J.C.S. Faraday I, 1980,76,2362-2373Thermodynamic Study of Disorder in Lithium BromideMonohydrateBY PAUL R. CLAYTON, ANTHONY G. DUNN, SUSAN HOLT? AND LIONEL A. K.STAVELEY *Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QRReceived 10th December, 1979The following quantities have been measured: (1) the heat capacity (C,) of anhydrous lithium bromidefrom 8 to 402 K, (2) C, of lithium bromide monohydrate from 17 to 405 K, (3) the integral heats ofsolution of these two salts in water at 298.15 K, (4) the water vapour dissociation pressure in theequilibrium between the two salts and water vapour from 371 to 423 K. The entropy S(ca1) of the a-formof the monohydrate at 298.15 K (the stable modification at this temperature) as derived from the heatcapacity measurements is 112.45 J K - ' mol- '.This is virtually identical with the value of112.47 J K- mol-' for S(eq), the entropy evaluated from the thermodynamics of the above equilibrium.The estimated uncertainty of the difference between S(ca1) and S(eq) is f 1.5 J K-' mol-'. The cr-formtherefore reaches a completely ordered condition at 0 K, or at least only retains frozen-in disorder to aminor extent.At 307.0 K the a-form transforms into a 0-modification. From previous structural and n.m.r. work ithad been concluded that in this form the water molecules are disordered among twelve possible orienta-tions per molecule and the lithium ions positionally disordered among the face-centred sites of the cubicunit cell. However, the entropy gain at the a - f p transition is only 6.87 J K-' mol-', Z R ln2.3.Thisfact, together with the conclusion that the cr-form is uniquely ordered at 0 K, implies that the 0-form (atleast just above the transition) is not nearly such a highly disordered structure as the previous studieshad suggested.Lithium bromide monohydrate exists in two forms. The low-temperature a-formtransforms into the high-temperature P-modification at 307 K. The p-form is ofparticular interest from the point of view of disorder, since it is believed to combinepositional disorder of the lithium ions with orientational disorder of the watermolecules. It has a perovskite-like shown in fig. l(b),with a = 4.207 A.The lithium ions are randomly disposed among the centres of the faces of the cubicunit cells, the probability of any one such site being occupied by a lithium ion beingone third.The water molecule at the centre of a cell might be expected to direct itstwo 0-H bonds at two of the surrounding bromide ions. This would give themolecule twelve possible distinguishable orientations. It appears from an n.m.r.study of the P-phase that the water molecule is undergoing rapid reorientationabout its twofold axis.2The a-form [fig. l(a)f is orthorhombic and has a unit cell approximately doublethe size of that of the p-form, with a = 7.974, h = 4.054 and c = 4.016 A. An n.m.r.investigation of the a-form showed that the water molecules are not undergoingreorientation,2 but this does not necessarily mean that they have adopted amutually ordered arrangement.Chihara et aL3 carried out X-ray, n.m.r.and dielectric absorption studies on therelated compound LiI - H20, the n.m.r. study being particularly thorough. At roomt nee CASSELL.236P. R . CLAYTON, A . G . DUNN, s. HOLT, L. A . K . STAVELEY 2363FIG. 1.-The structures of (a) the low-temperature, a-form and (b) the high-temperature, P-form oflithium bromide monohydrate.temperature this salt has the same structure as P-LiBr-H20, with the lithium ionsand water molecules disordered in the same way. When the iodide is cooled notransition is observed, at least down to 20 K. The Japanese workers concluded thatthe N lithium ions in a mole become randomly frozen in the 3 N sites available tothem and that the N water molecules are randomly frozen in the 12 N possibleorientations.Lithium chloride monohydrate exists at room temperature