows indicate that the species establish a more or less balanced equilibrium together. The relative lengths of the arrows have significance. T o illustrate, if a moderate acid (HSOa-) and its very weak conjugate base (S042-) are combined in equimolar amounts the net reaction will be deprotonation of the acid (see Fig. 3). A horizontal line bisecting the chart marks the point where pK. = pKb. This line is a convenient reference, since an acid and base lying on it are equally strong. Finally, Figure 2 shows the "equilibrium box9'for water. All species within the box equilibrate appreciably with their conjugates; water is a "differentiating" solvent for them.
BASES
ACIDS
BASES
Na(OH)*
NalOH)
H2O
OH-
HCI
CI-
PKa
H2O
OH-
Figure 2. Featwes of me conjugate acid-base chart, including the water equilibrium box and pK. = pK, line.
Figure 3. Acid-base chart for predicting If aqueous sail solutions are acidic or basic.
Volume 63
Number 11 November 1986
939
Predicting if a salt solution is acidic or basic due to hydrolysis is a simple matter with an acid-base chart. Often the task is no more difficult than characterizing the species present according to their classifications (see Figs. 2 and 3). A solution of ammonium chloride is acidic because NHaf is a weak acid and C1- is a negligible base. Sodium bisulfate is more complicated because its anion is amphoteric. Note that HSOa- is moderate as an acid but only neglibible as a base. Its predominant role is that of an acid; we can confidently predict that sodium bisulfate solutions are acidic. Ammonium bicarbonate requires a still more careful analysis since NHa+ is a weak acid and HC03- is a weak base. T o determine which of the two ions predominates we measure each one's distance from the pK. = pKh line. Notice that NHaf is farther from the line i n t h e weak acid direction than HC03is in the weak base direction. Ammonium bicarbonate is basic, due to hydrolysis on the anion. Calculating the pH of a salt solution is particularly simple if both ions lie within the equilibrium box. [H30+]is approximately independent of concentration for such solutions. The appropriate expression is (7)
where K, andKh are the dissociation constantsfor the cation and anion, respectively. Taking logarithms yields pH = PK"
P K ~ 7,0 +
2
From this equation, ammonium bicarbonate solutions have pH = 7.81. Metal Ions, Buffers, and pH Tltratlons Although commonly treated as a separate topic, metal ion hydrolysis is merely a special case of proton donation. The donor is a water molecule bound to the metal. The acid dissociation of hydrated calcium ion can be represented Ca(OHd2++ H20 a H30++ Cs(OH)+
OH- from a buret is added to an HL- solution, the proton transfer HL-
+ OH-
-
H20 + L2-
will go practically to completion (Ke4= 3.1 X lo8). Any acid weaker than HL- would be less suitable as a standard. A successful titration also requires a proper indicator. Figure 4 shows three candidates: alizarin yellow (HA), phenolphthalein (HPh), and crystalviolet (HVi). An indictor is merely an acid or base which is a different color than its conjugate. For our titration i t must be an acid which will react decisively with OH-, but onlvafter the HL- is totallvconsumed. HVi is unacceptable because of its strength; OH- would accept its protons in preference to those of HL- and a nremature color change would result. HA, on the other hand, is too weak to be acceptable; it would fail to give a sharp color change a t the equivalence point. The proper choice is HPh; its intermediate strength is an excellent compromise. I t will change from colorless to pink to signal the titration end. Organic Functional Groups and Nonaqueous Solvents Organic compounds frequently contain acidic or basic functional . Croups. . Fimre 5 lists a few representative compounds. For ~ X ~ ~ ~ I ~ , -represents C H ~ Naliphatic H ~ amines, which typically have pKh values in the 2.9-4.1 ranae. Knowing theapproximate-location of organic functional groups can be helpful when discussing molecules containing both an acidic and basic moiety. Consider glycine, the simplest amino acid. I t can undergo intramolecular autoprotolysis, NHKHCOOH
3
+NH3CH2COO-
The extent of reaction can be judged from Figure 5. Note that the aliphatic carboxvi lies consider" eroun - . (CH&OOH) . " ably below the aliphatic amine group ( c H ~ N H ~ )Proton .
BASES
for which pK. = 12.6. Calcium ion is therefore classified as a very weak arid?. It and several other metal ionsaredis~laved in Figure 3. As one might expect, proton donating abifity increases with the metal ion charge. The acid-base chart proves useful for designing buffers. Recall that the common buffer is simply a mixture of an acid and its coniueate base. Anv coniueate oair can serve as a buffer provided i t lies within thee&ilil;ruim box of water. The Henderson-Hasselbalch eauation eives the relations hi^ " between pH and concentration, pH = pK,
base] + log [conjugate [acid]
If equimolar concentrations of acid and conjugate base are present, the pH equals the pK, of the acid. The mechanism of buffering'can be explained with the chart. When a strong acid is added t o a buffer, for example, its protons are consumed by the buffer's conjugate base. The chart is also useful for designing titrations. Consider the standardization of aqueous NaOH by titration against a primary standard acid. The acid chosen must be strong enough to react nearly quantitatively with OH-. Potassium acid phthalate is a frequent choice. Figure 4 shows the position of acid phthalate ion (HL-) on the chart. Note that i t lies in the acid column well below OH- on the base side. As
The K, of a hydrated metal ion is not always reported as such in the literature. It can, however, be calculated from the formation constant of the hydroxo-metal complex. The required relationship is K. = K,. K,. For calcium ion Kt = 25. Hence, K. = 2.5 X 10-j3. 940
Journal of Chemical Education
Figure 4. Titration of aqueovs NaOH against acid pMhalate ion (HC-) de on me acid-base chart. Anows show tha'direction of proton tramifsr l titration and endpoint reactions. The lndicata of choice is phenolphthalein (HPh):others shown are alizarin yellow (HA) and crystal violet (HVi).
