The Determination of "Apparent" pK& An Experiment for Liberal Arts or Science Students John J. Cawley Villanova University, Villanova, PA 19085 This experiment is adapted from one that is presented by Helmkamp and Johnson ( I ) . It avoids any weighings. By judicious choice of stronger, more soluble acids, such as C12CHC02H,it avoids the use of the co-solvent dimethyl sulfoxide. This use of stronger acids also gives the science student an opportunity for some critical thinking concerning the Henderson-Hasselbach equation. pK,=pH+log- [HA] [A-I Experimental Reagents acetic acid
C2H402
0.1 f 0.002 M
sodium hydroxide
NaOH
0.1 7 f 0.002 M
acid unknowns
0K.k < 2.4
0.1 f 0.002 M
Unknowns CIGCOzH
trichloroacelic acid
F3CCOzH
trifluoroacetic acid
(C0zH)z
oxalic acid
CbCHCOzH
dichloroacetic acid
FzCHCOzH
difluoroacetic acid
cis-H@CCH=CHCOnH rnaleic acid HzNCHZCOZH
glycine
Typical Procedure To a dry 150-mL beaker add approximately 60 mL of 0.100 M acetic acid. Rinse a buret with this solution, and then overfiil it. Bring the meniscus down to 0.00 mL. FinaUy, run out as near to 50.00 mL as practical into another dry 150-mL beaker. Accurately record the volume of acid, for example, 49.95 mL. Place the magnetic stirring bar into this solution. Place the beaker on the magnetic stirrer, and place the pH electrode into the solution (carefully!). Record the initial pH. Using the 0.167 M sodium hydroxide solution fill a second buret using the procedure of the preceding paragraph. Begin to titrate with the basic solutionin 1.0-mLintervals. The Plots As you work, plot pH versus volume of sodium hydroxide added. When the slope of your curve starts to increase, switch to adding the basic solution in 0.5-mL intervals. Continue with 0.5-mL intervals until the pH increases sharply. Then add the basic solution dropwise until the slope effectively is infinity. That is the end point. From your plot find the pK,, which is the pH corresponding to one-half volume of titrant (Vm). Record the pK. for
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Journal of Chemical Education
acetic acid and the precise volume Vm for this 0.100 M acid. You may want to repeat this procedure as a test of reproducibility. The Unknown Next obtain an approximately 60-mL sample of 0.100 M unknown acid from your instructor or teaching assistant. Record the unknown code. Substituting your unknown for the acetic acid, repeat the previous procedure, up to the point of titrating with sodium hydroxide. Then deliver the precise volume Vm of sodium hydroxide solution into the acid in a single interval. Measure the pH, which should be the pK. of your unknown. Fill in all the relevant data on your unknown sheet, and turn it in to your teaching assistant before leaving the lab. Results and Discussion For Nonscience Students For the liberal arts student the focus is on the titration of acetic acid and its pK.. The unknown is just an opportunity for them to see how close they can come to the pH and pK.. For these students it is permissible, in this context, to choose 0.100 M HCl as one of the unknowns. See how close these students come to the correct pH of 1.42 and thus "apparent" pK, of 1.42. At our institution, this narrow focus is dictated by the time constraints: 110 min per week for one semester. For Science Students For the science student the discussion might start with the idea oftitrating 0.100 M HC1, arriving at an "apparent" pK, of 1.42. Ofcourse they will know this is incorrect. They could be led to the conclusion that the pK, of a fully ionized acid is minus infinity. The discussion should then center on the question, Wow strong can these weak acids be before this titration technique will fail?" Due to the choice of fairly strong acids, the science students can be told that they have a "correct" result for the pH at one-half titration, for example, 1.74 for the unknown, and that the unknown is dichloroacetic acid, C12CHC02H.They will then look up the pK. only to find its value to be 1.29. Next the student should be reminded of the concepts of K, and K, and the oRen forgotten idea that the sum of the molarities of all the monocations in solution is exactly equal to that of all the monoanions in solution. The low concentration of hydroxide can be ignored in this discussion. The student will then be able to derive an equation valid for the one-half titration point as expressed in eq 1 (see below). [RC027+ [RC02HI= [RCO2HlT= [total add1
Applying this equation to the acetic acid experiment, some students will see immediately that the [H+12in the numerator and the [Ht1 in the denominator may be ignored, leading to
but at one-half titration. For those who do not see this, plugging in all the numbers will still lead to the same arithmetic result therefore which is the pH a t one-half titration. Therefore this equation is valid for the acid end of the pK, scale. Areas of the pH Scale
because
If some of the science students are interested in analytical chemistry they may wonder about the other end of the pH scale. Using the identical ideas that generated eq 1,I express the same relationships below. In this derivation, [H'I may be ignored but not [OH-] when dealing with the idea that the sum of the molarities of the monocations must be equal to that of the monoanions. For a hypothetical acid of pK. = 12.00, the student will discover that the [HI] at one-half titration is 1.44 x 10-12, leading to a pH and an "apparent" pK, of 11.84. Therefore there is a problem with this experimental technique on the high as well as the low end of the pH scale. Reworking eq 3, we get
because [RC02HIT- [Na'l = [Na?
= INs*lIIf12 -K.W
(4)
[Ne'llKI + K,
it follows that [IF]'
+ [[N~'I + K,)[HT - K,[Na'l= 0
(1)
Solving for [H*] the student will discover that it is the exact value of the one-half titration point when the correct K. value is used. For the given case, ma+]= 0.03845 and
% = 0.0514 which yields [H'l = 0.01828 This corresponds to a pH and "apparent" pK. of 1.74. At this point the students might be encouraged to rework eq 1to discover the correct pK, from the "apparent" pK. to prepare them for when they will face this situation in the ~ "~this l vnew eauation to the future. Students should also a .. acetic acid experiment to see that there is no contradiction. They will fmd an equation of the following form.
When the students substitute the [H+la t one-half titration they will calculate K, = 5.14 x lo-'
When students substitute the [H+la t one-half titration, they will calculate K.
=
1x
and thus, Therefore this equation may be used a t the high end of the pH scale to calculate pK. from an "apparent" pK.. Again, to check the validity of this equation on the basic end of the pH scale, the student might want to apply the equation to a more normal case, for example, pK. = 9.00. Some students will see immediately that the Kw[Ht1term in the numerator and the K, term in the denominator may be ignored, leading to
pK, = the pH at one-half titration
The rest will plug in all the numbers and come to the same result. At this point some of the science students will realize that something interesting occurs in the pH range 4-10. If they are probing (e.g., a t pH 5 ) to discover when eq 2 reduces to
and thus, pK, = 1.29
Therefore this equation may be used a t the low end of the pH scale to calculate pK, from an "apparent" pK..
they will see that they can just as well use eq 4 with the same resuit. Likewise, if they are probing (e.g., a t pH 9) to see when eq 4 reduces to K. = [H+],they can just as well use eq 2 with the same result. Volume 70 Number 7 July 1993
597
Conclusions
For the liberal arts student, the objective of the experimerit is camfig out the titration and determining the =ap-
parent" pK.. For the science student the objective goes beyond that. It challenges the students to do some critical about the of the technique using pH at one-half titration over the whole pH scale. Additionally it
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Journal of Chemical Education
gives them the opportunity to see that they can obtain the PK. from the "apparent" pK, with a few equations that they can reasonably be expected to derive. Literature Clted I. Helmkalmkap, C.K.;Johnsan,dr, X W . S e k e t e d E ~ r i m n t s i nD~gonleCherniAry,3rd ed.; heman: N ~ YW~ & S ~ D~ran~rani~~, 1983;Q 169.
