Thermodynamics of Hydrobromic Acid in Dioxan+ Water Mixtures from Electromotive Force Measurements at Different Temperatures BY BIJOY K. DAS AND PRA~ANNA K. DAS* Chemistry Department, Ravenshaw College, Cuttack-753003, India Received 31st December, 1976 Electromotive force measurements of the cell Pt, Hz/HBr(m), dioxan(X) HzO( Y)/A@r/Ag have been made at 15, 25, 35 and 45°C for solvent compositions X = 10, 20, 30, 40, 60 %(w/w) of dioxan. These have been used to evaluate the standard potentials of the cell, the mean activity coefficient of HBr (molal scale) and the thermodynamic functions (mole-fraction scale) for the transfer of HBr from water to the respective dioxan+water media. The AG; (free energy of transfer of the acid from water to various solvents) values along with those for hydrochloric acid, are briefly discussed in relation to ion solvation. E.m.f.measurements of cells without liquid junction potentials have shed con- siderable light on the thermodynamic behaviour of hydrochloric acid in various aquo-organic solvents and in a few non-aqueous solvents. Very little is known about the effect of the changes in solvent composition on the thermodynamic behaviour of other halogen acids. The effect on such properties of hydrobromic acid in 10, 20, 30, 40 and 60 %(w/w) dioxan + water mixtures at 15, 25, 35 and 45°C are reported in this paper from the e.m.f. measurements of cell (I) : Pt, H,(g)/HBr(m) dioxan(X), H20( Y)/AgBr/Ag. (1) The standard potential of Ag-AgBr electrode has been determined by Feakins and Turner at 25°C in 20 and 45 %(w/w) dioxan +water mixtures using Owen’s borate- buffered cell, and by Mussini et aL2 in 5, 10, 15, 20, 45, 70 and 82 %(w/w) dioxan+ water mixtures in the temperature range 20-35°C using cell (I).The values of the standard potential of the Ag-AgBr electrode at 25°C in 20 and 45 %(w/w) mixtures reported by the former workers are 0.059 91 and 0.031 83 V and by the latter group are 0.060 15 and 0.034 47 V, respectively. This prompted us to reinvestigate cell (I). The solvent systems chosen were of 10, 20, 30, 40 and 60 %(w/w) dioxan+water mixtures, to correspond with our previous investigation on the Ag-AgC1 electrode using the same solvent compositions. EXPERIMENTAL Dioxan was of B.D.H. AnalaR quality and was purified as described earlier.4 E. Merck G.R.hydrobromic acid was diluted with triply distilled water to the approximate composition of the constant boiling mixture and was distilled. The middle fraction of the constant boiling mixture was collected. The bromide content was analysed gravimetrically and this was used as a stock solution. Experimental solutions of the desired concentrations were prepared by diluting known amounts of solution with known amounts of solvent. During handling of the solutions, exposure to air was avoided as far as practicable. The acid concentrations of the solutions were occasionally checked after the experiments. No significant change was detected. 22B. K. DAS AND P. K. DAS 23 The Ag-AgBr electrodes were of the thermal type described by Ives and Janz and these electrodes, in the solvent mixtures studied, were found to be stable for more than a month.Electrodes having a bias potential within +O.O5mV were used. The other experimental procedures were similar to those adopted with the Ag-AgC1 electrode described previ~usly.