in the a-form.Thistransforms at 368 K to the p-form which, however, melts only 4 K above thetransition temperature.It seemed worthwhile to carry out a thermodynamic study of lithium bromidemonohydrate, with the following objectives: (1) to throw light on the a e P tran-sition; (2) to discover if the a-form undergoes a further transition on cooling; (3) tofind if the salt retains entropy, and therefore disorder, at OK. This last part of theinvestigation required an estimate to be made of the true (equilibrium) entropy,S(eq), of the salt at some particular temperature, e.g., 298.15 K, for comparison withthe calorimetric entropy, S(cal), at the same temperature. S(eq) was determined bythe well-known procedure for a salt hydrate of measuring the thermodynamicparameters for its dissociation, that is in this case for the reaction(1)This particular reaction is a favourable one for such a study in that any residualentropy in the hydrate might be expected to be a relatively large fraction of S(eq),as contrasted with, say, the case of Na,S04.10H20, for which S(eq) - S(cal),which is approximately Rln2, is only of the order of one per cent of S(eq).AHo forreaction (1) was determined by measuring the enthalpy of solution of the anhydroussalt and the monohydrate, while AGO was found by measuring the water vapourdissociation pressure p(H,O). The heat capacity C, of both salts was also deter-mined.Values of C, for the anhydrous bromide were published by Paukov et uL4while our own experiments were in progress.The bromide system was chosen for this study in preference to the chloridebecause of the very limited range of existence of the p-form of the latter. It waspreferred to the iodide partly because there are indications that on dehydration thelithium iodide monohydrate may first form a hemihydrate and not the anhydrousLiBr.H,O(c) = LiBr(c) + H,O(g)2364 DISORDER I N LITHIUM BROMIDE MONOHYDRATEsalt and partly because it was expected that p(H,O) for the iodide system at a giventemperature would be smaller than that for the other two. (Whichever halide sys-tem had been selected, the experiments would have to have been carried out withdue awareness of the very hygroscopic character of both the anhydrous salt and themonohydrate.) Even for the bromide system the measurements of p(H,O) had to bemade well above room temperature to have values large enough to be determinedwith the required precision and consequently the C , measurements on the hydrateand anhydrous salt had to be extended to cover the temperature range of thedetermination of p(H,O).EXPERIMENTALLithium bromide monohydrate was prepared from the carbonate and aqueous hydrobromicacid, using the purest reagents available.The neutral solution of the bromide was then evapor-ated at 383 K. The crystals were separated by rapid filtration at 343 K and dried at 378 K. Thebromide content, as determined gravifnetrically as silver bromide, was 76.07% (theory, 76.20%).To prepare the anhydrous bromide, the hydrate was first heated for several hours at 440 K andthen in a platinum boat at 570 K in a stream of a mixture of hydrogen bromide and hydrogen.Finally, the anhydrous salt was fused. Stringent precautions were taken in handling both saltsto avoid the access of moisture, but nevertheless we shall see that the anhydrous bromidesample on which the heat capacity measurements were made appeared to contain a smallamount of the monohydrate, while the monohydrate sample was probably contaminated with asmall amount of the dihydrate.C , for the monohydrate from 17 to 119 K and for the anhydrous salt from 9 to 99 K weremeasured in the smaller of the two calorimeters used by Waterfield and Staveley.’ At highertemperatures, C, was determined with a calorimeter similar to that described by Andrews etbut fitted with an internal reservoir for liquid nitrogen so that measurements could bemade down to 85 K.Determinations of the heat capacity of synthetic sapphire with the lattercalorimeter, which will be described elsewhere, had given results in agreement with the bestavailable data to ~0.1%. For both salts, agreement between the heat capacity results given bythe two calorimeters in the overlap region ( z 85 to z 120 K) was satisfactory, differencesbetween the two sets usually not exceeding 0.3%. However, on account of the greater precisionafforded by the higher-temperature calorimeter, the results obtained with it were used to givethe smoothed values from 90 K upwards recorded in tables 1 and 2.The enthalpies of solution were measured with an L.K.B.8700 isoperibol calorimeter. Thechief experimental difficulty encountered here was in loading the ampoules through the rathernarrow aperture under dry-box conditions and in closing and weighing the ampoules. A specialweighing-bottle was devised in which they could be transferred from the dry-box to the balancewithout risk of spillage. Sealing the ampoules was found to be most easily and effectivelyaccomplished by closing the aperture with “microwax”. Fortunately, the availability of highquality enthalpy of dilution data for aqueous solutions of lithium bromide7 made it unnecess-ary to try and ensure that the concentration of the solutions produced in an enthalpy ofsolution determination was always the same.The reliability of the calorimeter was checked bymeasuring the enthalpy of solution of tris(hydroxymethy1)aminomethane (TRIS or THAM),with the satisfactory results recorded below.The equilibrium water vapour dissociation pressure p(H,O) for reaction (I) was measured ona U-tube mercury manometer, the limbs of which were constructed of precision bore tubing, i.d.16 mm. Approximately 10 cm3 of a mixture of approximately equal bulks of the hydrate andanhydrous salt were contained in a glass bulb which was connected through a capillary tubewith one limb of the manometer. The other limb was evacuated and sealed. The sample vessel,connecting tube and manometer formed a compact, transportable all-glass unit which was atfirst connected to a vacuum line, but which was eventually sealed off after the sample had beenthoroughly outgassed by being repeatedly cycled through the sequence cooling, evacuation andwarming.All measurements of p(HzO) were made above room temperature with the samplevessel immersed in a Haake thermostat filled with ethylene glycol, the temperature of whicP . R. CLAYTON, A . G . DUNN, s. HOLT AND L . A . K . STAVELEY 2365could be controlled to kO.01 K, with the mercury manometer in a separate glass-frontedwater-filled thermostat at 323.35 K and with the connecting capillary tube electrically heated toavoid any possible risk of condensation of water vapour.RESULTSHEAT CAPACITY MEASUREMENTSThe experimental C, values for the anhydrous salt and for the monohydrate aregiven in the Appendix.Smoothed values at regular temperature intervals and thevalues of derived thermodynamic functions are presented in tables 1 and 2. NoTABLE 1 .-MOLAR THERMODYNAMIC PROPERTIES OF ANHYDROUS LITHIUM BROMIDEW" - G)/ [-(Go - f G ) / yT/K CJJ K-' mol-' So/J K-' mol-' J mol- l J K-' mol-1020304050607080901001101201301401501601701801902002102202302402502602 70280290298.153003 203403603 804000.342.787.5512.5517.2521.6525.5528.83 1.4833.9135.9937.7739.3240.6041.5542.6143.5944.4245.1345.7646.3146.8247.3147.7648.2148.6349.0449.4549.8649.9850.1650.795 1.305 1.7352.1852.790.110.922.945.799.0912.6316.2619.9023.4526.8930.2233.3836.5439.4842.3145.0347.6450.1652.5854.9 157.1659.3361.4263.4465.4067.3069.1470.9472.6874.0674.3777.6680.7383.6786.4889.180.8513.465.0165.2314.2508.7744.710161318164519942363274831473558397944 1048505 308575262136678714976248 104858890779569100051047010 56511 57512 