The Entropy of Dissolution of Urea Miles Pickering Princeton University, Princeton, NJ 08544 The existence of endothermic, entropy-driven chemical reactions is of great theoretical importance, since this fact shows that free energy, not just enthalpy, is the driving force for chemicalchange. Yet there are few illustrative lab experiments. The ideal svstem would he a s i m.~ l .e .s~ontaneous . reaction where the e"qui1ihrium lies to the right, and yet there is a clear heat ahsorotion. These conditions are met by the dissolution of urea in water. If the reaction is conceptualized as the AH for the reaction will be the heat of solution, a large positive number (3.3 kcallmol). T h e AGO can he obtained by considering a saturated solution in which the solid is in equilibrium with the solution. For this condition, the equilibrium constant K will he
and this will simplify, given the usual convention of unit activity for the solid, to
K = [urea(aq)] Then AGO for the reaction will he AGO = -RTlnK where R is the gas constant and T the absolute temperature. From this argument it is easy to determine AGO once the concentration is known. If we make the approximation that AH = AH", then ASo for the dissolution of urea will be given AGO = AH" - T A P or, rearranging ASo =
AHo - AG" T
The measurement of AH is easy and routine in freshman chemistry ( I ) . To he absolutely correct, we should consider the difference between A H and AH" (the latter for the solution refers to a l-m standard state) and also the heat of dilution. However, for mixtures as dilute as those used here, the effect is negligible. The measurement of urea concentration can he done by using the sensitive colorimetric method used in clinical medicine for "blood urea nitroeen" (BUN). This assav is so sensitive that the saturated urea solutionhas to he diluted about 15.000- or 20.000-fold to eive suitable concentrations. This experiment thus combines colorimetric techniques, thermochemical techniques, and some volumetric work, as well as providing an actual measurement of entropy. It is conceptually simpler than experiments using the Gihhs Helmholtz relationship (2, 3), or cell potentials (4-7) and allows the measurement of entropy to be an experiment for an advanced freshmen lab. Experimental The heat of reaction of urea and water can be done hv the wellkno~vnroffee-cuprolorimeter method \ / I . Ahout 1 toSg oiurra will grvea measurablr drop in temprr~turrifdissolved in 5U ml.of 1 1 0 \V'r haw dpproximnted the urea-water specific heat at 1.00 ml dei: K.
Thermodynamics of Urea Dlssolutlon Average Student Value
AG(KcalImo1) AH(Kcal/mol) AS(cal/moledeg)
-1.38 i 0.15"
4.20 i 1.73b 18.4 -L. 6.6'
Fmm Keller. R. Basic Tables in Chemlsm: MuGrsw-Hill: Standard deviation.
Accepted Value' -1.64 3.3 16.6
New Y a k , 7967.
The students then prepare a saturated solution of urea in premixed henzoic acid solution (0.1%by wt). The benzoic acid acts as a preservative to retard bacterial attack. About 25 mL of water should be mixed with 35 g of urea. Then the mixture is allowed to stand at least overnight. The mixture is then gravity filtered, and a known aliquot of the saturated solution is weighed on an snalytical balance to determine the density. The saturated solution is then diluted 1:15,000 or 1:20,000 using volumetric ware, and a 0.4-mL sample is then used in the BUN assay following manufacturer's directions. This assay uses two premeasured solutions "BUN acid" and "BUN color reagent", whieh are supplied by Sigma Chemical Co. and mixed by the student on the day of the experiment. Then 4.6 mL of the mixture is dispensed into Spectronic 20 test tubes using a buret. Students oreoare . . a blank with distilled water. a known witha t~rras~l~~rion~fkn~\~nr~,ncentratiun lull-200mg 1.1.nnd theiamplr at' dilutcd unknown. There thrw tubrs arc then immerred in h i l i n g water f i x 10 mi", tmlcd fi,r 2-3 min.and them shsorl,anrc at 520 nm measured. The major experimental difficulty is contamination of reagents. Even traces of urea can he troublesome. Apparatus must he scrupulously clean, and students must be reminded not to put anything (even "clean" droppers) into reagent bottles, whieh should have dropper taps. The BUNacidand BUN color salutiansare poisonous and corrosive, and manufacturers' directions must be followed. The color intensity is linear with concentration and appears to follow Beer's law, at least within the uncertainty of the Spectronic 20. Hence one point using a known is sufficient to construct a calibration curve if the blank can he used to zero the Spectranic 20. The color intensity slowly fades, and the measurements must he done within afew minutes of the final cooling. The intensity of color varies between batches of reagent so calibration with a known is a nncessi'tv. .~ .....~ . "
Reagent solutions can be purchased from Sigma Chemicals and are not expensive. Urea is cheap, not very toxic (8) and biadegradable. A student procedure is available (9). Discussion The experiment was run by the 30 students in Princeton's advanced general chemistry lab. The values reported are somewhat more scattered than expected and are summarized in the table. There is reasonable agreement, except that the average of AH is on the high side in student work. The signs of AH are always positive since it is obvious that the solution gets colder. (The small molecular weight of urea contributes to making this effect striking). Since urea is also obviously very soluble, the free energy is negative in accord with the requirements of spontaneity. Thus, while the actual values of ASo will scatter from student to student, the entronv will alwavs have a oositive sien. Thus this e x ~ e r i m e nis t siperior to "more typical attempts to subtract' AGO from AH". where often small uncertainties in either AHo or AGO are magnified greatly in the differences between the quantities. Volume 64
Number 8
August 1987
723
The high entropy of dissolution is reasonable since the urea has a verv strone hvdroeen-bonded structure in the solid phase. Thkse hy&ogen bonds interfere with free rotation of amine erouus. - Dissolvin~the urea allows m a w more degrees of freedom to become active and thus produces greater disorder. If the instructor wishes, students can easily compute a theoretical value for the entropy of dissolution by considering the process to happen in two steps,
Since the observed entropy is 16 calldegmol, even the entroincrease uuon fusion is not the whole stow, and there must he mass.ive strurture breaking during t h i dissolution Dnrress itself. I t is also true that the aqueous urea solution is far from ideal. There is significant and complicated molecular association of a kind not easily described by simple mathemntical models. It is sometimer possihle to lead students to see that Kopp's rule will not apply to urea bv talking about how urea and aretone are isoelectronir but strikingly different in properties.
The first step is a melting, and the students can be instructed to usr I
