I Effect of Ionic Strength on Equilibrium M. D. Seymour

and Quintus Fernando I constants University of Arizona

Tucson, Arizona 85721 I The use of a pre-programmed or programmable pocket calculator in the laboratory

In the measurement of the acid dissociation constant of a Let the initial concentrations of the weak acid and the weak acid, it is mandatory to include a rigorous treatment of strong base be represented by CA and CB moleh, respectively. the activity concept. Quite often this important aspect of The acid HA, is dissolved in uo ml of solution and the volume equilibrium theory is omitted from the laboratory work owing of NaOH added at any point in the titration is u ml. The molar to limitations in laboratory time and computational facilities concentrations of the species A- and HA in solution are given that are available to students in the laboratory. One method by of overcoming the difficulty caused by a limitation in the number of available laboratory hours was described in this [A-I = *+ [Hf] - [OH-]

(UO + u) (3)

Journal ( I ) more than a decade ago. The experiment involved the determination of the acid dissociation constant of brom- [HA] = I.,. A - "'B .I\ - [H+] + [OH-] (4) cresol green by a s~ectro~hotometric method. Each student . . made his measurementsat aspecified ionicstrengthand the collective data set ohtained hv the whole class was used to ascertain the effect of ionic stringth on the acid dissociation constant.

In the experiment that is described below, the concepts of activity and activity coefficient are emphasized in the manner discussed previously ( I ) . The difference, however, is that in a single three-hour laboratory period, each student can per- form the laboratory work and obtain his own dataset. If nec- essary, all calculations can be carried out in the laboratory; it is assumed of course that each student will have access to either a pre-programmed or programmable pocket calculator (2).

The phenomenal rate a t which inexpensive pre-pro- grammed or programmable pocket calculators are being manufactured has been discussed in a recent review in this Journal (2). I t is reasonable to expect that within the next few years this type of calculator will become commonplace and consequently it should be possible to upgrade the level of undergraduate instruction in many fields.

Theoretical Considerations In the course of the titration of a weak monoprotic acid HA,

with a strong base NaOH, the p H of the solution that is measured with a commercial pH meter equipped with glass- saturated calomel electrode pair, and suitably calibrated is given by

E represent* the potential difference in millivolts a t 25OC between the glass electrode and the saturated calomel elec- trode, E' is a constant, and IH+1 and .YH+ the molar concen-

,-" . -, Substitution of these values in the expression for K.' gives

K.' = [H+]UCB (UOCA - uCd

(5)

if i t is assumed that [H+] and [OH-] are negligibly small in eqns. (3) and (4). At the equivalence point u, ml of the strong base has been added and

Substitution for U ~ C A in eqn. (5) and rearrangement gives [H+]u = KO%, - K,'u (7)

A plot of [H+] u versus u (for values of u < u,) should give a straight line which has a slope of -K,' and which intersects the abscissa a t the point u = u,, prouided that all the as- surnotions stated above are ualid. Values of the molar con- centrations of Hi are obtained from the measured pH values. If the calibration of the DH meter is carried out in an appro- priate manner, the measired pH values are very close tothose given by

lO-'~Hh"~..na [H+] =

YHf (8)

The activity coefficient of the hydrogen ion, y ~ + , can be cal- culated at a known ionic strength I, from a suitable modifi- cation of the Debye-Hiickel relationship. For example, the Davies modification (eqn. (9) in which A, B, and C are con- stants) can be used up to an ionic strength of 1.0.

A P + CI -1% YH+ = (9)

A simpler form which can he used in this experiment up to an ionic strength of about 0.5 is

0.51'12 -log YH+ = m (10)

A T .

tration and activity coefficient, iespekively, of the hydrogen Equations (7). (81, and (9) or (10) can be used to calculate ion. E' is a constant if the potential of the saturated calomel K,,, the apparent dissociation constant of a weak acid, in a electrode and the liquid junction potential remain constant. solution in which the ionic strength is maintained constant If the behavior of the glass electrode is Nernstian and the throughout the course ofthe titration. ~h~ molar concentra- measurements are carried out a t 25'C. the quantity, 59.16 is tion oftbe hydrogen ion, [H+], at five or six points, before the a constant. equivalence point in the titrations, is calculated from eqns.

