1011:
660:
352:
interaction with compound “y” the resulting enthalpy is exothermic. In the case of alcohol and its interactions with a hydrocarbon, the alcohol molecule participates in hydrogen bonding with other alcohol molecules, and these hydrogen bonding interactions are much stronger than alcohol-hydrocarbon interactions, which results in an endothermic heat of mixing.
1006:{\displaystyle {H_{k} \over {RT^{2}}}=Q_{k}{\biggl (}{\sum _{m}{\theta \psi '_{mk}} \over {\sum _{m}{\theta \psi _{mk}}}}-{\biggl (}\sum _{m}{{\theta _{m}\psi '_{k}m} \over {\sum _{n}\theta _{n}\psi _{nm}}}-{\theta _{m}\psi _{km}(\sum _{n}\theta _{n}\psi '_{nm}) \over {(\sum _{n}\theta _{n}\psi _{nm})^{2}}}{\biggr )}{\biggr )}}
360:
Enthalpy of mixing is often calculated experimentally using calorimetry methods. A bomb calorimeter is created to be an isolated system. With an insulated frame and a reaction chamber, a bomb calorimeter is used to transfer heat of a reaction or mixing into surrounding water which is then calculated
351:
When two substances are mixed the resulting enthalpy is not an addition of the pure component enthalpies, unless the substances form an ideal mixture. The interactions between each set of molecules determines the final change in enthalpy. For example, when compound “x” has a strong attractive
1818:
2479:
interactions result in a lower enthalpy of the mixture and a release of heat. If strong interactions only exist between like-molecules, such as H-bonds between water in a water-hexane solution, the mixture will have a higher total enthalpy and absorb heat.
1952:
2289:
1969:
is any in which the arithmetic mean (with respect to mole fraction) of the two pure substances is the same as that of the final mixture. Among other important thermodynamic simplifications, this means that enthalpy of mixing is zero:
1420:
654:
347:
Enthalpy of mixing is defined exclusively for the continuum regime, which excludes molecular-scale effects (However, first-principles calculations have been made for some metal-alloy systems such as Al-Co-Cr or β-Ti).
1671:
1586:
1511:
551:
1648:
It can be seen that prediction of enthalpy of mixing is incredibly complex and requires a plethora of system variables to be known. This explains why enthalpy of mixing is typically experimentally determined.
1304:
331:
205:
452:
2733:
454:(derived from the definition above) in conjunction experimentally determined total-mixture enthalpies and tabulated pure species enthalpies, the difference being equal to enthalpy of mixing.
344:
tend to be more difficult to determine experimentally. As such, enthalpy of mixing tends to be determined experimentally in order to calculate entropy of mixing, rather than the reverse.
1957:
In these equations, the excess and total enthalpies of mixing are equal because the ideal enthalpy of mixing is zero. This is not true for the corresponding Gibbs free energies however.
1640:
1087:
51:
is combined with any other substance or compound, the enthalpy of mixing is the consequence of the new interactions between the two substances or compounds. This enthalpy, if released
1829:
2129:
2028:
2079:
2404:
2360:
2454:
2116:
1185:
1119:
2321:
1214:
1148:
1046:
2700:
Chandran, Mahesh; Subramanian, P. R.; Gigliotti, Michael F. (2013-02-15). "First principles calculation of mixing enthalpy of β-Ti with transition elements".
2741:
1311:
2780:
Savini, C. G.; Winterhalter, D. R.; Kovach, L. H.; Van Ness, H. C. (1966-01-01). "Endothermic Heats of Mixing by
Isothermal Dilution Calorimetry".
2762:
557:
2766:
1813:{\displaystyle \left({\frac {\partial (\Delta G^{E}/T)}{\partial T}}\right)_{p}=-{\frac {\Delta H^{E}}{T^{2}}}=-{\frac {\Delta H_{mix}}{T^{2}}}}
1517:
1427:
2126:
The enthalpy of mixing for a ternary mixture can be expressed in terms of the enthalpies of mixing of the corresponding binary mixtures:
482:
1221:
253:
2467:
are the main constituent of changes in the enthalpy of a mixture. Stronger attractive forces between the mixed molecules, such as
111:
364:
2919:
Kohler, F. (1960). "Zur
Berechnung der thermodynamischen Daten eines ternären Systems aus den zugehörigen binären Systemen".
2903:
2581:
2551:
469:
is useful in calculating enthalpies of mixing for polymeric mixtures and considers a system from a multiplicity perspective.