5951362514665157150.020.250.771.652.814.155.627.208.8110.4512.113.715.417.018.620.1521.723.224.6526.1527.5529.030.3531.6533.034.2535.536.7537.938.9539.1541.543.745.847.949.2366 DISORDER IN LITHIUM BROMIDE MONOHYDRATETABLE MON MOLAR THERMODYNAMIC PROPERTIES OF LITHIUM BROMIDE MONOHYDRATE, LiBr * H 2 0(H" - fG)/ [-(Go - fG)/TI/J K-' mol- T/K C,/J K-' mol-' Sc/J K-' rnol-' J mol-'1020304050607080901001101201301401501601701801902002102202302402 50260270280290298.153003 20"340"360"380"400"(0.53)4.2810.5517.1723.5529.5634.9539.7543.6547.4951.0154.2657.3060.1662.9065.5768 .OO70.3272.4874.5576.5778.5380.4282.2283.9185.5087.0188.5390.179 1.7392.1398.10101.17104.53-108.551 13.66(0.18)1.424.318.2512.7517.5822.5427.5232.4337.2341.9246.5050.9555.3259.5663.7167.7571.7175.5779.348 3.0386.6490.1793.6397.02100.34103.50106.79109.93112.45113.02126.06132.1 1137.99143.75149.45(1.3)21.495.0233.7437.5703.010261399181622722764329138484436505 156936361705377678 502925810035108301 164012 47013 32014 18015 0601595516695168652088522880249352706529 290(0.05)0.351.142.414.005.867.8810.0512.2514.516.819.0521.3523.6525.928.1530.3532.5534.736.8538.9541.0543.145.1547.1549.151.053.054.956.4556.860.864.868.7572.5576.25transition or anomaly was expected to be exhibited by the anhydrous salt, but infact a small peak was observed in the heat capacity-temperature curve with itsmaximum at 307 K.Since this is the temperature of the a -+ fi transition in themonohydrate, there seemed little doubt that the sample contained a small propor-tion of this, possibly formed by adventitious contamination with water vapourduring the filling and closing of the sample vessel of the calorimeter. The enthalpygain at this small apparent thermal anomaly was 4.0 J(mo1 LiBr)- ', which from ourmeasured value of AH for the a + p transition in the monohydrate corresponds toa hydrate content in the calorimeter sample of 0.19mol%. All the heat capacityvalues for LiBr recorded in this paper have, therefore, been corrected for thisimpurity. Below 200 K this correction was <0.1% and above this temperature thP. R . CLAYTON, A.G. DUNN, s. HOLT AND L. A . K . STAVELEY 2367correction never exceeded 0.2%. Our C , results for LiBr are in good agreement withthose of Paukov et aL4 There are no systematic differences between the two setsand the average numerical difference is ~ 0 . 2 % . Our estimate of the calorimetricentropy at 298.15 K is 74.06 J K-l mol-'? while that obtained by Paukov et al. is74.0 0.1 J K-l mold'.The monohydrate underwent the expected transition a little above room tem-perature. Although there was some pre-transition increase in C,. the calorimetricbehaviour was consistent with most of the transformation being first-order. Ourestimate of the transition temperature is 307.0 & 0.1 K. The only published valueappears to be that of 306.1 K given by Kessis.' In addition to this transition, thereappeared to be a small anomaly giving a maximum in the heat capacity at z 315 Kwith an enthalpy increase of 74 J mol-'.If this is regarded as a genuine minortransition in the monohydrate, the entropy contribution is only 0.24 J K-l mol-I, aquantity too small seriously to influence the qualitative conclusions we shall laterreach. However, the careful study of the phase diagram by Kessis showed that at315.9 K the dihydrate breaks down into a saturated solution and the monohydrateand we believe that the anomaly we observed at 315 K was due to contamination ofour sample with dihydrate, Using a combination of thermodynamic data availablein the literature and our own results, we estimated that the dihydrate content was0.585 mol%.No heat capacity measurements on the dihydrate have yet been made,but an adequate estimate of the C, difference between the monohydrate and dihy-drate can be made by comparison of results for other hydrate systems. We find thatthe correction to the observed C, values of the monohydrate on our estimate of thedihydrate content amounts to a reduction of 0.25% and we have therefore correctedour heat capacity values for the monohydrate by this amount. We may remark herethat our analysis of the thermodynamics will be carried out with 298.15 K as thereference temperature. Between this temperature and a higher temperature T theheat capacity of the solid phases involved occurs in two terms of opposite sign, oneof the form (l/T)JC,dT, the others S(C,/T)dT.The degree of mutual cancellationhere is such that uncertainty in the heat capacity of the solid phases considerablygreater than ~ 0 . 