~ The cell potentials were measured with an accuracy of kO.05 mV by a Leeds Northrup K-2 potentiometer in conjugation with a matching galvanometer. The potentiometer was standardised against a certified Weston standard cell maintained at constant temperature. The cells attained equilibrium after 4 h in all the solvent mixtures studied at all temperatures except at 45"C, where equilibrium was reached in 33 h. TABLE 1 .-PARAMETERS NECESSARY FOR THE EVALUATION OF E'' OF EQN (3) IN D1OXAN-k WATER MIXTURES AT DIFFERENT TEhfPERATURES I0 % dioxan (Go = 19.57) 15°C 25°C 35°C DS 73.21 69.68 66.18 P s l m Hg 14.70 27.60 48.60 Almol-3 kg* 0.596 0.609 0.627 polkg m-3 1.0119 1.0058 1 .W17 l3lm-l mol-* kg* 0.3463 0.3489 0.3522 30 % dioxan (Go = 23.66) Dl 54.75 51.89 49.1 8 P s l m Hg 19.30 35.20 62.20 polkg m-3 1.0294 1.0217 1.0159 Almol-3 kg* 0.921 0.961 0.978 lo-'' l3lm-l mol-* kg* 0.4004 0.4062 0.4085 40 % dioxan (Go = 26.42) DS 45.42 42.97 40.65 P s l m Hg 21.90 38.80 68.40 polkg m-3 1.0362 1.0289 1.0217 A/mol-3 kg* 1.219 1.252 1.302 10-lo l3lm-l mol-3 kg* 0.4396 0.4436 0.4493 60 % dioxan (Go = 34.47) 0 s 27.37 25.85 24.41 P s l m Hg 25.80 44.20 77.60 polkg m-3 1.0441 1.03 62 1.0285 B/m-l mol-3.kgt 0.5663 0.5733 0.5799 Almol-3 kg3 2.605 2.695 2.799 45°C 63.11 82.00 0.9994 0.641 0.3549 46.62 102.20 1.0119 1.010 0.4130 38.46 118.80 1.0168 1.348 0.4546 23.05 124.20 1.0218 2.907 0.5874 Duplicate experiments were performed simultaneously in each case and the duplicates generally agreed within 40.5 mV.Vapour pressures of the solvent mixtures were obtained from the data of Hovorka, Schaefer and Dreisbach,6 interpolating or extrapolating where necessary. The e.m.f. readings were corrected to one atmosphere pressure using these vapour pressure data. The densities of the solvent mixtures were determined pyknometric- ally and the dielectric constants of the solvents were calculated using the equation proposed by Akerlof and Short.' The densities (po), dielectric constant (Ds), vapour pressure (ps) and the Debye-Huckel parameters (molar) for the solvent mixtures studied are reported in table 1.The Debye-Huckel parameters were calculated theoretically. For a 20 % dioxan+ water mixture the values of parameters were taken from Harned's work.*24 THERMODYNAMICS OF HBr IN DIOXAN + WATER TABLE 2.-E.M.F. OF CELL (I) (E/v) CORRECTED TO 1 atm. PRESSURE IN VARIOUS DIOXANf WATER MD(TURES AT DIFFERENT TEMPERATURES 1000 mHBr 2.99 3.94 4.99 6.00 7.01 7.98 8.97 10.01 19.61 29.77 40.77 49.92 60.09 69.87 79.62 90.00 100.41 2.89 3.79 4.99 6.04 6.94 8.01 9.06 10.20 19.91 29.86 40.15 50.01 59.97 69.89 80.19 90.27 99.92 3.30 3.94 4.92 5.95 7.03 8.13 9.01 9.91 20.22 29.10 40.09 15OC 25°C 35°C 10 % dioxan 0.3617 0.3479 0.3373 0.3286 0.3213 0.3149 0.3094 0.3044 0.271 8 0.2531 0.2396 0.2293 0.2209 0.2137 0.2075 0.2021 0.1971 0.3575 0.3438 0.3332 0.3246 0.3173 0.31 10 0.3055 0.3006 0.2685 0.2499 0.2368 0.2266 0.21 84 0.21 14 0.2053 0.2000 0.1953 0.3508 0.3373 0.3268 0.3183 0.3111 0.3050 0.2995 0.2947 0.2630 0.2447 0.23 17 0.3675 0.3533 0.3422 0.3333 0.3257 0.3191 0.3134 0.3082 0.2746 0.2550 0.2412 0.2309 0.2219 0.2144 0.2080 0.2023 0.1969 20 % dioxaii 0.3630 