3083:
2481:
723:
736:, which is a limiting law valid when the interactive forces between molecules approach zero, for example as the concentration approaches zero. Raoult's law is instead valid if the physical properties of the components are identical. The more similar the components are, the more their behavior approaches that described by Raoult's law. For example, if the two components differ only in
1071:
2284:. This equation shows that, for an ideal solution where each pure component has a different vapor pressure, the gas phase is enriched in the component with the higher vapor pressure when pure, and the solution is enriched in the component with the lower pure vapor pressure. This phenomenon is the basis for
2296:
In elementary applications, Raoult's law is generally valid when the liquid phase is either nearly pure or a mixture of similar substances. Raoult's law may be adapted to non-ideal solutions by incorporating two factors that account for the interactions between molecules of different substances. The
731:
Raoult's law is a phenomenological relation that assumes ideal behavior based on the simple microscopic assumption that intermolecular forces between unlike molecules are equal to those between similar molecules, and that their molar volumes are the same: the conditions of an ideal solution. This is
1851:
An ideal solution would follow Raoult's law, but most solutions deviate from ideality. Interactions between gas molecules are typically quite small, especially if the vapor pressures are low. However, the interactions in a liquid are very strong. For a solution to be ideal, the interactions between
2109:
The presence of these limited linear regimes has been experimentally verified in a great number of cases, though large deviations occur in a variety of cases. Consequently, both its pedagogical value and utility have been questioned at the introductory college level. In a perfectly ideal system,
747:. If the vapor pressure is less than predicted (a negative deviation), fewer molecules of each component than expected have left the solution in the presence of the other component, indicating that the forces between unlike molecules are stronger. The converse is true for positive deviations.
525:
1115:
to postulate that the vapor pressure above an ideal mixture of liquids is equal to the sum of the vapor pressures of each component multiplied by its mole fraction. Taking compliance with Raoult's Law as a defining characteristic of ideality in a solution, it is possible to
1509:
1709:
534:) is dissolved into a solvent A to form an ideal solution, the vapor pressure of the solution will be lower than that of the solvent. In an ideal solution of a nonvolatile solute, the decrease in vapor pressure is directly proportional to the mole fraction of solute:
705:
915:
398:
2528:, corresponding to a mixture that evaporates without change of composition. When these two components are mixed, the reaction is exothermic as ion-dipole intermolecular forces of attraction are formed between the resulting ions (H
904:
1282:
in the ideal solution. From this equation, other thermodynamic properties of an ideal solution may be determined. If the assumption that the vapor follows the ideal gas law is added, Raoult's law may be derived as follows.
726:
Vapor pressure of a binary solution that obeys Raoult's law. The black line shows the total vapor pressure as a function of the mole fraction of component B, and the two green lines are the partial pressures of the two
1963:
2691:
2189:
1852:
unlike molecules must be of the same magnitude as those between like molecules. This approximation is only true when the different species are almost chemically identical. One can see that from considering the
409:
2459:
1370:
2550:
If the deviation is large, then the vapor pressure curve shows a maximum at a particular composition and forms a positive azeotrope (low-boiling mixture). Some mixtures in which this happens are (1)
1381:
1198:
1601:
586:
592:
304:
Where two volatile liquids A and B are mixed with each other to form a solution, the vapor phase consists of both components of the solution. Once the components in the solution have reached
2547:
When the adhesion is weaker than cohesion, which is quite common, the liquid particles escape the solution more easily that increases the vapor pressure and leads to a positive deviation.
1841:
1773:
142:
2019:
1233:
228:
2497:
When the adhesion is stronger than the cohesion, fewer liquid particles turn into vapor thereby lowering the vapor pressure and leading to negative deviation in the graph.
1570:
1101:
822:
795:
2366:
2336:
1066:{\displaystyle p=p_{\text{A}}^{\star }(1-x_{\text{B}})+p_{\text{B}}^{\star }x_{\text{B}}=p_{\text{A}}^{\star }+(p_{\text{B}}^{\star }-p_{\text{A}}^{\star })x_{\text{B}}.}
2096:
2274:
2219:
2067:
1543:
1260:
318:
279:
172:
1989:
2477:
forces (between similar molecules) are not uniform between the two liquids. Therefore, they deviate from Raoult's law, which applies only to ideal solutions.
2243:
1593:
1308:
1280:
768:
299:
252:
196:
830:
3540:
2914:"Solute-Solvent Complex Switching Dynamics of Chloroform between Acetone and Dimethylsulfoxide Two-Dimensional IR Chemical Exchange Spectroscopy"
1862:
2520:) has a negative deviation from Raoult's law, indicating an attractive interaction between the two components that have been described as a
2120:
3242:
520:{\displaystyle p={\dfrac {p_{\text{A}}^{\star }n_{\text{A}}+p_{\text{B}}^{\star }n_{\text{B}}+\cdots }{n_{\text{A}}+n_{\text{B}}+\cdots }}}
2582:
and water. When these pairs of components are mixed, the process is endothermic as weaker intermolecular interactions are formed so that Î
2377:
1316:
743:
Comparing measured vapor pressures to predicted values from Raoult's law provides information about the true relative strength of
2524:. The system HClâwater has a large enough negative deviation to form a minimum in the vapor pressure curve known as a (negative)
1504:{\displaystyle \mu _{i,{\text{liq}}}^{\star }+RT\ln x_{i}=\mu _{i,{\text{vap}}}^{\ominus }+RT\ln {\frac {f_{i}}{p^{\ominus }}},}
3014:
750:
For a solution of two liquids A and B, Raoult's law predicts that if no other gases are present, then the total vapor pressure
2072:
If deviations from the ideal are not too large, Raoult's law is still valid in a narrow concentration range when approaching
1704:{\displaystyle \mu _{i,{\text{liq}}}^{\star }=\mu _{i,{\text{vap}}}^{\ominus }+RT\ln {\frac {f_{i}^{\star }}{p^{\ominus }}}.}
1130:
540:
3621:
700:{\displaystyle \Delta p=p_{\text{A}}^{\star }-p=p_{\text{A}}^{\star }(1-x_{\text{A}})=p_{\text{A}}^{\star }x_{\text{B}}.}
3606:
2859:
3082:
3287:
2884:
2763:
2725:
3235:
403:
In other words, the vapor pressure of the solution is the mole-weighted mean of the individual vapour pressures:
2110:
where ideal liquid and ideal vapor are assumed, a very useful equation emerges if Raoult's law is combined with
2102:). The solute also shows a linear limiting law, but with a different coefficient. This relationship is known as
1788:
1720:
3616:
3377:
2787:
2484:
Positive and negative deviations from Raoult's law. Maxima and minima in the curves (if present) correspond to
92:
2021:
must be equal to zero, and this can only be true if the interactions between the molecules are indifferent.