2 5 % would have a quite negligible effect on the final relevantentropy estimate.Three determinations were made of the enthalpy increase at the ct-+ p transitionin the monohydrate, which gave 2112, 2118 and 2098 J mol-I, the mean being2109 J mol-'. On the assumption that the transition takes place wholly isother-mally at 307.0 K, we obtain 6.87 J K-' mol-' (sRln2.3) for the entropy of tran-sition, ASf.ENTHALPY OF SOLUTION MEASUREMENTSIn the check experiments with THAM, z 0.60 g of this substance were dissolvedat 298.15 K in 100 cm3 of 0.100 mol dm-3 aqueous hydrochloric acid.The valuesobtained were - 29.789, - 29.794 and - 29.810 kJ mol- I, the mean of - 29.798being 0.15% larger, numerically, than that of - 29.752 kJ mol interpolated from theresults of Hill, Ojelund and Wadso,8 (see also Gunn" and Kilday and Prosen'").The results of the experiments with anhydrous lithium bromide and the mono-hydrate are recorded in table 3. Corrections to infinite dilution were made using theenthalpies of dilution given by Lange and S~hwartz.~ For the anhydrous bromide,the mean enthalpy increase when a mole of the salt is dissolved at 298.15 K to givean infinitely dilute solution is -48.81 f 0.17 kJ mol-l, in excellent agreement withthe value of Lange and Schwartz of -48.82 & 0.27 kK mol- For the solution o2368 DISORDER I N LITHIUM BROMIDE MONOHYDRATETABLE 3.-EXPERIMENTAL VALUES OF THE ENTHALPY OF SOLUTION, AH(soln), OF LiBr ANDLiBr - H 2 0 IN WATER AT 298.15 K AND OF THE CORRESPONDING ESTIMATES FOR INFINITE DILUTION,AH(w H20)mol solute/ AH(soln)/ AH(@JJy)/100 mol H20 kJ mol- l kJ mol-0.2050.15750.05950.05470.04670.1230.1210.1 150.1140.1 130.0287-48.362-48.394- 48.176- 48.945- 48.566meanLiBr - H 2 0- 22.222- 22.5 19- 22.485- 22.587-22.163- 22.433mean-48.855-48.825- 48.423-49.177-48.780- 48.8 1- 22.594- 22.892- 22.845- 22.940- 22.5 16- 22.592- 22.73“4 to 6 g of salt per 500ml of water” at 290K, Slonim and Huttig’l foundAH = -48.16 kJ mol-l, corresponding to -48.62 kJ mol- at infinite dilution.For lithium bromide monohydrate, our mean value for the enthalpy of solution atinfinite dilution is -22.73 & 0.16 kJ mol-’.The result of Slonim and Hiittig at290 K, corrected to infinite dilution, is -22.57 kJ mol-l.WATER VAPOUR PRESSURE MEASUREMENTS FOR THE SYSTEMLIB r - H 0 (c)/LiB r (c)Two separate runs were carried out, the results of which are recorded in table 4.Measurements of p ( H 2 0 ) made by Slonim and Huttig at lower temperatures arereasonably consistent with our values, but are ~ 5 ~ 1 0 % lower than would beexpected by extrapolation of our results. On the other hand, two values of p(H20)reported by Huttig and Reuscher’ for temperatures falling within the range of ourown measurements are z400/, greater than our estimates.DISCUSSIONWe recall that on structural and n.m.r.evidence it has been proposed that inD-LiBr.H,O and in the corresponding form of the iodide each water molecule hastwelve possible orientations, full and independent use of which would contribute aconfigurational term of Rln12 to the molar entropy of the salt. This should besupplemented by the positional disorder of the lithium ions. Since, however, theentropy lost on cooling at the P-+M. transition is only zRln2.3 and since thea-phase does not undergo any further transition, it is clearly worthwhile to see ifthis phase retains entropy at 0 K by comparing S(eq) with S(ca1) at some particulartemperature, for which 298.15 K was chosenP. R . CLAYTON, A. G. DUNN, s. HOLT AND L . A. K . STAVELEY 2369TABLE 4.