0.3489 0.3380 0.3290 0.3215 0.3151 0.3093 0.3044 0.271 1 0.2519 0.2382 0.2278 0.21 92 0.2120 0.2058 0.2002 0.1953 30 % d' ioxan 0.3539 0.3399 0.3291 0.3204 0.3130 0.3066 0.3010 0.2960 0.2634 0.2445 0.23 1 1 0.3708 0.3561 0.3447 0.3354 0.3276 0.3209 0.3149 0.3095 0.2750 0.2549 0.2406 0.2295 0.2205 0.2129 0.2062 0.2004 0.1950 0.3666 0.3520 0.3407 0.3315 0.3238 0.3171 0.3 112 0.3060 0.271 8 0.2520 0.2379 0.2271 0.21 83 0.2108 0.2044 0.1987 0.1936 0.3574 0.3429 0.3318 0.3227 0.3 151 0.3085 0.3027 0.2976 0.2640 0.2446 0.2308 450c 0.3737 0.3585 0.3468 0.3372 0.3292 0.3222 0.31 60 0.3106 0.2748 0.2540 0.2394 0.2280 0.21 87 0.2109 0.2041 0.1981 0.1927 0.3681 0.3530 0.3413 0.3319 0.3239 0.3170 0.31 10 0.3055 0.2703 0.2500 0.2355 0.2243 0.2152 0.2075 0.2008 0.1949 0.1896 0.3583 0.3435 0.3320 0.3227 0.3148 0.3080 0.3020 0.2968 0.2622 0.2423 0.2281B .K . DAS AND P. K . DAS 25 1000 mEiBr 50.02 59.02 70.06 80.12 89.92 100.12 3.07 3.99 5.01 5.97 6.99 8.10 9.00 9.98 19.92 29.51 40.01 50.10 59.89 70.01 76.27 88.98 101.01 2.96 4.02 4.95 6.06 7.0 1 7.93 9.00 9.98 20.04 28.99 40.30 49.19 58.96 70.03 79.82 90.30 100.23 15°C 25°C 35OC 30 % dioxan (contd.) 0.2217 0.2207 0.2202 0.2136 0.2123 0.2117 0.2067 0.2052 0.2043 0.2008 0.1990 0.1980 0.1956 0.1931 0.1924 0.1908 0.1881 0.1874 0.3441 0.3308 0.3205 0.3122 0.3051 0.2991 0.2937 0.2890 0.2581 0.2402 0.2276 0.2179 0.2099 0.2032 0.1973 0.1922 0.1875 0.3047 0.2922 0.2828 0.2750 0.2686 0.2630 0.2582 0.2538 0.2259 0.2099 0.1985 0.1896 0.1824 0.1762 0.1709 0.1662 0.1628 40 % dioxan 0.3445 0.3307 0.3201 0.3115 0.3043 0.2980 0.2925 0.2876 0.2559 0.2375 0.2245 0.2145 0.2062 0.1995 0.1995 0.1883 0.1836 60 % dioxan 0.3047 0.2919 0.2822 0.2743 0.2676 0.2619 0.2569 0.2525 0.2237 0.2071 0.1951 0.1854 0.1775 0.1708 0.1639 0.1 578 0.1526 0.3447 0.3305 0.3196 0.3107 0.3032 0.2968 0.2912 0.2861 0.2534 0.2345 0.2212 0.2209 0.2025 0.1954 0.1893 0.1838 0.1789 0.3021 0.2890 0.2790 0.2708 0.2638 0.2583 0.2532 0.2485 0.2193 0.2018 0.1888 0.1790 0.1707 0.1633 0.1568 0.1511 0.1460 450c 0.2173 0.2083 0.2008 0.1943 0.1885 0.1834 0.3446 0.3300 0.31 87 0.3096 0.3019 0.2953 0.2895 0.2844 0.2508 0.23 13 0.2175 0.2069 0.1980 0.1906 0.1842 0.1782 0.1740 0.2973 0.2841 0.2738 0.2656 0.2588 0.2530 0.2478 0.2432 0.2135 0.1953 0.1826 0.1709 0.1632 0.1557 0.1489 0.1418 0.1371 RESULTS AND DISCUSSION The e.m.f.(E) values of cell (I) after correction to 1 atm pressure in the usual way are reported in table 2. The e.m.f. expression of cell (I) is given by : where E: is the standard molal potential of the cell, A* is the mean molal activity E = Eg-2 k log (in&) (1)26 THERMODYNAMICS OF HBr I N DIOXAN + WATER coefficient of HBr at the molality m and k equals 2.3026 RTJF. The mean activity coefficient A* is given by eqn (2)9 AC4 1 +BaoC4 -logA* = +pm +log (1 f0.002 Gorn).In this equation A and B are the Debye-Huckel constants on the molar scale, a, is the ion-size parameter, j? is an adjustable parameter and Go is the average molecular weight of the solvent. Substituting eqn (2) in eqn (I) and rearranging, we obtain, E'' = ~ + 2 k l o g m- 2kAc3 -2k log (1 +0.002 G0m) = Ei-2kprn. 1 + Baoc* (3) From eqn (3) it is expected that Eo' should be a linear function of m when a suitable value of ion-size parameter is chosen. The a. values for different solvent mixtures TABLE 3.