2861:
466:
458:
94:
2373:
This method requires that the interactions between two species are unaffected by the addition of the third species.
2034:
can be assumed to mix ideally, as can hydrocarbons and liquids with similar molecular interactions and properties.
1594:
1947:{\displaystyle \left({\frac {\partial (\Delta G^{E}/T)}{\partial (1/T)}}\right)_{p}=\Delta H^{E}=\Delta H_{mix}}
1053:
2284:{\displaystyle \Delta H_{123}=(1-x_{1})^{2}\Delta H_{23}+(1-x_{2})^{2}\Delta H_{13}+(1-x_{3})^{2}\Delta H_{12}}
2633:
Liu, Xuan L.; Gheno, Thomas; Lindahl, Bonnie B.; Lindwall, Greta; Gleeson, Brian; Liu, Zi-Kui (2015-04-13).
1973:
44:
2815:
Dang, Dinh; Tassios, Dimitrios P. (1986-01-01). "Prediction of enthalpies of mixing with a UNIFAC model".
2499:
337:
2599:"Gibbs paradox of entropy of mixing: experimental facts, its rejection and the theoretical consequences"
2472:
2635:"First-Principles Calculations, Experimental Study, and Thermodynamic Modeling of the Al-Co-Cr System"
2048:
2376:
2332:
1662:
2949:
2489:
2417:
2084:
1155:
2406:
is then evaluated for a binary concentration ratio equal to the concentration ratio of species
83:
2851:
2504:
1094:
2646:
2476:
2464:
2299:
1192:
1126:
1024:
87:
71:
8:
2650:
2677:
2634:
2519:
1661:
Gibbs free energy of mixing can be related to the enthalpy of mixing by the use of the
52:
40:
82:
mixing. In ideal mixtures, the enthalpy of mixing is null. In non-ideal mixtures, the
2964:
2899:
2857:
2832:
2797:
2756:
2682:
2664:
2577:
2547:
2509:
2042:
341:
48:
2928:
2824:
2789:
2709:
2672:
2654:
2613:
2038:
2713:
2878:
2659:
1658:
67:
58:
Enthalpy of mixing can often be ignored in calculations for mixtures where other
2896:
Thermodynamics - Applications in
Chemical Engineering and the Petroleum Industry
1415:{\displaystyle X_{m}={\sum _{i}x_{i}N_{mi} \over \sum _{i}x_{i}\sum _{k}N_{ki}}}
1966:
63:
20:
86:
of each component is different from its concentration by multiplying with the
2958:
2836:
2801:
2668:
2468:
2031:
233:
2362:
is the molar enthalpy of mixing of the binary mixture consisting of species
649:{\displaystyle {\overline {\Delta H_{i}}}=\sum _{k}N_{ki}(H_{k}-H_{ki}^{*})}
2686:
2514:
247:
Enthalpy of mixing can also be defined using Gibbs free energy of mixing
75:
2828:
2793:
2932:
79:
2598:
472:
Calculations of organic enthalpies of mixing can be made by modifying
2817:
Industrial & Engineering
Chemistry Process Design and Development
1581:{\displaystyle \psi _{mn}^{*}={\delta \over \delta T}({\psi _{m}n})}
1506:{\displaystyle \psi _{mn}=exp{\biggl (}-{Za_{mn} \over 2T}{\biggr )}}
2618:
2494:
546:{\displaystyle \Delta H_{mix}=\sum x_{i}{\overline {\Delta H_{i}}}}
36:
2121:
1299:{\displaystyle \theta _{m}={Q_{m}X_{m} \over \sum _{n}Q_{n}X_{n}}}
2779:
473:
462:
1652:
326:{\displaystyle \Delta G_{mix}=\Delta H_{mix}-T\Delta S_{mix}}
2699:
200:{\displaystyle H_{(mixture)}=\Delta H_{mix}+\sum x_{i}H_{i}}
2041:
or mixture has a non-zero enthalpy of mixing with an ideal
361:
for temperature. A typical solution would use the equation
105:
For a liquid, enthalpy of mixing can be defined as follows
59:
447:{\displaystyle H_{mixture}=\Delta H_{mix}+\sum x_{i}H_{i}}
93:
One approximation for calculating the heat of mixing is
2632:
2420:
2379:
2335:
2302:
2132:
2087:
2051:
1976:
1832:
1674:
1597:
1520:
1430:
1314:
1224:
1195:
1158:
1129:
1097:
1056:
1027:
663:
560:
485:
367:
256:
114:
74:: when the enthalpy of mixing is positive, mixing is
2880:
2118:, and is equivalent to the excess internal energy.
