A Continuous Variation Study of Heats of Neutralization Dennis W. Mahoney, J o y c e A. Sweeney, and Derek A. Davenport Purdue University, West Lafayette, IN 47907 Richard W. Ramette Carleton College, Northfield. MN 55057 Neutralization of an aqueous acid by a hase is rapid and exothermic, and measurement of the heat accompanying such neutralizations is often the first thermochemical experiment performed by the beginning student. The usual procedure is to mix equal volumes of 1M solutions of acid and hase in some suitable calorimeter and to measure the rise in temperature, AT. Providing the solutions have been allowed to achieve room temperature overnight and handling is kept to a minimum surprisingly accurate values for the heat of neutralization of a strong acid by a strong hase can he ohtained even when using graduated cylinders and expanded polystyrene cups Ht(aaI
+ OH-(aa)
-
H90(1), AH = -13.6 f 0.2keal
Since the hterature value is known to all the students beforehand, reported accuracy may occasionally he higher than warranted and once the measurement has been made there is virtually nothing further to ponder or to discuss. A better approach is to have the students study heats of neutralization of a 1 M solution of an unknown acid by 1 M solutions of a strong base such as sodium hydroxide using the method of continuous variations. By using volume ratios 90110, 80120, 70130, etc., in the manner made pedagogically familiar by the Chemical Bond Approach (11,values for A T such as those shown in Figure 1 are readily obtained. Each student (or pair of students) obtains nine data sets for a given unknown acid. All data are then collected, tabulated and processed. In our case a simple average was used hut more sophisticated data treatment is obviously possible, even deI
Figure 1 . acids.
I
A continuous variation study of the heats of neutralization of various
sirable. Each student then plots all the averaged class data and is asked to interpret the results both qualitatively and quantitatively. The values of AT for strong haselstrong acid interactions are as might he expected. The plots are linear, they maximize a t a 111 volume ratio, and they yield values for the heats of neutralization of hydrochloric, hydrohromic and nitric acids very close to literature values. The acetic acid plot is also linear, it maximizes a t a 111 ratio and yields a heat of neutralization not much less than that for a strong acid, a fact which should at first puzzle the better student. After all acetic acid is only slightly ionized and the overall reaction is principally HCzHxOdaq)
HCnHiOdaq)
730
Journal of Chemical Education
CzHqOz-(ad+ HzOil)
-
Ht(aq)
+ CzHDdaq)
arbitrary, but they will enable others to compare their results more readily with ours. Furthermore the 68/32 and 71/29 ratios ohtained from the intersection of these lines do not imply that the neutralization ratios are other than 211 and 311, respectively. For sulfuric acid, positive deviations begin a t about the 50150 volume ratio, hut the maximum AT of 10.5"C does occur a t a 211 volume ratio. In the case of phosphoric acid, however, the maximum A T of 9.1°C does not occur a t a 311
I
A continuous variation study of Me NaOHIH2S04 reaction.
-
Clearly the heat of ionization of acetic acid must he very small for thecalculated heat of neutralization to be sosimilar to that of a strong acid. Accurate measurement gives a value of about 0.1 kcallmol a t infinite dilution (2). The results for the neutralization of sulfuric acid and phosphoric acid are superficially somewhat unexpected. More detailed graphs are shown in Figures 2 and 3 where the averaged class data is supplemented and the recalculated 100year-old data of Julius Thomsen is added. There is something very pleasing in the fact that several hundred average-butaveraged freshmen armed with expanded polystyrene cups can collectiuely harmonize with the master calorimetrist himself (3).It will be seen that the extreme base1acid volume ratios give experimental AT'S which are very close to linear, hut in the intermediate region considerable deviations from
80
Figure 2 .
+ OH-(aq)
This may he written as the sum of two steps:
--.
_'
4,o
0
I
V NAOH*lBL2
Figure 4.
Computer calculated values for a Continuous variation study of Me NaOH/H2S04 reaction.