79:
in the mixture. In consequence, the relative lowering of vapor pressure of a dilute solution of nonvolatile
3530:
3072:
1994:
305:
3611:
3460:
3228:
1853:
3515:
3143:
3007:
1206:
231:
3407:
1991:, equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that
2930:
201:
3392:
3327:
3199:
3174:
3057:
2025:
1968:
This is always negative, so mixing is spontaneous. However, the expression is, apart from a factor
2682:
2653:
1548:
1112:
1079:
800:
773:
60:
3347:
3189:
3184:
3164:
3102:
2344:
2308:
1117:
710:
If the solute associates or dissociates in the solution, the expression of the law includes the
3445:
3440:
3297:
3169:
2925:
2657:
2747:
393:{\displaystyle p=p_{\text{A}}^{\star }x_{\text{A}}+p_{\text{B}}^{\star }x_{\text{B}}+\cdots .}
3601:
3545:
3525:
3194:
3000:
744:
711:
2075:
308:, the total vapor pressure of the solution can be determined by combining Raoult's law with
3259:
3251:
3107:
2912:
Kwak, Kyungwon; Rosenfeld, Daniel E.; Chung, Jean K.; Fayer, Michael D. (6 November 2008).
2814:
2474:
2339:
2302:
2252:
2197:
2031:
1521:
1287:
1238:
257:
150:
2614:
8:
3372:
3342:
3209:
2686:
75:
is equal to the vapor pressure of the pure component (liquid or solid) multiplied by its
2818:
2368:, is a correction for interactions in the liquid phase between the different molecules.
1971:
3626:
3204:
3097:
2948:
2913:
2832:
2228:
1578:
1293:
1265:
1121:
824:
of the two components. Thus the total pressure above the solution of A and B would be
753:
284:
237:
181:
86:
Mathematically, Raoult's law for a single component in an ideal solution is stated as
52:
899:{\displaystyle p=p_{\text{A}}^{\star }x_{\text{A}}+p_{\text{B}}^{\star }x_{\text{B}}.}
3550:
3509:
3412:
3138:
3062:
2953:
2880:
2855:
2783:
2759:
2721:
2704:
2836:
3485:
3480:
3312:
3272:
3179:
3067:
2943:
2935:
2822:
2700:
2599:
2567:
175:
64:
25:
2624:
3455:
3387:
3352:
3337:
3332:
3317:
3282:
3052:
3042:
2480:
2469:
In many pairs of liquids, there is no uniformity of attractive forces, i.e., the
2111:
309:
3520:
3475:
3465:
3382:
3277:
3267:
2806:
2743:
2619:
2103:
68:
56:
2069:
in a binary solution then, for the second component, the same must also hold.
770:
above the solution is equal to the weighted sum of the "pure" vapor pressures
3595:
3565:
3402:
3362:
3307:
3112:
2604:
2521:
2298:
2277:
2222:
733:
76:
3422:
3417:
3023:
2957:
2285:
2297:
first factor is a correction for gas non-ideality, or deviations from the
1778:
For the ideal gas, pressure and fugacity are equal, so introducing simple
3575:
3490:
1958:{\displaystyle \Delta _{\text{mix}}G=nRT(x_{1}\ln x_{1}+x_{2}\ln x_{2}).}
2850:
Felder, Richard M.; Rousseau, Ronald W.; Bullard, Lisa G. (2004-12-15).
1575:
The corresponding equation when the system consists purely of component
3570:
3560:
3555:
3432:
2687:"Recherches expérimentales sur les tensions de vapeur des dissolutions"
2629:
2575:
2501:
2939:
2827:
2801:
2184:{\displaystyle x_{i}={\frac {y_{i}p_{\text{total}}}{p_{i}^{\star }}},}
3580:
3535:
3450:
3220:
3133:
2755:
2689:[Experimental research on the vapor pressures of solutions].
2609:
2525:
2485:
531:
530:
If a non-volatile solute B (it has zero vapor pressure, so does not
3397:
2563:
2470:
1779:
1515:
3500:
3302:
3292:
3128:
2579:
2571:
2559:
2551:
2509:
2454:{\displaystyle y_{i}\phi _{p,i}p=x_{i}\gamma _{i}p_{i}^{\star }.}
1714:
Subtracting these equations and re-arranging leads to the result
737:
722:
3047:
2992:
2028:
that if Raoult's law holds over the entire concentration range
80:
3322:
3148:
2555:
37:
34:
1365:{\displaystyle \mu _{i,{\text{liq}}}=\mu _{i,{\text{vap}}}.}
2371:
This modified or extended Raoult's law is then written as
83:
is equal to the mole fraction of solute in the solution.