-EXPERIMENTAL VALUES OF THE EQUILIBRIUM WATER VAPOUR PRESSURE, p(H,O), FORTHE REACTION L i B r .H , O ( c ) e LiBr(c) + H20(g) AND THE DERIVED VALUES OF AS" (298.15 K)FOR THIS REACTIONrun T/KAS"(298.15 K)/p(H20)/kN m-, J K-' mol-'11212211221211212121371.36378.1 1378.40383.15383.46388.34388.74393.12393.25398.35398.67403.19403.27408.27409.25413.08413.184 1 7 . 9 4418.11422.860.8281.2211.2351.6131.6412.1292.1792.7312.7503.5733.6354.5414.5505.7986.0617.2347.3019.0559.14911.299mean150.30150.33150.29150.33150.33150.31150.32150.301 50.30150.32150.33150.32150.3 1150.32150.30150.28150.31150.30150.3 1150.31150.31For the reaction (1) at some temperature T we haveAG; = AH: - TAS;.(2)We take one atmosphere (= 101 325 N m- 2, as the standard pressure.For AG; we haveAG; = -RTlnp(H,O). (3)The assumption that water vapour is an ideal gas, so that the measured pressurecan be used instead of the fugacity, does not introduce an error into the calculatedvalue of ASo (298.15 K) of ~0.004 J K-' mol-l.AH; and AS; are given by the following equations:r T rTAH; = AH"(298.15 K) + J C,(LiBr, c) dT + J ~ ~ ( ~ 2 0 9 8) d~298.1 5 298.15307.0 T298.15 307.0 -/ C,(a-LiBr*H,O)dT - AHt - f C,(P-LiBr - H20) dT (4)AS; = AS"(298.15 K) + IT [C,(LiBr, c)/T] dT +298.1 5307.0 T298.15 307.0 -1 [C,(a-LiBr - H20)/T] d T - ASt - f [C,(P-LiBr - H,O)/T] dT.(5)1-72370 DISORDER I N LITHIUM BROMIDE MONOHYDRATEIn eqn (4) and (5), AHt and ASl refer to the a + p transition.Accordingly, forAS"(298.15 K) for reaction (1) we haveTAS"(298.15 K) = R In p(H20) + AH"(298.15 K)/T +- 307.0 + J T C,(H20,g)dT - - J C,(a-LiBr * H20) d T- AHt/T - -- 1298.15 298.15C,(p-LiBr.H2O) dT307.0T[C,(LiBr, c)/T] d T -298.15~ 3 0 7 . 0+ J [C,(a-LiBr .H20)/T] d T + ASl298.1 5rT+ 1 [C,(P-LiBr * H,O)/T] d T307.0AH"(298.15 K) for reaction (1) is the sum of the enthalpies of the following reac-tions, all at 298.15 K:LiBr.H20(c) + coH20 = LiBr(coH20) + H20(1)LiBr(mH20) = LiBr(c) + coH20(1)H20(1) = H 2 0 (g, 1 atm, ideal).Taking the enthalpy of vaporization of water at 298.15 K as 44.016 kJ mol-','3 weobtain AH" (298.15 K) = 70.10 kJ mol? To evaluate the integrals in eqn (6) whichinvolve heat capacities, the experimental C, values for crystalline anhydrous lith-ium bromide and the monohydrate were fitted to polynomials.For water vapour inan ideal state, C, = 4R + C(vib), where C(vib) is the contribution from the internalvibrations. Using the data of Friedmann and Haar,14 C(vib) can be adequatelyrepresented over the relevant temperature range by the equationC(vib)/J K-' mol-' = -3.061 x lOP3T/K + 1.386 x lO-'(T/K)'.The partial cancellation in the evaluation of AS"(298.15 K) from eqn (6) of errorsin the C, values has already been mentioned. A similar effect reduces the conse-quences of an uncertainty in the enthalpy of transition AH,.An error of onepercent (21 Jmol-') in this would only bring about a difference of0.007 J K-' mol-' in ASo (298.15 K), depending on whether this last quantity wasevaluated by putting T = 370 K or T = 420 K.ASo (298.15 K) was evaluated at each of the temperatures at which p(H,O) forreaction (1) was measured, with the results shown in table 4. There is a satisfactoryconstancy in the values obtained, the mean being 150.31 J K- 'mol-'. Taking theentropy of a mole of ideal water vapour at one atmosphere and 298.15 K as188.72 J K-' mol-1,13 we obtain for the "true" entropy of the monohydrate, S(eq),S(eq) = S"(LiBr, 298.15 K) + S"(H,O, g, 1 atm, 298.15 K) - AS"(298.15 K)= 112.47 J K - ' mol-'P . R . CLAYTON, A. G . DUNN, s. HOLT AND L . A . K .STAVELEY 2371Hence, since S(ca1) = 112.45 J K-' mol-' (table 2), for the residual entropy of themonohydrate at 0 K we haveS(res) = S(eq) - S(ca1) = 