16:
Change in enthalpy during the mixture of substances
2448:
2398:
2354:
2315:
2283:
2110:
2073:
2022:
1946:
1812:
1634:
1580:
1505:
1414:
1298:
1208:
1179:
1142:
1113:
1081:
1040:
1005:
648:
545:
465:models, allow prediction of enthalpies of mixing.
446:
325:
199:
1498:
1458:
998:
991:
785:
708:
2956:
2731:
218:is the total enthalpy of the system after mixing
2122:Mixing binary mixtures to form ternary mixtures
2849:
78:, while negative enthalpy of mixing signifies
1960:
55:, can in an extreme case cause an explosion.
2761:: CS1 maint: multiple names: authors list (
2814:
2606:Electronic Journal of Theoretical Chemistry
1653:Relation to the Gibbs free energy of mixing
1642:= Temperature dependent coordination number
1635:{\displaystyle Z=35.2-0.1272T+0.00014T^{2}}
2782:Journal of Chemical & Engineering Data
2765:) CS1 maint: numeric names: authors list (
2732:CB,378-2590,224-2707, Richard Rowley,350.
1422:= mole fraction of group m in the mixture
1082:{\displaystyle {\overline {\Delta H_{i}}}}
2676:
2658:
2617:
2856:. Oxford University Press. p. 167.
2574:Chemical Engineering Design - SI Edition
2459:
2850:Atkins, Peter; de Paula, Julio (2010).
2541:
2957:
2918:
2576:(5th ed.). Elsevier. p. 95.
2571:
2546:(2nd ed.). Elsevier. p. 52.
2023:{\displaystyle \Delta H_{mix,ideal}=0}
1187:= excess enthalpy of group k in pure i
2893:
2843:
2876:
2870:
2727:
2725:
2723:
2567:
2565:
2563:
2537:
2535:
1089:= partial molar excess enthalpy of i
100:
2950:Can. J. Chem. Eng. Duran Kaliaguine
2596:
62:terms exist, or in cases where the
13:
2380:
2336:
2268:
2223:
2178:
2133:
2052:
1977:
1925:
1909:
1873:
1847:
1841:
1778:
1743:
1715:
1689:
1683:
1060:
564:
524:
486:
399:
304:
279:
257:
152:
14:
2976:
2943:
2898:. Editions Technip. p. 232.
2720:
2560:
2532:
1121:= number of groups of type k in i
457:More complex models, such as the
2323:is the mole fraction of species
2912:
2887:
2702:Journal of Alloys and Compounds
355:
2808:
2773:
2693:
2626:
2590:
2259:
2239:
2214:
2194:
2169:
2149:
2074:{\displaystyle \Delta H_{mix}}
1890:
1876:
1868:
1844:
1710:
1686:
1575:
1557:
977:
940:
935:
896:
643:
609:
144:
120:
1:
2714:10.1016/j.jallcom.2012.10.141
2525:
2399:{\displaystyle \Delta H_{ij}}
2355:{\displaystyle \Delta H_{ij}}
95:Flory–Huggins solution theory
39:liberated or absorbed from a
2660:10.1371/journal.pone.0121386
2544:Hazardous Chemicals Handbook
1150:= excess enthalpy of group k
1074:
578:
538:
236:of component i in the system
7:
2500:Enthalpy change of solution
2483:
2449:{\displaystyle x_{i}/x_{j}}
2030:. Any gas that follows the
1216:= area parameter of group k
1048:= liquid mole fraction of i
338:Gibbs free energy of mixing
10:
2981:
2853:Atkins' Physical Chemistry
2111:{\displaystyle X_{1}X_{2}}
1961:Ideal and regular mixtures
1306:= area fraction of group m
1180:{\displaystyle H_{ki}^{*}}
2883:. Macmillan. p. 263.
2542:Carlson, Phillip (2002).
2045:. Under this assumption,
243:is the enthalpy of pure i
225:is the enthalpy of mixing
2414:in the ternary mixture (
1663:Gibbs-Helmholtz equation
2877:Rock, Peter A. (1969).
2490:Apparent molar property
97:for polymer solutions.
2921:Monatshefte fĂĽr Chemie
2572:Sinnot, Ray K (2009).