2879:(seventh ed.), New York: McGraw-Hill, p. 545,
1545:, as a fraction of the pressure in the reference state,
1310:
must be the same in the liquid and gas states. That is,
2911:
2748:"Thermodynamics of Fluid Phase and Chemical Equilibria"
1193:{\displaystyle \mu _{i}=\mu _{i}^{\star }+RT\ln x_{i},}
2660:[General law of vapor pressures of solvents].
1375:
Substituting the formula for chemical potential gives
909:
Since the sum of the mole fractions is equal to one,
16:
Law of thermodynamics for vapour pressure of a mixture
2875:
Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2005),
2849:
2658:"Loi générale des tensions de vapeur des dissolvants"
2380:
2347:
2311:
2255:
2231:
2200:
2123:
2078:
2034:
1997:
1974:
1865:
1791:
1723:
1604:
1581:
1551:
1524:
1384:
1319:
1296:
1268:
1241:
1209:
1133:
1082:
918:
833:
803:
776:
756:
595:
543:
420:
412:
321:
287:
260:
240:
204:
184:
153:
95:
43:
3541:
List of boiling and freezing information of solvents
1111:
Raoult's law was first observed empirically and led
581:{\displaystyle p=p_{\text{A}}^{\star }x_{\text{A}},}
40:
31:
2877:
Introduction to
Chemical Engineering Thermodynamics
2874:
28:
2742:
2453:
2360:
2330:
2268:
2237:
2213:
2183:
2090:
2061:
2013:
1983:
1957:
1835:
1767:
1703:
1587:
1564:
1537:
1503:
1364:
1302:
1274:
1254:
1227:
1192:
1095:
1065:
898:
816:
789:
762:
699:
580:
519:
392:
293:
273:
246:
222:
190:
166:
136:
2746:; Corti, David S.; Mallinson, Richard G. (2008).
2532:O and Cl) and the polar water molecules so that Î
740:content, then Raoult's law is essentially exact.
3593:
1235:is the chemical potential in the pure state and
2902:(8th ed., W. H. Freeman 2006) p. 146.
1106:
1076:This is a linear function of the mole fraction
1514:as the gas-phase mole fraction depends on its
3236:
3008:
2677:
2675:
2648:
2646:
1124:of each component of the liquid is given by
2852:Elementary Principles of Chemical Processes
1290:, the chemical potential of each component
198:in the gaseous mixture above the solution,
3243:
3229:
3015:
3001:
2793:
2692:Journal de Physique Théorique et Appliquée
1836:{\displaystyle p_{i}=x_{i}p_{i}^{\star }.}
1768:{\displaystyle f_{i}=x_{i}f_{i}^{\star }.}
2978:Chapter 24, D. A. McQuarrie, J. D. Simon
2947:
2929:
2868:
2826:
2738:
2736:
2734:
2672:
2643:
137:{\displaystyle p_{i}=p_{i}^{\star }x_{i}}
2980:Physical Chemistry: A Molecular Approach
2752:Albright's Chemical Engineering Handbook
2479:
721:
3594:
3250:
2799:
2731:
2681:
2652:
281:is the mole fraction of the component
3224:
2996:
2542:
2492:
2014:{\displaystyle \Delta _{\text{mix}}H}
1782:to this result yields Raoult's law:
2473:(between dissimilar molecules) and
2291:
13:
2982:. University Science Books. (1997)
1999:
1867:
1854:Gibbs free energy change of mixing
1262:is the mole fraction of component
596:
14:
3638:
2970:Atkins and de Paula, p. 184.
2464:
1595:in equilibrium with its vapor is
1286:If the system is ideal, then, at
1228:{\displaystyle \mu _{i}^{\star }}
301:in the liquid or solid solution.
3081:
3022:
2989:. Clarendon Press. Oxford (1993)
24:
2964:
2905:
2782:(MacMillan 1969), p. 261.
1846:
2892:
2843:
2772:
2750:. In Albright, Lyle F. (ed.).
2711:
2705:10.1051/jphystap:0188900800500
2082:
2056:
2041:
1949:
1891:
1047:
1011:
959:
940:
663:
644:
223:{\displaystyle p_{i}^{\star }}
1:
2987:Basic Chemical Thermodynamics
2802:"Raoult's Law Is a Deception"
2636:
2488:or constant boiling mixtures.
717:
312:of partial pressures to give
59:. Proposed by French chemist
3531:Inorganic nonaqueous solvent
2098:for the majority phase (the
1565:{\displaystyle p^{\ominus }}
1107:Thermodynamic considerations
1096:{\displaystyle x_{\text{B}}}
817:{\displaystyle p_{\text{B}}}
790:{\displaystyle p_{\text{A}}}
63:in 1887, it states that the
7:
2898:P. Atkins and J. de Paula,
2800:Hawkes, Stephen J. (1995).
2592:
2500:For example, the system of
2361:{\displaystyle \gamma _{i}}
2331:{\displaystyle \phi _{p,i}}
10:
3643:
3622:Engineering thermodynamics
3516:Acid dissociation constant
3144:Spinning band distillation
2024:It can be shown using the
232:equilibrium vapor pressure
3607:Eponymous laws of physics
3499:
3431:
3361:
3258:
3157:
3121:
3090:
3079:
3030:
1103:, as shown in the graph.
3073:Vaporâliquid equilibrium
2718:A to Z of Thermodynamics
714:as a correction factor.