0.02 J K-l mol-'.With regard to the uncertainty in S(res), the chief contribution to this most prob-ably originates in the enthalpy of solution measurements. A combined error ofk330 J mol-' in the two enthalpies of solution involved would lead to an error inS(eq) of 1.1 J K-' mol- '. Our estimate of the uncertainty in S(ca1) at 298.15 Kfor each of the two solids is +0.2%. All in all, we consider that a reasonable figurefor the overall uncertainty in S(res) is f 1.5 J K-' mol-'. We therefore concludethat the a-phase of LiBr. H 2 0 reaches a completely ordered condition at 0 K, or atleast, if there is any frozen-in disorder then this is only on a very minor scale.In cubic P-LiBr.H,O, the twelve possible orientations of a water molecule areequivalent, disregarding any influence of the position of the lithium ions. When thisphase transforms to the low-temperature orthorhombic form, some of the bromideions are brought nearer to a water molecule while others move further away, thuslifting the degeneracy of the twelve orientations.These, in fact, divide into threegroups, the four orientations within any one group being equivalent, but with oneof the three groups being energetically preferred to the other two. The volumechange at the transition is quite small, not exceeding one percent, and it mighttherefore be expected that the entropy change at the transition is essentially con-figurational.The experimental value of 6.87 J K- ' mol- ' is, however, appreciablyless than Rln12/4 = 9.13 J K- ' mol- '. Also, as we have seen, S(res) is probablyzero, or at least very much smaller than Rln4, = 11.53 J K- mol-', the valuewhich would correspond to each water molecule being randomly frozen-in amongfour equivalent orientations. It therefore appears that the P-phase of LiBr H,O, atleast just above the a + P transition, is disordered to a much smaller extent thanmight have been expected from the previous studies of this phase and of thecorresponding phase of LiI * H20.While the orientational disorder of the water molecules should make a muchlarger contribution to any configurational entropy than the positional disorder ofthe lithium ions among the possible face-centred lattice sites, the involvement of thelatter should not be overlooked.Chihara et aL3 concluded from their comprehen-sive study of the corresponding lithium iodide system that while the dynamics ofthe diffusion of the lithium ions and the reorientation of the water molecules in themonohydrate are interrelated, the static aspects of the two kinds of disorder areindependent. This can scarcely be literally the case. The average number of lithiumions to be found at the face-centres of any one unit cell is two. For a given positionof one of these ions, on energetic grounds the likeliest position for the other is onthe opposite face. So a strong tendency towards at least a local ordering of thecations might be anticipated.This in turn would be expected to favour particularorientations of the water molecules and it may be that this is why, in the P-phase,these molecules seem to be far from making full, independent use of all twelvedistinguishable orientations available to them. Be this as it may, it is clear thatfurther work on the monohydrates of the lithium halides is desirable. Neutrondiffraction studies on the deuterated forms carried down to low temperatures mightbe especially informative.We thank Mr. M. Gascoyne for carrying out the analysis of the lithium bromidemonohydrate2372 DISORDER IN LITHIUM BROMIDE MONOHYDRATE' J.