Richard W. Ramene
Corleton College Northfield, Minnesota
I
(
1
The Dissociation Quotient of Bromcresol Green A class study of ionic strength effects
A
few years ago I proposed an experiment on the solubility of calcium sulfate as a function of ionic strength (1).one major purpose of which was to allow the student to use his own analytical data to learn something about activity coefficients. It still seems naive to try to teach equilibrium theory without a good treatment of the activity concept, and the present paper deals with a more sophisticated experiment which has involved the cooperation of the entire class. The purposes of this study include the use of spectrophotometry, a thorough application of various acid-base equilibrium principles, and a realistic look at the behavior of activity coefficients. Bromcresol green has been chosen as the acid-base system for the study for three reasons: it behaves as a simple monoprotic acid, apparently with no complications such as low solubility, diierization, decomposition; the two members of the conjwate pair show greatly differing absorption spectra and even a simple filter photometer is excellent for the measurements; the dissociation quotient is in the same range as that of acetic acid, thus making the easy-to-handle acetate-acetic acid buffer system eminently suited for pH control. Methyl red could also serve well for this experiment, and indeed h a been proposed for student work in determining dissociation quotients ( 2 ) , but it has the disadvantage of being a diprotic acid with fairly close dissociation constants (3).
If we regard the acid form of bromcresol green as HByellow
+ H 2 0 =blue B- + H 8 0 i
simply HB-, then and in terms of activities:
If the symbol Q is used to represent the dissociation quotient in terms of molarities at equilibrium, then K
=
Q.f or pQ = p K + l o g f
(2)
where f is really a ratio of activity coefficients. However, at low ionic strength according to the DebyeHuckel theory the activity coefficients of H30+ and HB- should approximately cancel because both are singly-charged ions, although there would be some difference because of ionic size considerations. Then, iff is taken to represent only the activity coefficient of the doubly-charged B= ion the Debye-Huckel equation would predict (taking 7 as the diameter of the ion (4)) :
Therefore, it would be expected that a plot of experimental values of pQ versus corresponding values of the 252
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Journal of Chemical
Educofion
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2.3p'"), hereafter referred to as quantity p'/'/(l for simplicity, should be linear with a slope of -2.04 and an extrapolated intercept equal to the thermodynamic value of t,he dissociation constant, pK. As the ionic strength increases equation (3) becomes less and less accurate, and usually gives log f values which are increasingly too negative. Therefore equation (3) is often supplemented with an empirical term, Cp, where the value of C depends on the system under study. I n this experiment the instructor may choose to deal with this constant by asking the students to attempt its evaluation after the class results are in.
p'
+
Laboroto~yDirections. Into s loam1 volumetric flask pipet 10 ml of 3 X lo-* M hromcresol green solution and 5 ml of 0.200 M sodium acetate solution. Use s. siphon huret t o add the quantity of 1.00 M potassium chloride which is assigned on an individual basis, such that the maximum ionic strength to he used is 0.50. (Of course, the instructor can set any arhitrmy maximum depending on how much interest he wishes to attach to deviations from the Debye-Hiickel predictions). Dilute to the mark with distilled water, mix, and pour "quantitatively" into a 250-ml beaker. Clean the volumetric flask, pipet 25 ml of 1.00 M acetic acid, and again use the siphon huret t o add not only the assigned amount of potassium chloride hut also s n additional amount t o make the ionic strength of the resulting solution tho same as that of the sodium acetate solution. Dilute, and mix. Use the filter photometer to determine the absorption spectrum of the sodium acetate solution of hromcresol green, taking care t o mske a precise measurement a t the wsvclength where there is maximum absorption. Pour the sample hack into the beaker, being careful not to law any because the volumes must he known for the calculations. Add precisely 2.00 ml (from pipet or huret) of the acetic acid solution. Mix well with a stirring rod, and measure the absorbance a t the wavelength of maximum absorption of the blue form of the dye. Repent this procedure for additional 2.00-ml increments of acetic acid, and (for the record) determine the absorption spectrum in the case of the buffer which is equimolar in acetate and acetic acid. After five such measurements have been made, add 1.0 ml of 3 M hydrochloric acid and again measure the entire spectrum. Correct all absorbance readings for the effectof dilution by multiplying each observed value by the factor (100 v)/100, where v is the volume of acetic acid (and hydrochloric acid) added. Plot the three absorption spectra on s single sheet of graph paper. Calculrute the five values of the bromcresol meen dissociation nnnt,ient,. heine careful t o use the Droner valueif the acetic acid
+
buffer pH, and corrected absorhsnce. Calculate the values of r and r' for your solutions, enter the values along with your average pQ in the table on the bulletin board, and also place a map tack representing your results on the large graph of pQ versus r'. After most of the class results me posted, choose about ten values which seem to be renresentative of the set., soresd over the entire range of r', and mske s graph for your notebook. Evaluate the thermodynamic value, pK, by drawing a line having the theoretical Debye-Hiickel slope through the points of lower ionic strength. I n your notebook comment on the agreement, or lack thereof, between the class results and the Debye-Hiickel predictions. By considering a few of the points deviating a t higher ionic strength, ~~
~~~
~
.
estimate a value for the Hiickel extension constant, C. Suggest ways in which the experiment might be improved.