-ION-SIzE PARAMETER (IN A) wt. %dioxan 15°C 25°C 35°C 45°C 10 5.0 5.0 5.0 5.0 20 5.2 5.2 5.2 5.0 30 5.2 5.3 5.2 5.0 40 5.3 5.2 5.2 5.0 60 5.8 5.7 5.5 4.8 at different temperatures are chosen in such a way that the deviation from linearity of the plot between EO' and m is minimum. A deviation of k0.2 mV in E; was seen when the a.value was varied within k0.3 A of the chosen value. The values of a, TABLE 4.-sTANDARD MOLAL POTENTIALS (EiIV) OF THE Ag-AgBr ELECTRODE IN DIOXANf WATER MIXTURES AT VARIOUS TEMPERATURES wt % dioxan 15°C 25°C 3 5°C 45°C 10 0.0698 0.0654 0.0584 0.05 1 1 20 0.0648 0.0601 0.0534 0.0445 30 0.0570 0.0497 0.0429 0.0334 40 0.0486 0.0385 0.0282 0.0174 60 0.0013 - 0.0097 - 0.0236 - 0.0405 TABLE 5 . V A L U E S OF THE CONSTANTS a, b AND C [See q n (411. wt. % dioxan alv 1 0 4 bIv(cq-1 106 c~v("c)-~ 10 0.0651 5.56 7.33 20 0.0601 5.61 10.63 30 0.0502 7.23 5.55 40 0.0385 10.20 1.68 60 - 0.0097 12.48 14.60 and E; are recorded in tables 3 and 4, respectively. The average standard deviation in A': is k0.l mV for 10, 20 and 30 % dioxan+water mixtures and k0.2 mV for 40 and 60 % dioxan+water mixtures.The E; values for each solvent composition were fitted by the method of least squares to eqn (4) Eg = a-b(t-25)-~(t-25)~ (4)B . K. DAS AND P. K . DAS 27 where t is the temperature in "C. The constants a, b and c are listed in table 5 . The Eg value at 25°C in 20 % dioxan determined by us is intermediate between the value of Feakins and Turner and Mussini et aL2 TABLE 6.-MEAN MOLAL ACTIVITY COEFFICIENT OF HBr IN VARIOUS DIOXAN+ WATER MIXTURES AT 25°C wt. % dioxan m 10 20 30 40 60 0.003 0.005 0.008 0.010 0.020 0.050 0.080 0.100 0.93 1 0.914 0.896 0.886 0.853 0.799 0.779 0.773 0.917 0.896 0.875 0.862 0.823 0.765 0.734 0.720 0.895 0.870 0.843 0.830 0.782 0.717 0.684 0.676 0.865 0.834 0.801 0.784 0.727 0.650 0.544 0.534 0.733 0.683 0.632 0.608 0.532 0.449 0.426 0.425 The stoichiometric mean activity coefficient A* of HBr in various solvent media was calculated with the help of eqn (1).The values of A* were plotted against m on a large scale and from the plots the activity coefficients at rounded molalities were read off and these values at 25°C are given in table 6. An error of k0.05 mV in the e.m.f. values corresponds to an error of -1-0.002 in the value of A* at 25°C. The values of activity coefficient at a particular molality decrease with increasing dioxan content in the medium, as expected from Debye-Hiickel theory. The standard thermodynamic quantities (AG,", AS," and AH,") for the transfer process : HBr (in water) + HBr (in various dioxan + water media) can be calculated from the standard e.m.f.of the cell in water and in respective dioxan+water media on the mole-fraction scale using Feakin's method.1° These are tabulated in table 7. The probable uncertainties in AG; are +, 16 J mol-l, in AH," are k21 J mol-l, and in AS; are k0.5 J K-l mol-' in 10,20 % solvent composition and -1- 1.0 J K-' mol-l in 30, 40, 60 % solvent composition. The standard Gibbs free energies of transfer, AG; are observed to be positive for all the solvent compositions and increase with increasing temperature. The positive AG; values indicate that HBr is in a higher free energy