-J. Kessis, Bull. SOC. chim. France, 1965, 32, 48.2E. Weiss, H. Hensel.and H. Kuhr, Chem.Ber., 1969, 102, 632.3H. Chihara, T. Kawakami and G. Soda, J. Magnetic Resonance 1969, 1, 75.41. E. Paukov, M. P. Anisimov and I. G. Luk'yanova, Russ. J. Phys. Chem., 1974, 48,946.'C. G. Waterfield and L. A. K. Staveley, Trans. Faraday SOC., 1967, 63,2349.6J. T. S. Andrews, P. A. Norton and E. F. Westrum Jr, J. Chem. Thermodynamics, 1978, 10, 1211.'E. Lange and E. Schwartz, Z. phys. Chem., 1928, 133, 129.a J. 0. Hill, G. Ojelund and I. Wadso, J. Chem. Thermodynamics, 1969,1, 11." S . R. Gunn, J. Chem. Thermodynamics, 1970,2, 535.'OM. V. Kilday and E. J. Prosen, NBS Report No. 10621, (National Bureau of Standards, Washington' C. Slonim and G. F. Huttig, Z. anorg. Chem., 1929, 181, 55."G. F. Huttig and F. Reuscher, Z. anorg. Chem., 1924, 137, 155.' International Council of Scientific Unions, Committee of Data for Science and Technology,14A. S. Friedmann and L. Haar, J. Chem. Phys., 1954, 22, 2051.D.C., 1971).CODATA Recommended Key Values for Thermodynamics, 1973, Bulletin 10.APPENDIXEXPERIMENTAL VALUES OF THE MOLAR HEAT CAPACITY, c,, OF ANHYDROUS LITHIUMBROMIDE, LiBr(All values below 81 K and those marked with an asterisk were obtained with the calorimeterdescribed by Waterfield and Sta~eley.~)T/K CP/J K-' mol-I T/K C,/J K-' mol-' T/K C,/J K - ' mol-'8.0510.8613.1815.0316.8518.862 1.2424.1 126.7729.6032.6835.8139.5944.4649.2152.6255.9261.1767.9578.9880.7883.5484.9385.7088.9189.3392.0395.090.2610.4580.6821.1151.6252.3553.324.795.9457.378.8810.9512.3614.6516.9118.6019.9822.1024.7528.8929.4029.6730.28*30.2731.183 1.26*32.0232.7698.0998.72101.04103.93106.2 1110.041 13.79117.50121.14124.46129.58134.60140.29146.65152.90159.06165.14171.16177.11183.02188.87194.69200.47206.19209.29216.72224.09231.3933.4833.46*34.1634.7735.2435.9936.7137.3537.9638.5139.2739.9340.6641.2741.8942.4043.1043.7644.2344.5845.1445.4445.8546.2046.1646.5747.0147.36238.63245.82253.23260.85268.44275.98283.39290.85293.48300.93306.38309.87316.40317.77324.63325.88335.29338.23344.88354.65364.37374.05383.70393.28402.8 147.7148.0648.3948.7248.9949.2249.4949.8849.5850.2052.88"51.34"50.8250.5850.865 1.265 1.9051.395 1.4051.6151.8652.0052.2052.5152.88" High values, attributed to presence of small amount of LiBr.H20 in sampleP .R . CLAYTON, A . G. DUNN, s. HOLT AND L . A . K . STAVELEY 2373EXPERIMENTAL VALUES OF THE MOLAR HEAT CAPACITY, c,, OF LITHIUMBROMIDE MONOHYDRATE, LiBr * HzO(All values below 88 K and those marked with an asterisk were obtained with the calorimeterdescribed by Waterfield and Staveley.')T/K C,/J K-' mol-' T/K C,/J K-' mol-' T/K C,/J K-' mol-'17.0119.1221.3223.2526.1129.9934.1434.9535.7937.5938.2439.4439.5239.9042.2244.3746.4448.6850.8 152.7755.0557.5059.5361.3563.5266.5670.0672.6374.5076.5478.4579.1280.0582.2282.4783.2584.8986.7987.0987.3088.3990.5491.9892.0392.6992.952.6253.7755.366.378.0010.5713.2113.8414.2915.5316.2016.7516.9217.0618.5619.9621.3322.6824.0525.1627.7528.2029.2530.523 1.9633.0234.9736.2037.2337.9538.9639.9639.4040.8741.3141.0641.8942.8042.7342.6643.0043.8844.51*44.41"44.91*44.60*93.0593.2193.4297.7497.9398.32100.34101.94102.75103.35106.02107.43107.63107.78108.16110.86111.9411 1.97112.301 12.80116.10116.36116.401 17.29119.48121.78127.05132.21138.31143.73148.90154.13159.19164.18164.64169.55174.39179.16183.87188.53193.13197.69202.20207.1 12 12.43217.6744.8945.12*45.0146.6646.57*47.02*47.51*48.2148.17*48.37*49.6649.99*50.30*50.13*50.53*51.315 1.66*5 1.47*51.83*51.80*53.57*53.0953.21*53.54*54.17*54.8456.4857.8659.5661.3362.7464.0865.3666.5966.7067.8968.9770.0771.1372.2373.1774.0775.0276.0677.1 178.08222.88223.62230.40237.1 1243.71250.23256.67263.07269.40275.67281.88287.95292.15294.05298.09300.13303.31306.22306.9 1307.01307.09307.17307.45308.37309.653 10.94312.21313.57315.053 16.47317.94319.4032 1 .OO327.34334.39341.39348.33355.1936 1.99368.74375.42382.56390.13397.59404.9579.0079.2580.478 1.6782.8083.8685.0185.9886.9887.9788.9789.8090.2990.9291.5892.0495.882581550198017901720695100.197.4398.37100.1"116.29"132.75"98.5698.2098.0498.2499.16100.35101.35102.75103.65104.5106.3107.7109.2111.9112.9115.15" High values, attributed to presence of small amount of LiBr.2H20.(PAPER 9/1962