Calculation of p H Values
From the definition of Q, it is necessary to know the [HzO+]of each buffer solution used in the absorbance measurements. Although it would be possible to use a pH meter for an approximate determination, in this experiment it is more accurate to calculate the pH because the dissociation quotient of acetic acid is accurately known (5) in a variety of electrolyte solutions. For convenience, Table 1 lists the values for a Table 1.
Dissociation Quotient of Acetic Acid in KC1 at 25OC
connected with straight line segments to emphasize that the filter instrument does not allow the precise shape of the curves to be determined. Table 2 shows the calculated results obtained in this case. It can be judged from the precision of agreement among the Q values that the simple photometer is quite adequate for the task. Figure 2 shows a few typical results from the range of ionic strength used. It is seen that the line with the theoretical slope fits nicely the points a t lower ionic strength (a p' value of 0.215 corresponds to an ionic strength of 0.18), in spite of the Table 2. Student Results for Bromcrerol Green Study (Data of Oren Anderson) (of HOAcl
A
buffer aH
Q.1W
0 2.00 4.00
0721 0.465 0.342 0.2i2 0.225 0.191 0.002
basic 4.983 4.682 4.506 4.381 4.284 acidic
1.88 1.86 1.86 1.85 1.84
v
6.00
series of potassium chloride solutions a t 25'C. The instructor should provide a carefully-made graph of these values, so that each student can read off the appropriate value for his particular ionic strength. Two graphs are best: one for the entire range, and one with an expanded scale for the lower ionic strength range only. In this way the student can obtain a reliable value for. ,, Q Since the quantities of sodium acetate and acetic acid have all been measured precisely, a reliable set of values for [H30+]is easily calculated:
8.00 10.00
+ HC1
wQ
... 4:7k 4.730 4.730 4.732 4.736 average Pp: 4.731
where the acetic acid : acetate ratio is expressed in terms of millimoles. Interpretation of the Spectrophotometric Data
It has already been mentioned that the absorbance values should be corrected for the effect of dilution. In the initial sodium acetate solution the pH is high enough (students should prove this) that the bromcresol green is virtually entirely in the blue form, and the absorbance is symholized by AB. At the end of the experiment, when the hydrochloric acid has been added, the pH is low enough (prove this also) to insure "complete" conversion to the yellow form, and the final (corrected) absorbance is AHB. The five intermediate solutions are a series of acetate-acetic acid buffers, the pH values such that a mixture of the blue and yellow forms are present, and if the absorbance is designated as A for a given solution, then it can be shown that the ratio of blue to yellow form in that buffer is given by:
Figure 1 . Absorption spectra of bromsrerol .green as determined with o filter photometer. Upper curve; sodium ocetote solution. Middle curve8 equimolar metic acid, sodium acetate buffer. Lower curve: offer addition of rliaht excess of hvdrochloric acid. Abrorbonses corrected for diiu-
Thus, the results of equations (4) and (5) can be combined for the calculation of the bromcresol green dissociation quotient for each of the five solutions. Typical Student Results
Figure 1 shows the absorption spectra of bromcresol green as obtained by a student in the course of this experiment, using a Leitz-Ruoy photometer. The points corresponding to the 10 filter choices have been
Figure 2. Typical slorr rervlts in the determination of pK for bromcresol green. See text for definition of #'.
Volume 40, Number 5, May 1963
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fact that no effort v a s made to control temperature effects. The extrapolated intercept of pK = 4.89 is in excellent agreement with the literature values for bromcresol green (0-8). In conclusion, this experiment has worked exceptionally well in student hands, and since the actual laboratory work may he done rather quickly, it is not necessary to have a large number of filter photometers available. By the time the student has carried out the calculations, he has learned not only some spectrophotomet,ric principles, but also has had a pretty thorough workout on a variety of acid-base calculations. The cooperation of the class leads to a better understanding Of the effects of ionic and the value and limitations of the Debye-Hiickel equation.
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Journal o f Chemical Education
Literature Cited
R . W.,THrsJOURNA4 33, ti 35,514 (195s). (3) RAMETTE, R. W., DRATZ, E. A,, AND I~EI.I.Y, P. W., J. Phy.5. Chem., 66,527 (1962). (4) KIELLAND, J., J . Am. Chem. Sac., 59,1675 (lP37). (5) HARNED, H. S., AND OWEN,B. B., "Tho Phy8ie;tl Chemistry of Electrolytic Solutions," 3rd ed., Reinhold Publishing Corp., iiew York, 1958, p. 676. The original rofercnco ia HARNED, H. S., AND HICKEY, F. C., J . d m . C h m . SOC., 59, 1284 (1937); 59,2303 (1937). ( 6 ) INDELLI, A., AND SAGLIE~TO, G., ram. ~ n r n d a ySoc., 58, 1033 (1962). (7) GUOOENHEIM, E. A., AND SCHINDLER, T. D., J. Phys. Chem., 38, 543 (1934). (8) CHASE,E. F., AND I