Figure 5. Computer calculated values tor a continuous variation study of the NaOH/H3P04 reaction.
volume ratio, and there is very considerable negative deviation from linearity. The values of the heats of neutralization calculated from the student data are listed in the table where they are compared with those of Thomsen whose experimental conditions are quite comparable to ours. The agreement confirms that there is not merelv safetv but even nrecision in numbers. How can we account analitativelv. even auantitativelv. for the experimental results? It is important io rernemheithat the familiar analvsis of continuous variation data introduced
Heats of Reaction of Variws Acids with Sodium Hydroxide in Aqueous
acid were infinitely strong di- and tri-protic acids or-if the enthalpies of ionization of successive steps were, like that of acetic acid, close to zero then we might expect linear behavior with maxima a t the expected 211 and 311 ratios. Most students realize that the first of these assumptions is untrue and reference to tables of thermodynamic data (5) reveal the following standard heats of formation HSo~-(aq)-212.08 kcallmol S042-(aq) -217.32 kcallmol
HaPOn(aq) -307.92 HzPO4-(aq) -309.82 HP0h2-(aq)-308.83 Pod3-(aq) -306.3
kcallmol kcal/mol keallmol kcallmol
Clearly the second assumption is not true either. However, these data can readily he used to understand the qualitative nature of the experimental results; more importantly they allow theoretical values to he calculated. Several years ago, one of us (RWR) developed a computer program called TICURVE which serves to calculate the concentration of all ionic species during the titration of polyprotic acids by base making allowance for dilution and for the effect of changing ionic strength on activity coefficients ( 6 ) .An initial sample of 100 mL of 1M acid is assumed and the total enthalpy change as 1M NaOH is progressively added is calculated by introducing the standard enthalpies of formation of the various ionic species into a suitably weighted equation q =
ZAHp[ni(mixture)- ni (initial solutions)]
The results are converted to the constant variation format by scaling to a constant volume of 100 mL, and the computer plots are reproduced as Figures 4 and 5. The x-axes are reversed from those in Figure 2 and 3 while the y-axes are in units of calories per 100 mL of combined solutions. The clustering of calculated values around the equivalence points betrays the purpose of the original TICURVE program which used evenly spaced pH intervals. The correspondence between experimental and calculated
Solution a AcidlBase System
+ + + +
HCI NaOH HNOp NaOH NaOH HBr NaOH HOAc H2S04+ NaOH 2 NaOH H,SO, H3P04 1 NaOH HlPOl 2 NaOH HIPOl 3 NaOH
+
+ + +
All data in kilocalories per mol of acid. Calculated using a constant assumed value af 0.98csllcmgdegar heat addiflve volumes of reaction mixture. ~ 97 and 99. ~homssn'rdata is tabulated sr calimoi ~homsen,o p c p.
capacmfor
values is very striking, indeed for phosphoric acid it is virtually perfect Calculated
A Tm at BaseIAcid
9.2' -70130
Found 9.1° 71129
For sulfuric acid, the theoretical values show a continuous curvature on the acid side while the experimental results, perhaps with a little coaxing from the mind's eye, would appear to he nearly linear until a 50150 haselacid ratio is reached. Once again the agreement between experiment and theory is remarkable Calculated
A Twc at BaseIAcid
10.6' 211
The heats of neutralization of many other soluble acids remain to be studied bv the method of continuous variations. One would he surprised if there were no surprises. A mimeographed experimental write-up is available from the auLiterature Cited (1) '"Chemical System.(( M c C m HiU,Nev Ynrk. 1964.ThcmimeographedTeschemOuide fu the CBA labocatorymanual "Investigating Chemical Systems" remains amine of useful infomation. (2) Mortlmer, C. T.. "Reaction Heats and Bond Stnngthg." A d d i s o n ~ W d q :Reading, 1982. n ifX -.
(3) Thomsen. Julius."Themochemistcy: Longmans-Green. London, 1908, pp. 97-99. ( I ) la) Job, M. P., Ann. Chim., (101 9, 113 (1828).(b) Job, M. P., Ann Chim.,[ i l l 6.97
,.""",.
,>oae,
( 5 ) Selected Values of Chemical Themdynamic Propertios. Ci& SW. US. Government Printing Office. Washington, 1952, passim. (6) Ramette, R. W.."Chemical Equilibrium and Analyak:Addwn-Wesley, Reading, MA,
1981, p. 329.
Volume 58 Number 9
September 1981
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