67:of each component of an
3481:Solubility table (data)
3348:Apparent molar property
3103:Continuous distillation
2780:Chemical Thermodynamics
55:, with implications in
3446:Total dissolved solids
3441:Solubility equilibrium
3366:and related quantities
2854:. Wiley. p. 293.
2489:
2455:
2362:
2332:
2270:
2239:
2215:
2185:
2092:
2091:{\displaystyle x\to 1}
2063:
2015:
1985:
1959:
1837:
1769:
1705:
1589:
1566:
1539:
1505:
1366:
1304:
1276:
1256:
1229:
1194:
1097:
1067:
900:
818:
791:
764:
728:
701:
582:
521:
394:
295:
275:
248:
234:of the pure component
224:
192:
168:
138:
51:law) is a relation of
3617:Equilibrium chemistry
3546:Partition coefficient
3526:Polar aprotic solvent
2578:and ethanol, and (5)
2483:
2456:
2363:
2333:
2271:
2269:{\displaystyle y_{i}}
2240:
2216:
2214:{\displaystyle x_{i}}
2186:
2093:
2064:
2062:{\displaystyle x\in }
2016:
1986:
1960:
1838:
1770:
1706:
1590:
1567:
1540:
1538:{\displaystyle f_{i}}
1506:
1367:
1305:
1277:
1257:
1255:{\displaystyle x_{i}}
1230:
1195:
1113:François-Marie Raoult
1098:
1068:
901:
819:
792:
765:
745:intermolecular forces
725:
702:
583:
522:
395:
296:
276:
274:{\displaystyle x_{i}}
249:
225:
193:
169:
167:{\displaystyle p_{i}}
139:
61:François-Marie Raoult
3461:Enthalpy of solution
3388:Volume concentration
3383:Number concentration
3108:Fractionating column
3091:Industrial processes
3058:McCabeâThiele method
2758:. pp. 255â392.
2378:
2345:
2340:activity coefficient
2309:
2303:fugacity coefficient
2253:
2229:
2198:
2121:
2076:
2032:
2026:GibbsâDuhem equation
1995:
1972:
1863:
1789:
1721:
1602:
1579:
1549:
1522:
1382:
1317:
1294:
1266:
1239:
1207:
1131:
1080:
916:
831:
801:
774:
754:
593:
541:
410:
319:
285:
258:
238:
202:
182:
151:
93:
3373:Molar concentration
3343:Dilution (equation)
2924:(44): 13906â13915.
2819:1995JChEd..72..204H
2447:
2338:). The second, the
2301:. It is called the
2175:
1829:
1761:
1685:
1653:
1627:
1458:
1407:
1224:
1161:
1046:
1028:
1007:
979:
939:
882:
854:
683:
643:
619:
564:
465:
437:
370:
342:
219:
123:
3612:Physical chemistry
3413:Isotopic abundance
3378:Mass concentration
3252:Chemical solutions
3122:Laboratory methods
3098:Batch distillation
2900:Physical Chemistry
2720:by Pierre Perrot.
2543:Positive deviation
2493:Negative deviation
2490:
2451:
2433:
2358:
2328:
2266:
2235:
2211:
2181:
2161:
2088:
2059:
2011:
1984:{\displaystyle -T}
1981:
1955:
1833:
1815:
1765:
1747:
1701:
1671:
1631:
1605:
1585:
1562:
1535:
1501:
1436:
1385:
1362:
1300:
1272:
1252:
1225:
1210:
1190:
1147:
1122:chemical potential
1093:
1063:
1032:
1014:
993:
965:
925:
896:
868:
840:
814:
787:
760:
729:
712:van 't Hoff factor
697:
669:
629:
605:
578:
550:
517:
515:
451:
423:
390:
356:
328:
291:
271:
244:
220:
205:
188:
164:
134:
109:
53:physical chemistry
3589:
3588:
3218:
3217:
3139:Rotary evaporator
3063:Theoretical plate
2940:10.1021/jp806035w
2828:10.1021/ed072p204
2238:{\displaystyle i}
2176:
2157:
2052:
2005:
1873:
1696:
1645:
1619:
1588:{\displaystyle i}
1496:
1450:
1399:
1355:
1334:
1303:{\displaystyle i}
1275:{\displaystyle i}
1090:
1057:
1039:
1021:
1000:
987:
972:
956:
932:
890:
875:
862:
847:
811:
784:
763:{\displaystyle p}
732:analogous to the
691:
676:
660:
636:
612:
572:
557:
514:
504:
491:
473:
458:
445:
430:
378:
363:
350:
335:
294:{\displaystyle i}
247:{\displaystyle i}
191:{\displaystyle i}
178:of the component
3634:
3486:Solubility chart
3313:Phase separation
3273:Aqueous solution
3245:
3238:
3231:
3222:
3221:
3085:
3068:Partial pressure
3017:
3010:
3003:
2994:
2993:
2971:
2968:
2962:
2961:
2951:
2933:
2918:J. Phys. Chem. B
2909:
2903:
2896:
2890:
2889:
2872:
2866:
2865:
2847:
2841:
2840:
2830:
2797:
2791:
2776:
2770:
2769:
2740:
2729:
2715:
2709:
2708:
2679:
2670:
2669:
2650:
2600:Antoine equation
2568:carbon disulfide
2460:
2458:
2457:
2452:
2446:
2441:
2432:
2431:
2422:
2421:
2406:
2405:
2390:
2389:
2367:
2365:
2364:
2359:
2357:
2356:
2337:
2335:
2334:
2329:
2327:
2326:
2292:Non-ideal mixing
2275:
2273:
2272:
2267:
2265:
2264:
2244:
2242:
2241:
2236:
2220:
2218:
2217:
2212:
2210:
2209:
2190:
2188:
2187:
2182:
2177:
2174:
2169:
2160:
2159:
2158:
2155:
2149:
2148:
2138:
2133:
2132:
2097:
2095:
2094:
2089:
2068:
2066:
2065:
2060:
2050:
2020:
2018:
2017:
2012:
2007:
2006:
2003:
1990:
1988:
1987:
1982:
1964:
1962:
1961:
1956:
1948:
1947:
1932:
1931:
1919:
1918:
1903:
1902:
1875:
1874:
1871:
1842:
1840:
1839:
1834:
1828:
1823:
1814:
1813:
1801:
1800:
1774:
1772:
1771:
1766:
1760:
1755:
1746:
1745:
1733:
1732:
1710:
1708:
1707:
1702:
1697:
1695:
1694:
1684:
1679:
1670:
1652:
1647:
1646:
1643:
1626:
1621:
1620:
1617:
1594:
1592:
1591:
1586:
1571:
1569:
1568:
1563:
1561:
1560:
1544:
1542:
1541:
1536:
1534:
1533:
1510:
1508:
1507:
1502:
1497:
1495:
1494:
1485:
1484:
1475:
1457:
1452:
1451:
1448:
1432:
1431:
1406:
1401:
1400:
1397:
1371:
1369:
1368:
1363:
1358:
1357:
1356:
1353:
1337:
1336:
1335:
1332:
1309:
1307:
1306:
1301:
1281:
1279:
1278:
1273:
1261:
1259:
1258:
1253:
1251:
1250:
1234:
1232:
1231:
1226:
1223:
1218:
1199:
1197:
1196:
1191:
1186:
1185:
1160:
1155:
1143:
1142:
1102:
1100:
1099:
1094:
1092:
1091:
1088:
1072:
1070:
1069:
1064:
1059:
1058:
1055:
1045:
1040:
1037:
1027:
1022:
1019:
1006:
1001:
998:
989:
988:
985:
978:
973:
970:
958:
957:
954:
938:
933:
930:
905:
903:
902:
897:
892:
891:
888:
881:
876:
873:
864:
863:
860:
853:
848:
845:
823:
821:
820:
815:
813:
812:
809:
796:
794:
793:
788:
786:
785:
782:
769:
767:
766:
761:
706:
704:
703:
698:
693:
692:
689:
682:
677:
674:
662:
661:
658:
642:
637:
634:
618:
613:
610:
587:
585:
584:
579:
574:
573:
570:
563:
558:
555:
526:
524:
523:
518:
516:
513:
506:
505:
502:
493:
492:
489:
482:
475:
474:
471:
464:
459:
456:
447:
446:
443:
436:
431:
428:
421:
399:
397:
396:
391:
380:
379:
376:
369:
364:
361:
352:
351:
348:
341:
336:
333:
300:
298:
297:
292:
280:
278:
277:
272:
270:
269:
253:
251:
250:
245:
229:
227:
226:
221:
218:
213:
197:
195:
194:
189:
176:partial pressure
173:
171:
170:
165:
163:
162:
143:
141:
140:
135:
133:
132:
122:
117:
105:
104:
65:partial pressure
50:
49:
46:
45:
42:
39:
36:
33:
30:
3642:
3641:
3637:
3636:
3635:
3633:
3632:
3631:
3592:
3591:
3590:
3585:
3495:
3456:Solvation shell
3427:
3365:
3357:
3353:Miscibility gap
3338:Serial dilution
3333:Supersaturation
3283:Buffer solution
3254:
3249:
3219:
3214:
3153:
3117:
3086:
3077:
3053:Fenske equation
3026:
3021:
2975:
2974:
2969:
2965:
2931:10.1.1.560.3553
2910:
2906:
2897:
2893:
2887:
2873:
2869:
2862:
2848:
2844:
2798:
2794:
2778:Rock, Peter A.
2777:
2773:
2766:
2744:Chao, Kwang-Chu
2741:
2732:
2716:
2712:
2680:
2673:
2651:
2644:
2639:
2634:
2595:
2585:
2545:
2538:
2531:
2519:
2515:
2507:
2495:
2467:
2442:
2437:
2427:
2423:
2417:
2413:
2395:
2391:
2385:
2381:
2379:
2376:
2375:
2352:
2348:
2346:
2343:
2342:
2316:
2312:
2310:
2307:
2306:
2294:
2260:
2256:
2254:
2251:
2250:
2230:
2227:
2226:
2205:
2201:
2199:
2196:
2195:
2170:
2165:
2154:
2150:
2144:
2140:
2139:
2137:
2128:
2124:
2122:
2119:
2118:
2077:
2074:
2073:
2033:
2030:
2029:
2002:
1998:
1996:
1993:
1992:
1973:
1970:
1969:
1943:
1939:
1927:
1923:
1914:
1910:
1898:
1894:
1870:
1866:
1864:
1861:
1860:
1849:
1824:
1819:
1809:
1805:
1796:
1792:
1790:
1787:
1786:
1756:
1751:
1741:
1737:
1728:
1724:
1722:
1719:
1718:
1690:
1686:
1680:
1675:
1669:
1648:
1642:
1635:
1622:
1616:
1609:
1603:
1600:
1599:
1580:
1577:
1576:
1556:
1552:
1550:
1547:
1546:
1529:
1525:
1523:
1520:
1519:
1490:
1486:
1480:
1476:
1474:
1453:
1447:
1440:
1427:
1423:
1402:
1396:
1389:
1383:
1380:
1379:
1352:
1345:
1341:
1331:
1324:
1320:
1318:
1315:
1314:
1295:
1292:
1291:
1267:
1264:
1263:
1246:
1242:
1240:
1237:
1236:
1219:
1214:
1208:
1205:
1204:
1181:
1177:
1156:
1151:
1138:
1134:
1132:
1129:
1128:
1109:
1087:
1083:
1081:
1078:
1077:
1054:
1050:
1041:
1036:
1023:
1018:
1002:
997:
984:
980:
974:
969:
953:
949:
934:
929:
917:
914:
913:
887:
883:
877:
872:
859:
855:
849:
844:
832:
829:
828:
808:
804:
802:
799:
798:
781:
777:
775:
772:
771:
755:
752:
751:
720:
688:
684:
678:
673:
657:
653:
638:
633:
614:
609:
594:
591:
590:
569:
565:
559:
554:
542:
539:
538:
501:
497:
488:
484:
483:
470:
466:
460:
455:
442:
438:
432:
427:
422:
419:
411:
408:
407:
375:
371:
365:
360:
347:
343:
337:
332:
320:
317:
316:
286:
283:
282:
265:
261:
259:
256:
255:
239:
236:
235:
214:
209:
203:
200:
199:
183:
180:
179:
158:
154:
152:
149:
148:
128:
124:
118:
113:
100:
96:
94:
91:
90:
27:
23:
17:
12:
11:
5:
3640:
3630:
3629:
3624:
3619:
3614:
3609:
3604:
3587:
3586:
3584:
3583:
3578:
3573:
3568:
3563:
3558:
3553:
3548:
3543:
3538:
3533:
3528:
3523:
3521:Protic solvent
3518:
3513:
3505:
3503:
3497:
3496:
3494:
3493:
3488:
3483:
3478:
3473:
3468:
3466:Lattice energy
3463:
3458:
3453:
3448:
3443:
3437:
3435:
3429:
3428:
3426:
3425:
3420:
3415:
3410:
3405:
3400:
3395:
3390:
3385:
3380:
3375:
3369:
3367:
3359:
3358:
3356:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3318:Eutectic point
3315:
3310:
3305:
3300:
3295:
3290:
3285:
3280:
3278:Solid solution
3275:
3270:
3268:Ideal solution
3264:
3262:
3256:
3255:
3248:
3247:
3240:
3233:
3225:
3216:
3215:
3213:
3212:
3207:
3202:
3197:
3192:
3187:
3182:
3177:
3172:
3167:
3161:
3159:
3155:
3154:
3152:
3151:
3146:
3141:
3136:
3131:
3125:
3123:
3119:
3118:
3116:
3115:
3110:
3105:
3100:
3094:
3092:
3088:
3087:
3080:
3078:
3076:
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3034:
3032:
3028:
3027:
3020:
3019:
3012:
3005:
2997:
2991:
2990:
2983:
2973:
2972:
2963:
2904:
2891:
2885:
2867:
2861:978-0471687573
2860:
2842:
2813:(3): 204â205.
2807:J. Chem. Educ.
2792:
2771:
2764:
2730:
2710:
2671:
2662:Comptes rendus
2641:
2640:
2638:
2635:
2633:
2632:
2627:
2622:
2617:
2615:DĂŒhring's rule
2612:
2607:
2602:
2596:
2594:
2591:
2583:
2544:
2541:
2536:
2529:
2517:
2513:
2505:
2494:
2491:
2466:
2465:Real solutions
2463:
2462:
2461:
2450:
2445:
2440:
2436:
2430:
2426:
2420:
2416:
2412:
2409:
2404:
2401:
2398:
2394:
2388:
2384:
2355:
2351:
2325:
2322:
2319:
2315:
2293:
2290:
2263:
2259:
2234:
2208:
2204:
2192:
2191:
2180:
2173:
2168:
2164:
2153:
2147:
2143:
2136:
2131:
2127:
2087:
2084:
2081:
2058:
2055:
2049:
2046:
2043:
2040:
2037:
2010:
2001:
1980:
1977:
1966:
1965:
1954:
1951:
1946:
1942:
1938:
1935:
1930:
1926:
1922:
1917:
1913:
1909:
1906:
1901:
1897:
1893:
1890:
1887:
1884:
1881:
1878:
1869:
1848:
1845:
1844:
1843:
1832:
1827:
1822:
1818:
1812:
1808:
1804:
1799:
1795:
1776:
1775:
1764:
1759:
1754:
1750:
1744:
1740:
1736:
1731:
1727:
1712:
1711:
1700:
1693:
1689:
1683:
1678:
1674:
1668:
1665:
1662:
1659:
1656:
1651:
1641:
1638:
1634:
1630:
1625:
1615:
1612:
1608:
1584:
1559:
1555:
1532:
1528:
1512:
1511:
1500:
1493:
1489:
1483:
1479:
1473:
1470:
1467:
1464:
1461:
1456:
1446:
1443:
1439:
1435:
1430:
1426:
1422:
1419:
1416:
1413:
1410:
1405:
1395:
1392:
1388:
1373:
1372:
1361:
1351:
1348:
1344:
1340:
1330:
1327:
1323:
1299:
1271:
1249:
1245:
1222:
1217:
1213:
1201:
1200:
1189:
1184:
1180:
1176:
1173:
1170:
1167:
1164:
1159:
1154:
1150:
1146:
1141:
1137:
1108:
1105:
1086:
1074:
1073:
1062:
1053:
1049:
1044:
1035:
1031:
1026:
1017:
1013:
1010:
1005:
996:
992:
983:
977:
968:
964:
961:
952:
948:
945:
942:
937:
928:
924:
921:
907:
906:
895:
886:
880:
871:
867:
858:
852:
843:
839:
836:
807:
780:
759:
719:
716:
708:
707:
696:
687:
681:
672:
668:
665:
656:
652:
649:
646:
641:
632:
628:
625:
622:
617:
608:
604:
601:
598:
588:
577:
568:
562:
553:
549:
546:
528:
527:
512:
509:
500:
496:
487:
481:
478:
469:
463:
454:
450:
441:
435:
426:
418:
415:
401:
400:
389:
386:
383:
374:
368:
359:
355:
346:
340:
331:
327:
324:
290:
268:
264:
243:
217:
212:
208:
187:
161:
157:
145:
144:
131:
127:
121:
116:
112:
108:
103:
99:
57:thermodynamics
15:
9:
6:
4:
3:
2:
3639:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3599:
3597:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3511:
3507:
3506:
3504:
3502:
3498:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3449:
3447:
3444:
3442:
3439:
3438:
3436:
3434:
3430:
3424:
3421:
3419:
3416:
3414:
3411:
3409:
3408:Mass fraction
3406:
3404:
3403:Mole fraction
3401:
3399:
3396:
3394:
3391:
3389:
3386:
3384:
3381:
3379:
3376:
3374:
3371:
3370:
3368:
3364:
3363:Concentration
3360:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3308:Phase diagram