2450:
2400:
2356:
2327:in the ternary mixture
2317:
2285:
2112:
2075:
2024:
1948:
1814:
1636:
1582:
1507:
1416:
1300:
1210:
1181:
1144:
1115:
1114:{\displaystyle N_{ki}}
1083:
1042:
1007:
650:
547:
448:
327:
201:
84:thermodynamic activity
47:. When a substance or
2597:Lin, Shu-Kun (1996).
2505:Excess molar quantity
2465:Intermolecular forces
2460:Intermolecular forces
2451:
2401:
2357:
2318:
2316:{\displaystyle x_{i}}
2286:
2113:
2081:scales linearly with
2076:
2025:
1949:
1815:
1637:
1583:
1508:
1417:
1301:
1211:
1209:{\displaystyle Q_{k}}
1182:
1145:
1143:{\displaystyle H_{k}}
1116:
1084:
1043:
1041:{\displaystyle x_{i}}
1008:
651:
548:
476:using the equations
449:
328:
202:
2894:Vidal, Jean (2003).
2418:
2377:
2333:
2300:
2130:
2085:
2049:
1974:
1830:
1672:
1595:
1518:
1428:
1312:
1222:
1193:
1156:
1127:
1095:
1054:
1025:
661:
558:
483:
365:
254:
112:
88:activity coefficient
72:enthalpy of reaction
2829:10.1021/i200032a004
2794:10.1021/je60028a009
2651:2015PLoSO..1021386L
1538:
1176:
934:
825:
745:
642:
70:is the same as for
2933:10.1007/BF00899814
2446:
2396:
2352:
2313:
2281:
2108:
2071:
2020:
1944:
1810:
1632:
1578:
1521:
1503:
1412:
1395:
1375:
1340:
1296:
1272:
1206:
1177:
1159:
1140:
1111:
1079:
1038:
1003:
952:
919:
908:
840:
813:
799:
758:
730:
725:
646:
625:
595:
543:
444:
323:
197:
25:enthalpy of mixing
2905:978-2-7108-0800-8
2583:978-0-7506-8551-1
2553:978-0-7506-4888-2
2510:Entropy of mixing
2043:entropy of mixing
1894:
1823:or equivalently
1808:
1767:
1722:
1555:
1494:
1410:
1386:
1366:
1331:
1294:
1263:
1077:
987:
943:
899:
865:
831:
790:
778:
749:
716:
691:
586:
581:
541:
342:entropy of mixing
101:Formal definition
2972:
2937:
2936:
2916:
2910:
2909:
2891:
2885:
2884:
2874:
2868:
2867:
2847:
2841:
2840:
2812:
2806:
2805:
2777:
2771:
2770:
2760:
2752:
2750:
2749:
2740:. Archived from
2734:"Heat_of_Mixing"
2729:
2718:
2717:
2697:
2691:
2690:
2680:
2662:
2630:
2624:
2623:
2621:
2603:
2594:
2588:
2587:
2569:
2558:
2557:
2539:
2469:hydrogen-bonding
2455:
2453:
2452:
2447:
2445:
2444:
2435:
2430:
2429:
2405:
2403:
2402:
2397:
2395:
2394:
2361:
2359:
2358:
2353:
2351:
2350:
2322:
2320:
2319:
2314:
2312:
2311:
2290:
2288:
2287:
2282:
2280:
2279:
2267:
2266:
2257:
2256:
2235:
2234:
2222:
2221:
2212:
2211:
2190:
2189:
2177:
2176:
2167:
2166:
2145:
2144:
2117:
2115:
2114:
2109:
2107:
2106:
2097:
2096:
2080:
2078:
2077:
2072:
2070:
2069:
2039:regular solution
2029:
2027:
2026:
2021:
2013:
2012:
1953:
1951:
1950:
1945:
1943:
1942:
1921:
1920:
1905:
1904:
1899:
1895:
1893:
1886:
1871:
1864:
1859:
1858:
1839:
1819:
1817:
1816:
1811:
1809:
1807:
1806:
1797:
1796:
1795:
1776:
1768:
1766:
1765:
1756:
1755:
1754:
1741:
1733:
1732:
1727:
1723:
1721:
1713:
1706:
1701:
1700:
1681:
1641:
1639:
1638:
1633:
1631:
1630:
1587:
1585:
1584:
1579:
1574:
1570:
1569:
1556:
1554:
1543:
1537:
1532:
1512:
1510:
1509:
1504:
1502:
1501:
1495:
1493:
1485:
1484:
1483:
1467:
1462:
1461:
1443:
1442:
1421:
1419:
1418:
1413:
1411:
1409:
1408:
1407:
1394:
1385:
1384:
1374:
1364:
1363:
1362:
1350:
1349:
1339:
1329:
1324:
1323:
1305:
1303:
1302:
1297:
1295:
1293:
1292:
1291:
1282:
1281:
1271:
1261:
1260:
1259:
1250:
1249:
1239:
1234:
1233:
1215:
1213:
1212:
1207:
1205:
1204:
1186:
1184:
1183:
1178:
1175:
1170:
1149:
1147:
1146:
1141:
1139:
1138:
1120:
1118:
1117:
1112:
1110:
1109:
1088:
1086:
1085:
1080:
1078:
1073:
1072:
1071:
1058:
1047:
1045:
1044:
1039:
1037:
1036:
1012:
1010:
1009:
1004:
1002:
1001:
995:
994:
988:
986:
985:
984:
975:
974:
962:
961:
951:
938:
930:
918:
917:
907:
895:
894:
882:
881:
871:
866:
864:
863:
862:
850:
849:
839:
829:
821:
812:
811:
801:
798:
789:
788:
779:
777:
776:
775:
774:
757:
747:
746:
741:
724:
714:
712:
711:
705:
704:
692:
690:
689:
688:
675:
674:
665:
655:
653:
652:
647:
641:
636:
621:
620:
608:
607:
594:
582:
577:
576:
575:
562:
552:
550:
549:
544:
542:
537:
536:
535:
522:
520:
519:
504:
503:
453:
451:
450:
445:
443:
442:
433:
432:
417:
416:
395:
394:
332:
330:
329:
324:
322:
321:
297:
296:
275:
274:
206:
204:
203:
198:
196:
195:
186:
185:
170:
169:
148:
147:
64:mixture is ideal
2980:
2979:
2975:
2974:
2973:
2971:
2970:
2969:
2955:
2954:
2946:
2941:
2940:
2917:
2913:
2906:
2892:
2888:
2875:
2871:
2864:
2848:
2844:
2813:
2809:
2778:
2774:
2754:
2753:
2747:
2745:
2730:
2721:
2698:
2694:
2645:(4): e0121386.
2631:
2627:
2619:10.1002/ejtc.27
2601:
2595:
2591:
2584:
2570:
2561:
2554:
2540:
2533:
2528:
2520:Miedema's Model
2486:
2462:
2440:
2436:
2431:
2425:
2421:
2419:
2416:
2415:
2387:
2383:
2378:
2375:
2374:
2343:
2339:
2334:
2331:
2330:
2307:
2303:
2301:
2298:
2297:
2275:
2271:
2262:
2258:
2252:
2248:
2230:
2226:
2217:
2213:
2207:
2203:
2185:
2181:
2172:
2168:
2162:
2158:
2140:
2136:
2131:
2128:
2127:
2124:
2102:
2098:
2092:
2088:
2086:
2083:
2082:
2059:
2055:
2050:
2047:
2046:
1984:
1980:
1975:
1972:
1971:
1963:
1932:
1928:
1916:
1912:
1900:
1882:
1872:
1860:
1854:
1850:
1840:
1838:
1834:
1833:
1831:
1828:
1827:
1802:
1798:
1785:
1781:
1777:
1775:
1761:
1757:
1750:
1746:
1742:
1740:
1728:
1714:
1702:
1696:
1692:
1682:
1680:
1676:
1675:
1673:
1670:
1669:
1655:
1626:
1622:
1596:
1593:
1592:
1565:
1561:
1560:
1547:
1542:
1533:
1525:
1519:
1516:
1515:
1497:
1496:
1486:
1476:
1472:
1468:
1466:
1457:
1456:
1435:
1431:
1429:
1426:
1425:
1400:
1396:
1390:
1380:
1376:
1370:
1365:
1355:
1351:
1345:
1341:
1335:
1330:
1328:
1319:
1315:
1313:
1310:
1309:
1287:
1283:
1277:
1273:
1267:
1262:
1255:
1251:
1245:
1241:
1240:
1238:
1229:
1225:
1223:
1220:
1219:
1200:
1196:
1194:
1191:
1190:
1171:
1163:
1157:
1154:
1153:
1134:
1130:
1128:
1125:
1124:
1102:
1098:
1096:
1093:
1092:
1067:
1063:
1059:
1057:
1055:
1052:
1051:
1032:
1028:
1026:
1023:
1022:
997:
996:
990:
989:
980:
976:
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963:
957:
953:
947:
939:
923:
913:
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903:
887:
883:
877:
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872:
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855:
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835:
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783:
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748:
734:
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713:
707:
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700:
696:
684:
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676:
670:
666:
664:
662:
659:
658:
637:
629:
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612:
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571:
567:
563:
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531:
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493:
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438:
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372:
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358:
311:
307:
286:
282:
264:
260:
255:
252:
251:
242:
231:
224:
217:
191:
187:
181:
177:
159:
155:
119:
115:
113:
110:
109:
103:
68:sign convention
33:excess enthalpy
17:
12:
11:
5:
2978:
2968:
2967:
2953:
2952:
2945:
2944:External links
2942:
2939:
2938:
2911:
2904:
2886:
2869:
2862:
2842:
2807:
2772:
2738:www.et.byu.edu
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2473:induced-dipole
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2019:
2016:
2011:
2008:
2005:
2002:
1999:
1996:
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1911:
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1199:
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1000:
993:
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979:
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966:
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933:
929:
926:
922:
916:
912:
906:
902:
898:
893:
890:
886:
880:
876:
869:
861:
858:
854:
848:
844:
838:
834:
828:
824:
820:
816:
810:
806:
797:
793:
787:
782:
773:
770:
766:
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737:
733:
729:
723:
719:
710:
703:
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687:
683:
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619:
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492:
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259:
245:
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146:
143:
140:
137:
134:
131:
128:
125:
122:
118:
102:
99:
53:exothermically
29:heat of mixing
21:thermodynamics
15:
9:
6:
4:
3:
2:
2977:
2966:
2963:
2962:
2960:
2951:
2948:
2947:
2934:
2930:
2926:
2923:(in German).
2922:
2915:
2907:
2901:
2897:
2890:
2882:
2881:
2873:
2865:
2863:9780199543373
2859:
2855:
2854:
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2838:
2834:
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2826:
2822:
2818:
2811:
2803:
2799:
2795:
2791:
2787:
2783:
2776:
2768:
2764:
2758:
2744:on 2020-07-15
2743:
2739:
2735:
2728:
2726:
2724:
2715:
2711:
2707:
2703:
2696:
2688:
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2652:
2648:
2644:
2640:
2636:
2629:
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2615:
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2600:
2593:
2585:
2579:
2575:
2568:
2566:
2564:
2555:
2549:
2545:
2538:
2536:
2531:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2487:
2481:
2478:
2477:dipole-dipole
2474:
2470:
2466:
2457:
2441:
2437:
2432:
2426:
2422:
2413:
2409:
2391:
2388:
2384:
2369:
2365:
2347:
2344:
2340:
2329:
2326:
2308:
2304:
2296:
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2276:
2272:
2263:
2253:
2249:
2245:
2242:
2236:
2231:
2227:
2218:
2208:
2204:
2200:
2197:
2191:
2186:
2182:
2173:
2163:
2159:
2155:
2152:
2146:
2141:
2137:
2119:
2103:
2099:
2093:
2089:
2066:
2063:
2060:
2056:
2044:
2040:
2035:
2033:
2032:ideal gas law
2017:
2014:
2009:
2006:
2003:
2000:
1997:
1994:
1991:
1988:
1985:
1981:
1968:
1967:ideal mixture
1958:
1939:
1936:
1933:
1929:
1922:
1917:
1913:
1906:
1901:
1896:
1887:
1883:
1879:
1865:
1861:
1855:
1851:
1835:
1826:
1825:
1824:
1803:
1799:
1792:
1789:
1786:
1782:
1772:
1769:
1762:
1758:
1751:
1747:
1737:
1734:
1729:
1724:
1718:
1707:
1703:
1697:
1693:
1677:
1668:
1667:
1666:
1664:
1660:
1650:
1627:
1623:
1619:
1616:
1613:
1610:
1607:
1604:
1601:
1598:
1591:
1571:
1566:
1562:
1551:
1548:
1544:
1539:
1534:
1529:
1526:
1522:
1514:
1490:
1487:
1480:
1477:
1473:
1469:
1463:
1453:
1450:
1447:
1444:
1439:
1436:
1432:
1424:
1423:
1404:
1401:
1397:
1391:
1387:
1381:
1377:
1371:
1367:
1359:
1356:
1352:
1346:
1342:
1336:
1332:
1325:
1320:
1316:
1308:
1288:
1284:
1278:
1274:
1268:
1264:
1256:
1252:
1246:
1242:
1235:
1230:
1226:
1218:
1201:
1197:
1189:
1172:
1167:
1164:
1160:
1152:
1135:
1131:
1123:
1106:
1103:
1099:
1091:
1068:
1064:
1050:
1033:
1029:
1021:
1020:
1019:
1018:
1017:
981:
971:
968:
964:
958:
954:
948:
944:
931:
927:
924:
920:
914:
910:
904:
900:
891:
888:
884:
878:
874:
867:
859:
856:
852:
846:
842:
836:
832:
826:
822:
818:
814:
808:
804:
795:
791:
780:
771:
768:
764:
760:
754:
750:
742:
738:
735:
731:
727:
721:
717:
701:
697:
693:
685:
681:
677:
671:
667:
657:
638:
633:
630:
626:
622:
617:
613:
604:
601:
597:
591:
587:
583:
572:
568:
554:
532:
528:
516:
512:
508:
505:
500:
497:
494:
490:
479:
478:
477:
475:
470:
468:
467:Flory-Huggins
464:
460:
459:Flory-Huggins
455:
439:
435:
429:
425:
421:
418:
413:
410:
407:
403:
396:
391:
388:
385:
382:
379:
376:
373:
369:
353:
349:
345:
343:
339:
318:
315:
312:
308:
301:
298:
293:
290:
287:
283:
276:
271:
268:
265:
261:
250:
249:
248:
238:
235:
234:mole fraction
227:
220:
213:
212:
211:
192:
188:
182:
178:
174:
171:
166:
163:
160:
156:
149:
141:
138:
135:
132:
129:
126:
123:
116:
108:
107:
106:
98:
96:
91:
89:
85:
81:
77:
73:
69:
65:
61:
56:
54:
50:
46:
42:
38:
34:
30:
26:
22:
2924:
2920:
2914:
2895:
2889:
2879:
2872:
2852:
2845:
2823:(1): 22–31.
2820:
2816:
2810:
2788:(1): 40–43.
2785:
2781:
2775:
2746:. Retrieved
2742:the original
2737:
2705:
2701:
2695:
2642:
2638:
2628:
2609:
2605:
2592:
2573:
2543:
2463:
2411:
2407:
2372:
2367:
2363:
2324:
2292:
2125:
2036:
1964:
1956:
1822:
1656:
1647:
1015:
471:
456:
359:
356:Calculations
350:
346:
335:
246:
209:
104:
92:
57:
32:
28:
24:
18:
2708:: 501–508.
2612:: 135–150.
2515:Calorimetry
76:endothermic
2927:(4): 738.
2748:2017-02-22
2526:References
80:exothermic
2837:0196-4305
2802:0021-9568
2669:1932-6203
2381:Δ
2337:Δ
2269:Δ
2246:−
2224:Δ
2201:−
2179:Δ
2156:−
2134:Δ
2053:Δ
1978:Δ
1926:Δ
1910:Δ
1874:∂
1848:Δ
1842:∂
1779:Δ
1773:−
1744:Δ
1738:−
1716:∂
1690:Δ
1684:∂
1608:−
1563:ψ
1549:δ
1545:δ
1535:∗
1523:ψ
1464:−
1433:ψ
1388:∑
1368:∑
1333:∑
1265:∑
1227:θ
1173:∗
1075:¯
1061:Δ
965:ψ
955:θ
945:∑
921:ψ
911:θ
901:∑
885:ψ
875:θ
868:−
853:ψ
843:θ
833:∑
815:ψ
805:θ
792:∑
781:−
765:ψ
761:θ
751:∑
732:ψ
728:θ
718:∑
639:∗
623:−
588:∑
579:¯
565:Δ
539:¯
525:Δ
509:∑
487:Δ
422:∑
400:Δ
336:However,
305:Δ
299:−
280:Δ
258:Δ
216:(mixture)
175:∑
153:Δ
41:substance
35:) is the
2965:Enthalpy
2959:Category
2757:cite web
2687:25875037
2639:PLOS ONE
2495:Enthalpy
2484:See also
932:′
823:′
743:′
49:compound
37:enthalpy
2678:4395364
2647:Bibcode
2293:Where:
1620:0.00014
1016:Where:
232:is the
210:Where:
2902:
2860:
2835:
2800:
2685:
2675:
2667:
2580:
2550:
2475:, and
1659:excess
1611:0.1272
474:UNIFAC
463:UNIFAC
66:. The
45:mixing
27:(also
23:, the
2602:(PDF)
43:upon
2900:ISBN
2858:ISBN
2833:ISSN
2798:ISSN
2767:link
2763:link
2683:PMID
2665:ISSN
2578:ISBN
2548:ISBN
2366:and
1657:The
1605:35.2
461:and
340:and
60:heat
31:and
2929:doi
2825:doi
2790:doi
2710:doi
2706:550
2673:PMC
2655:doi
2614:doi
2456:).