ACIDS
BASES
yellow) A-(red)
Ph-
HVi
(yellow)
(pink1
V i - (blue)
Figure 6. Equilibrium boxes fa various sdvents positioned on the acid-bare chart for water.
Figure 5. Organic compounds on the acid-base chart of water.
transfer occurs nearlv to cornoletion. and the elvcine mole. cule exists mostly in zwitterionic form. Autoprotolysis is not favored for all bifunctional molecules. In the case of maminophenol, the equilibrium NH2CsH40H a +NH3CsH40-
is shifted well to the left. For practical purposes the zwitterion is nonexistent. This conclusion can be obtained from Figure 5 by considering the relative positions of the aromatic hydroxyl and amine groups. Our discussion thus far has concerned only aqueous solutions. Acid-base reactions in nonaqueous solvents are less well understood, and attempts t o systematize them are fraught with complications. K, and Kb values change dramaticallv with solvent. Nevertheless. an imoortant eeneralization &ows us to extend the chart to so1;ents otLer than water: The relative strenpths of acids or bases are annroximately solvent independent (8).For many purposeske can assume the rankings on the chart do not change as we move from one solvent to another. An important characteristic of a solvent is its own proton donating and accepting ability. This determines the placement of its equilibrium box relative to solutes. Figure 6 locates the eauilibrium boxes for several common solvents on the acid-base chart for water (3,6,8).For simplicity this chart omits much detail. At the top and bottom of each box one should find written the appropriate conjugate pairs for the solvent. Consider liauid ammonia for examole. NHa+ and and NH3 establish the bottom of its box NH2- define the top. Note that acetic acid. which is weak in water, lies below the ammonia equilibrium box. I t acts as strong acid in this basic solvent. The elongated box for benzene results because this aprotic solvent displays no acid or base behavior. I t is unable to level even the strongest acids or bases.
while-^^^
Nonaqueous titrations can he readily understood through acid-base charts. Suppose we want to determine acetate ion by titration with perchloric acid. If water is the solvent, HCIO4 is leveled to H30+ (see Fig. 1).Consequently, in this solvent the titration involves the reaction of H30+ and CzH302-. Note that H30+ is below C2H302-, hut not overwhelmingly. The neutralization would not be quantitative a t the eauivalence ooint. T o achieve more c o m ~ l e t reaction e an arididsolvent mist he used. Aretic acid is &ite suitahle (9,. In this solvent oerchloric acid is leveled onh. to H-S ,-H ",O.-,'. The titration then involves the reaction O ~ " H ~ C ~ H and ~O~+ C~Hx02-.the stroneest acid and stroneest base which can e&t inacetir arid. A proper indicator for the titrntion can beselected from Fiaure 4. Of the three indicators liited, onlv crystal violet is sufficiently acidic. It is deprotonated in thk initial solution of acetate ion in acetic acid. As the titration proceeds, perchloric acid added first neutralizes the acetate ion; a t the equivalence point i t protonates the crystal violet turning i t from blue to yellow. The two reactions can he diagrammed on an appropriately constructed acid-base chart.3 Literature Clted I11 Guenther, W.B. "Chemicsl Equilibrium': Plenum:New York, 1975: pp 1-7. I21 Rametfe,R. W."ChemicalEquilibriumandAnalyais":Addiron-Wesley:Reading. MA.
..
1981: oo 257-312.
13 4
5
.
H u ~ P P I . .P~ ' ln~.rganxChemts~wPnns~plc.d 91ralrt
ir? and K e a n . \ l t ~ ' 3m . cd H X o c r B Rou hew Y l r k . l9K1.110329.144 t n I n a n d h ~ l c31 and ~ h y r : e r " wrb nl CRC P C ~ Wwr.c Wnlm H ~ s r h . P I I. V ' J ppD.lrh.'>l I L , h E 'St31111 r y C n n l t m l l hIet.1 Ion ( ' o m p l e t ~ ~Sp.#nl '. N . n i'h. ~ ' h ~ ~ , ~ I W~ pp~ +:1s ~ ~ ~ t ~ .
rhcm,mj
P,C~.
.
.
(6) Bell, R. P. "The Profon in Chemistry", 2nd ed.: Cormll Univenity: Ifhaea, NY, 1973:
ppS6-92.
171 Butler, J. N. "IonicRluilibrium A Mathematical Approaeh",Addiaon-Wesley: Reading. M A , 1861: pp 112-168. I81 Bell. R. P. "Acids and Bases Their Quantitative Behavior"; Methuen: London, 1869: PP 26-39. I81 Latimer. G.W., Jr. J. Chcm. Educ. 1366.43.215.
Cautlon: Solutions of perchloric' acid in organic solvents are potentially explosive, particularly if heated. Follow published procedures rigorously for this titration. Volume 63
Number 11 November 1986
941
~
~
~
d