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3288:FloryâHuggins
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3265:
3263:
3261:
3257:
3253:
3246:
3241:
3239:
3234:
3232:
3227:
3226:
3223:
3211:
3208:
3206:
3203:
3201:
3198:
3196:
3193:
3191:
3188:
3186:
3183:
3181:
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3162:
3160:
3156:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3126:
3124:
3120:
3114:
3113:Spinning cone
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3095:
3093:
3089:
3084:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3035:
3033:
3029:
3025:
3018:
3013:
3011:
3006:
3004:
2999:
2998:
2995:
2988:
2984:
2981:
2977:
2976:
2967:
2959:
2955:
2950:
2945:
2941:
2937:
2932:
2927:
2923:
2919:
2915:
2908:
2901:
2895:
2888:
2886:0-07-310445-0
2882:
2878:
2871:
2863:
2857:
2853:
2846:
2838:
2834:
2829:
2824:
2820:
2816:
2812:
2809:
2808:
2803:
2796:
2789:
2785:
2781:
2775:
2767:
2765:9780824753627
2761:
2757:
2753:
2749:
2745:
2739:
2737:
2735:
2727:
2726:0-19-856556-9
2723:
2719:
2714:
2706:
2702:
2698:
2695:(in French).
2694:
2693:
2688:
2684:
2683:Raoult, F.-M.
2678:
2676:
2667:
2664:(in French).
2663:
2659:
2655:
2654:Raoult, F.-M.
2649:
2647:
2642:
2631:
2628:
2626:
2625:Köhler theory
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2605:Atomic theory
2603:
2601:
2598:
2597:
2590:
2589:is positive.
2588:
2581:
2577:
2573:
2569:
2565:
2561:
2557:
2553:
2548:
2540:
2539:is negative.
2535:
2527:
2523:
2522:hydrogen bond
2511:
2503:
2498:
2487:
2482:
2478:
2476:
2472:
2448:
2443:
2438:
2434:
2428:
2424:
2418:
2414:
2410:
2407:
2402:
2399:
2396:
2392:
2386:
2382:
2374:
2373:
2372:
2369:
2353:
2349:
2341:
2323:
2320:
2317:
2313:
2304:
2300:
2299:ideal-gas law
2289:
2287:
2283:
2279:
2278:mole fraction
2261:
2257:
2248:
2232:
2225:of component
2224:
2223:mole fraction
2206:
2202:
2178:
2171:
2166:
2162:
2151:
2145:
2141:
2134:
2129:
2125:
2117:
2116:
2115:
2113:
2107:
2105:
2101:
2085:
2079:
2070:
2053:
2047:
2044:
2038:
2035:
2027:
2022:
2008:
1978:
1975:
1952:
1944:
1940:
1936:
1933:
1928:
1924:
1920:
1915:
1911:
1907:
1904:
1899:
1895:
1888:
1885:
1882:
1879:
1876:
1859:
1858:
1857:
1855:
1830:
1825:
1820:
1816:
1810:
1806:
1802:
1797:
1793:
1785:
1784:
1783:
1781:
1762:
1757:
1752:
1748:
1742:
1738:
1734:
1729:
1725:
1717:
1716:
1715:
1698:
1691:
1687:
1681:
1676:
1672:
1666:
1663:
1660:
1657:
1654:
1649:
1639:
1636:
1632:
1628:
1623:
1613:
1610:
1606:
1598:
1597:
1596:
1582:
1573:
1557:
1553:
1530:
1526:
1517:
1498:
1491:
1487:
1481:
1477:
1471:
1468:
1465:
1462:
1459:
1454:
1444:
1441:
1437:
1433:
1428:
1424:
1420:
1417:
1414:
1411:
1408:
1403:
1393:
1390:
1386:
1378:
1377:
1376:
1359:
1349:
1346:
1342:
1338:
1328:
1325:
1321:
1313:
1312:
1311:
1297:
1289:
1284:
1269:
1247:
1243:
1220:
1215:
1211:
1187:
1182:
1178:
1174:
1171:
1168:
1165:
1162:
1157:
1152:
1148:
1144:
1139:
1135:
1127:
1126:
1125:
1123:
1119:
1114:
1104:
1084:
1060:
1051:
1042:
1033:
1029:
1024:
1015:
1008:
1003:
994:
990:
981:
975:
966:
962:
950:
946:
943:
935:
926:
922:
919:
912:
911:
910:
893:
884:
878:
869:
865:
856:
850:
841:
837:
834:
827:
826:
825:
805:
778:
757:
748:
746:
741:
739:
735:
734:ideal gas law
724:
715:
713:
694:
685:
679:
670:
666:
654:
650:
647:
639:
630:
626:
623:
620:
615:
606:
602:
599:
589:
575:
566:
560:
551:
547:
544:
537:
536:
535:
533:
510:
507:
498:
494:
485:
479:
476:
467:
461:
452:
448:
439:
433:
424:
416:
413:
406:
405:
404:
387:
384:
381:
372:
366:
357:
353:
344:
338:
329:
325:
322:
315:
314:
313:
311:
307:
302:
288:
266:
262:
241:
233:
215:
210:
206:
185:
177:
159:
155:
129:
125:
119:
114:
110:
106:
101:
97:
89:
88:
87:
84:
82:
78:
77:mole fraction
74:
70:
69:ideal mixture
66:
62:
58:
54:
48:
21:
3602:Distillation
3471:Raoult's law
3470:
3423:Ternary plot
3418:Mixing ratio
3210:Vacuum-based
3043:Dalton's law
3038:Raoult's law
3037:
3024:Distillation
2986:
2985:E. B. Smith
2979:
2966:
2921:
2917:
2907:
2899:
2894:
2876:
2870:
2851:
2845:
2810:
2805:
2795:
2779:
2774:
2751:
2717:
2713:
2696:
2690:
2668:: 1430â1433.