2410:to
2142:123
1965:An
223:mix
19:In
2961::
2925:91
2831:.
2821:25
2819:.
2796:.
2786:11
2784:.
2759:}}
2755:{{
2736:.
2722:^
2704:.
2681:.
2671:.
2663:.
2653:.
2643:10
2641:.
2637:.
2608:.
2604:.
2562:^
2534:^
2471:,
2277:12
2232:13
2187:23
2037:A
1665::
221:ΔH
90:.
2935:.
2931::
2908:.
2866:.
2839:.
2827::
2804:.
2792::
2769:)
2751:.
2716:.
2712::
2689:.
2657::
2649::
2622:.
2616::
2610:1
2586:.
2556:.
2442:j
2438:x
2433:/
2427:i
2423:x
2412:j
2408:i
2392:j
2389:i
2385:H
2368:j
2364:i
2348:j
2345:i
2341:H
2325:i
2309:i
2305:x
2273:H
2264:2
2260:)
2254:3
2250:x
2243:1
2240:(
2237:+
2228:H
2219:2
2215:)
2209:2
2205:x
2198:1
2195:(
2192:+
2183:H
2174:2
2170:)
2164:1
2160:x
2153:1
2150:(
2147:=
2138:H
2104:2
2100:X
2094:1
2090:X
2067:x
2064:i
2061:m
2057:H
2018:0
2015:=
2010:l
2007:a
2004:e
2001:d
1998:i
1995:,
1992:x
1989:i
1986:m
1982:H
1940:x
1937:i
1934:m
1930:H
1923:=
1918:E
1914:H
1907:=
1902:p
1897:)
1891:)
1888:T
1884:/
1880:1
1877:(
1869:)
1866:T
1862:/
1856:E
1852:G
1845:(
1836:(
1804:2
1800:T
1793:x
1790:i
1787:m
1783:H
1770:=
1763:2
1759:T
1752:E
1748:H
1735:=
1730:p
1725:)
1719:T
1711:)
1708:T
1704:/
1698:E
1694:G
1687:(
1678:(
1628:2
1624:T
1617:+
1614:T
1602:=
1599:Z
1576:)
1572:n
1567:m
1558:(
1552:T
1540:=
1530:n
1527:m
1499:)
1491:T
1488:2
1481:n
1478:m
1474:a
1470:Z
1459:(
1454:p
1451:x
1448:e
1445:=
1440:n
1437:m
1405:i
1402:k
1398:N
1392:k
1382:i
1378:x
1372:i
1360:i
1357:m
1353:N
1347:i
1343:x
1337:i
1326:=
1321:m
1317:X
1289:n
1285:X
1279:n
1275:Q
1269:n
1257:m
1253:X
1247:m
1243:Q
1236:=
1231:m
1202:k
1198:Q
1168:i
1165:k
1161:H
1136:k
1132:H
1107:i
1104:k
1100:N
1069:i
1065:H
1034:i
1030:x
999:)
992:)
982:2
978:)
972:m
969:n
959:n
949:n
941:(
936:)
928:m
925:n
915:n
905:n
897:(
892:m
889:k
879:m
860:m
857:n
847:n
837:n
827:m
819:k
809:m
796:m
786:(
772:k
769:m
755:m
739:k
736:m
722:m
709:(
702:k
698:Q
694:=
686:2
682:T
678:R
672:k
668:H
644:)
634:i
631:k
627:H
618:k
614:H
610:(
605:i
602:k
598:N
592:k
584:=
573:i
569:H
533:i
529:H
517:i
513:x
506:=
501:x
498:i
495:m
491:H
440:i
436:H
430:i
426:x
419:+
414:x
411:i
408:m
404:H
397:=
392:e
389:r
386:u
383:t
380:x
377:i
374:m
370:H
319:x
316:i
313:m
309:S
302:T
294:x
291:i
288:m
284:H
277:=
272:x
269:i
266:m
262:G
241:i
239:H
230:i
228:x
214:H
193:i
189:H
183:i
179:x
172:+
167:x
164:i
161:m
157:H
150:=
145:)
142:e
139:r
136:u
133:t
130:x
127:i
124:m
121:(
117:H
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