The acid dissociation wnstant of the weak acid HA, is given (8) ,d (9) (10). ~h~ apparent dissociation constant, K,,, by the expression is then obtained bv calculation of the s l o ~ e of the straight line

- [Ht1lA-I .YH+YA- = KalyH+yA. (2) given by eqn. (7) by means of a linear leak squares tecLique. a - TiT By employing a range of ionic strengths (from 0.01-0.50), the

The value of K.' changes with the ionic strength of the soh- manner in which K,' varies with the ionic strength can be tion and is a constant onlv if the activitv coefficients YH+ and investigated. YA- are constant. The activity coefficient, y ~ ~ , of theneutral An instructive experiment that can be carried out in a single species is asxumd to be nnity at the ionic strennhs employed three-hom laboratory period is the determination of the ac~d &d all the quantities in square brackets represent-molar dissociation constant of potassium acid phthalate a t various concentrations. ionic strengths. The compound is readily available in a very

Volume 54, Number 4, April 1977 1 225

pure form, it is water soluble, and the effect of varying the ionic strength on the value of K,' is much more pronounced than fora neutral monoproticacid, and the c o n c k a t i o n of the undissoriated species of phthalic acid is nealieihle in the p H range that is employed in this experiment. ireo over, the DK. of the compound is approximatelv 5.5, and as a conse- quence p H readings between 4.5 and fir5 are sufficient to es- tablish the slope of the straight line defined by eqn. (7). Also, in this pH range and at the concentration of potassium acid phthalate suggested below, the concentratims of H and OH- can be neglGted in eqns. (3) and (4). Owing to the water sol- ubility of the compound, solutions that are 10-2-10-W can be titrated and the validity of the results will not be affected by the small amount of carbon dioxide that is invariably present in the solution that is being titrated.

Laboratory Directions Sufficient quamitier of the following stork solutrona rhould he

prepared: a ~rnndard solution (-4.01 A l l of carl,cmate free NaOll. N.H.S. buffers at oH 4.0 and 7.0 for cal~hrntion of the DH meter. and a standard solutibn (4.001 M) of potassium acid phihalate.

'

Weigh out accurately 0.20 g of potassium acid phthalate, dissolve it in water, and make up to the mark in a 1-1 volumetric flask. The resulting solution is approximately 0.001 M. Pipet six 100-ml aliquots into six titration vessels. To each of these vessels add calculated amounts of solid NaCl to maintain a constant ionic strength between 0.01 and 0.50.

Calibrate the DH meter with the two N.B.S. buffers. Titrate each ~ ~~ ~~ ~

of the six solutions with the standard NoOH sulution and meacure rhepH after theaddition deauh increment of NnOH Iris nerrssary toadd only fivr or aix incrrmcnt~dNaOH toeach solution murder to obtain pH values between 4.5 and 6.5.

Construct a table similar to Table 1, for each titration, with the following column headings: u ml NaOH added; (pH)measured; [H+]calculated from eqn. (8); [Ht]u.

A plot of [H+]u against u (eqn. (7)) gives a straight line of slope K.'. The best value of the apparent acid dissociation constant K,' can be obtained a t each ionic strength by carrying out a linear least squares analysis of each data set (Table I), With the aid of a pre-programmed pocket calculator. A typical set of results is shown in the figure, in which the chanee in slope with ionic streneth is ouite evident.

~ q k o n (i2) which shows tbeUrelatio&hip between K, and K,', the second dissociation constant of ohthalic acid. is analogous tueqn. (2) . Equation (131 ~huws ;he.et'fect of ionic strennh on DK.' if it is assumed that theactivitv coefficients of the hydrogen ion and the acid phthalate anion are ap- proximately equal, and that the activity coefficient of the phthalate ion, P2-, is given by the simplified Debye-Hiickel relationship

-log yp*- = 0 . 5 ~ ~ 1 ' / ~ 1CI'" (11)

where z is the charge on the phthalate ion and I the ionic strength of the solution.

K, = K,'yp2. = K,'10-2""/(1+""' (12) 21'"

PK.' = PK. - (13)

The validity of eqn. (13) can be tested from the experimental data obtained. A a lot of oK,' versus I W i l + 114 should eive a straight line wiih a slopeof -2 (~able .2) . If n&essary,;he Davies modification of the Dehye-Hiickel relationship (eqn. (9)) can be used to calculate the activity coefficients of the ions H+. HP-. and P2- to obtain a better fit of the exoerimental data. '

The above method for the determination of the effect of ionic strength on the apparent acid dissociation constant of a weak acid, is based on the method that was originally de- scribed by Gunnar Gran for locating the equivalence point in a potentinmetric titration (3. 4). Recentlv, much has been &itten about the errors that are associated k t h this method and the experimental conditions that must be adhered to for

Titratim of 100 ml of 9.90 X lo-' Mmssivn acid pMhalate wilh 1.03 X 10 MNaOH at me fallowirg ionic &en&: (a) 0.013. (b10.030. (c) 0.086. (dl 0.132. (e) 0.224, (f) 0.558. The tibation curve (pH vmw ml NaOH) was obtained at an ionic sbeogth of 0.132.