2665:
2661:
2586:
2549:
2546:
2533:
2499:
2496:
2468:
2370:
2295:
2286:distillation
2281:
2246:
2193:
2112:Dalton's Law
2108:
2099:
2071:
2023:
1967:
1850:
1847:Ideal mixing
1777:
1713:
1574:
1513:
1374:
1285:
1202:
1110:
1075:
908:
749:
742:
730:
709:
529:
402:
310:Dalton's law
303:
146:
85:
72:
20:Raoult's law
19:
18:
3576:Lyonium ion
3491:Miscibility
3476:Henry's law
3205:Steam-based
3200:Salt-effect
3175:Destructive
2699:(1): 5â20.
2620:Henry's law
2104:Henry's law
1288:equilibrium
727:components.
306:equilibrium
3596:Categories
3571:Amphiphile
3566:Lipophilic
3561:Hydrophile
3556:Hydrophobe
3433:Solubility
3328:Saturation
3298:Suspension
3190:Fractional
3185:Extractive
3165:Azeotropic
3158:Techniques
3031:Principles
2788:1891389327
2637:References
2630:Solubility
2576:chloroform
2502:chloroform
2486:azeotropes
718:Principles
3627:Solutions
3581:Lyate ion
3536:Solvation
3451:Solvation
3393:Normality
3170:Catalytic
3134:Kugelrohr
2926:CiteSeerX
2756:CRC Press
2610:Azeotrope
2526:azeotrope
2444:⋆
2425:γ
2393:ϕ
2350:γ
2314:ϕ
2282:gas phase
2172:⋆
2083:→
2039:∈
2000:Δ
1976:−
1937:
1908:
1868:Δ
1826:⋆
1780:pressures
1758:⋆
1692:⊖
1682:⋆
1667:
1650:⊖
1633:μ
1624:⋆
1607:μ
1558:⊖
1492:⊖
1472:
1455:⊖
1438:μ
1421:
1404:⋆
1387:μ
1343:μ
1322:μ
1221:⋆
1212:μ
1175:
1158:⋆
1149:μ
1136:μ
1120:that the
1043:⋆
1030:−
1025:⋆
1004:⋆
976:⋆
947:−
936:⋆
879:⋆
851:⋆
680:⋆
651:−
640:⋆
621:−
616:⋆
597:Δ
561:⋆
532:evaporate
511:⋯
480:⋯
462:⋆
434:⋆
385:⋯
367:⋆
339:⋆
216:⋆
120:⋆
3551:Polarity
3510:Category
3398:Molality
3260:Solution
3195:Reactive
2958:18855462
2837:95146940
2685:(1889).
2656:(1886).
2593:See also
2564:methanol
2475:cohesive
2471:adhesive
2247:solution
1516:fugacity
738:isotopic
3501:Solvent
3303:Colloid
3293:Mixture
3129:Alembic
2949:2646412
2815:Bibcode
2580:glycine
2572:acetone
2560:benzene
2552:ethanol
2510:acetone
2280:in the
2276:is its
2245:in the
2221:is the
2100:solvent
230:is the
174:is the
73:liquids
3048:Reflux
2956:
2946:
2928:
2883:
2858:
2835:
2786:
2762:
2724:
2574:, (4)
2566:, (3)
2558:, (2)
2508:) and
2249:, and
2194:where
2051:
1203:where
1118:deduce
254:, and
147:where
81:solute
3323:Alloy
3149:Still
2833:S2CID
2556:water
2504:(CHCl
2156:total
2954:PMID
2881:ISBN
2856:ISBN
2784:ISBN
2760:ISBN
2722:ISBN
2570:and
2562:and
2554:and
2516:COCH
797:and
3180:Dry
2944:PMC
2936:doi
2922:112
2823:doi
2701:doi
2666:104
2584:mix
2537:mix
2512:(CH
2004:mix
1872:mix
1644:vap
1618:liq
1449:vap
1398:liq
1354:vap
1333:liq
71:of
3598::
2952:.
2942:.
2934:.
2920:.
2916:.
2831:.
2821:.
2811:72
2804:.
2754:.
2733:^
2674:^
2645:^
2288:.
2114::
2106:.
1934:ln
1905:ln
1856::
1664:ln
1572:.
1518:,
1469:