state in dioxan +water mixtures than in water, suggesting that water has more affinity for HBr (or the proton) than for dioxan+water mixtures.Similar conclusions were also drawn for HC1 in dioxan+water mixtures.ll The values of AS: and AH," are negative for all the solvent mixtures, so the enthalpy in dioxan+ water mixture is less than in pure water and hence the net amount of order created by HBr in dioxan+water mixtures is more than in pure water. Since single-ion values of free energy are not available presently for the solvent mixture studied, the method adopted by Khoo and Chan l2 was followed to study the ion-solvent interaction. In this method, consider a function AG;' on the mole fraction scale given by eqn (5) The difference between the free energies of transfer of hydrochloric and hydrobromic acids gives the difference between the freeenergies of transfer of the chloride and bromide ions AG,"(cl- ~ and AGt(Br-) respectively.The AG:(HcI) values required here were calculated from Harned's data l3 for 20 % dioxan and for 10, 30, 40 and28 THERMODYNAMICS OF HBr IN DIOXAN 4- WATER 60 % dioxan from data reported el~ewhere.~ The values of AG,"' at 25°C are given below : wt. Xdioxan 10 20 30 40 60 AGP'/Jmol-l 235 757 1149 1948 2473. AG,"' for all the solvent compositions is positive and increases with increasing concentration of dioxan in the mixed solvents. This is qualitatively in agreement with the Born theory which predicts that the bromide ion should be in a lower free TABLE 7.-FREE-ENERGY, ENTHALPY AND ENTROPY OF TRANSFER OF HBr FROM WATER TO D1OXAN-k WATER MIXTURES AT DIFFERENT TEMPERATURES T/"C 15 25 35 45 15 25 35 45 15 25 35 45 15 25 35 45 15 25 35 45 AG; /J mol-1 AHo/J mol-1 10 % dioxan 200 - 351 165 - 467 306 - 370 41 5 - 305 20 % dioxan 252 - 514 230 - 650 328 - 612 577 - 424 30 % dioxan 520 - 992 734 - 1002 835 - 1021 1124 - 853 40 % dioxan 808 - 2343 1271 - 2349 1687 -2180 2076 - 2045 60 % dioxan 4093 - 2006 4603 - 2405 5324 - 2161 6260 - 1718 ASo/J K-1 mol-1 - 1.98 -2.12 -2.19 - 2.26 - 2.75 - 2.95 - 3.05 -3.15 - 5.44 - 5.83 - 6.02 - 6.22 -11.33 - 12.14 - 12.55 - 12.95 - 21.93 - 23.50 - 24.29 - 25.08 energy state than the chloride ion in mixed solvents of lower dielectric constant than water.Therefore, the Born equation may be expected to fit increasingly better as the dioxan content of the mixture is increased. The same observations were made by Feakins and Turner.l It may be possible to split the AG," values into two parts, as Roy, Vernon and Bothwell l4 have done, a " non-electrostatic " or " chemical " contribution, denoted in their terminology by AG&, and an " electrostatic " contribu- tion AGE, which has been calculated from the Born equation [eqn (6)].AG,",, = (Ne2/2) (jS - - ;J($+;) -B . K . DAS AND P. K. DAS 29 where the radius of hydrogen ion (r+) may be taken as 2.76AI5 and that of the bromide ion (r-) as 1.95A;16 0, and Dw are the dielectric constants of the mixed solvent and water respectively. To calculate the electrostatic part of the entropy of transfer : eqn (6), after differentiation and algebraic manipulation, yields where the values of d In DJdTand d In D,/dTcan be evaluated from simple empirical eqn (8) :17 d In D/dT = - l/O (8) in which 8 is a constant, characteristic of medium. So eqn (7) may be written as : From the slopes of the linear plots of log D against T for the respective dioxan + water mixtures, the following values of 0 were calculated: wt.