Table 1. Titration Data for the Calculation of the Acid Dissociation Constant of Potassium Acid Phthalate a t an

IonieStrength of 0.132 ffipure, linedl.

V m l NaOH P H ~ ~ ~ ~ ~ ~ ~ ~ I H + I IH'I V

Table 2. Effect of Ionic Strength on the Acid Dmocistion Constant of Potassum Acid Phthalate.

The pKy'-mlues are calculated from t h e slopes of t h e s t ra ight liner in t he figure.

(5.6). Hence. if the K.' values of other acids such as NHA+ or HSO~- are dkermineh, the experimental conditions must be carefullv selected and rieorous eauations used for the Gran - plots.

This method has several advantaees over the ~otentiometric methods that are usually employed for the determination of the dissociation constant of a weak acid. For examnle. the Ko' . . - value can be calculated by merely measuring the p H of a so- lution of a weak acid or a weak base of known concentration. This is poor experimental design if the K.' value is based on a single measurement of pH. Moreover, the buffer capacity of the solution, especially that of a weak base, may he so small that traces of carbon dioxide from the atmosphere will com- pletely vitiate the results. Titration of the soiution of a weak acid or base to the halt-equivalence point results in a solution that has a better buffer capacity but the method suffers from several drawbacks: the K.' value is based on a single p H measurement. the exact eouivalence m i n t must be nre-de- ~~ ~~ .~ ~ - ~~ -

termined for ;he titration ;o be stopded at the half-equiva- lence point and finally, the pH at the half-equivalence point is not equal to thepK,' if the p H measurement ismadein the vicinitv 012. (for the HSOA- ion) or 10 (for the NHt7 ion). The

maximum~accuracy in the location of the equivalence point

226 I Journal of Chemical Education

potentiometric titration ensures that the calchated

K.' value is hased on many experimental points. The con- ventional method of calculation is hased on as many p H measurements as ~ossihle in the buffer rekon, and on a knowledge of the exact concentrations CA and-CBO~ the weak acid and the strone hase. res~ectivelv. In the method that is . . proposed above the only quantities that must he determined accuratelv are the hvdroaen ion concentration, IH+l, and u, . - the corresponding volume of hase added hefori'the.equiva- lence point (eqn. ( I ) ) . It is not necessary to know accurately either CA or Ce, the initial concentration of the weak acid or of the NaOH, provided that the [H+] values are obtained within the pH range specified above for the KHP titration so that [H+] and [OH-] are negligibly small in eqns. (3) and (4). Another important advantage is that an increase in the ionic strength from 0.01-0.50 changes the pK.' value significantly (fig.) and that allnecessary calculations can he carried out in a few minutes with the aid of a pre-programmed pocket cal- culator.

A linear least squares analysis of each data set for eqn. (7) gives not only the slope, K,', hut also the intercept on the y-axis, Kalu,, from which u,, the volume at the equivalence point could be calculated. If the same amount of KHP is used in each titration, u, should he a constant. The precision with which the buret is read and the DH measurements are made ~~~-~~ ~~~~ ~

will he reflected in the precision'of the calculated value of u,. This method of locating theeauivalence point is the familiar - -

Gran's method; the of intersectionof the best straight line given by eqn. (7) and the X-axis O, = 0) is the equivalence point, which is usually obtained graphically (3 ,4) .

Literature Cited (1) Ramette, R. W., J. CHEM. EOUC.,4O, 252, (1963). 121 Karp.S.. J. CHEM. EDUC.. 52. A346 (1975). 13) Cran.G..Aeto Chem Scond.. 4.559. (1950). (4) Cran,G..Anolyst. 77,661, (1952). (5) Hansson. I.. and Jagner. D., A n d Chim. Aclo.. 65.363. 119731 16) Burden. S. L..and Euler, D. E., A n d CAem., 47,793, (1975).

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