% dioxan 0 10 20 30 40 60 0 220 202 194 187 181 175. From a knowledge of AG,", and AS;,, the electrostatic part of the enthalpy change AH& has been computed. The chemical contribution of the free energy of transfer (AG,",), entropy of transfer (ASCh) and enthalpy of transfer (AH&,) can then be obtained by subtracting the respective electrostatic contribution values from the molar quantities. These values so calculated at 25°C are presented in table 8.It is TABLE 8.-ELECTRICAL AND CHEMICAL PART OF THE THERMODYNAMIC QUANTITIES ACCOMPANY- ING THE TRANSFER OF HBr FROM WATER TO DIOXAN+ WATER MIXTURES AT 25'C Wt % 10 502 -337 -709 242 -4.06 1.94 20 1152 -922 -1332 682 -8.33 5.38 30 2025 -1290 -2149 1147 -14.00 8.17 40 3263 -1992 -3272 923 -21.92 9.78 60 8035 -3432 -7031 4626 -50.53 27.03 dioxan AG& A c t h q, AH& AS& AS&# evident from an examination of this table that the chemical contribution of the free energy of transfer AGC, is negative and appears to be a solvent parameter which measures the increase in basicity in the dioxan + water mixture. Thus, considering only the chemical contribution of the free energy AGE, which has negative values, the dioxan + water mixture appears to be more basic than water, but the electrostatic factors predominate over the chemical contribution or the solvation, resulting in an overall unfavourable effect on the transfer process from water to dioxan + water mixtures ; hence dioxan + water mixture is more acidic than water.The electrostatic part of the enthalpy and entropy have negative values, whereas the chemical contri- bution of the enthalpy and entropy is positive. The authors thank the Council of Scientific and Industrial Research, New Delhi, India for award of a research fellowship to one of them (B. K. D.).30 THERMODYNAMICS OF HBr I N DIOXAN + WATER D. Feakins and D. J. Turner, J. Chem. SOC., 1965,4986. T. Mussini, C. M. Formaro and P. Andrigo, J. Electroanalyt. Chem., 1971, 33, 177. P. K. Das and U. C. Misra, Electrochim. Acta, 1977, 22, 59. S. C. Mohanty, U. C. Misra, K. C. Singh and P. K. Das, J. Indian Chem. SOC., 1973,50, 302. D. J. G. Ives and G. J. Jam, Reference Electrodes-Theory and Practice (Academic Press, New York, 1969), p. 208. F. Hovorka, R. A. Schaefer and D. Dreisbach, J. Amer. Chem. SOC., 1936, 58,2264. ' G. Akerlof and 0. A. Short, J. Amer. Chem. SOC., 1936,58, 1241. * H. S. Harned and J. G. Donelson, J. Amer. Chem. SOC., 1938,60, 339. E. Huckel, Phys. Z., 1925,26,93. lo D. Feakins and P. Watson, J. Chem. SOC., 1963,4734. l1 B. K. Das, U. C. Misra and P. K. Das, J. Indian Chem. SOC., communicated. l2 K. H. Khoo and C. Y . Chan, Austral. J. Chem., 1975, 28,721. l3 H. S. Harned, J. Amer. Chem. SOC., 1938, 60, 334. l4 R. N. Roy, W. Vernon and A. L. M. Bothwell, Electrochim. Acta, 1972, 17, 5 . l5 M. Paabo, R. G. Bates and R. A. Robinson, J. Phys. Chem., 1966,70,247. l6 L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithica, New York, 3rd edn, l7 R. W. Gurney, Ionic Processes in Solution (McGraw Hill, New York, 1953), p. 16. 1960), p. 521. (PAPER 6 123 64)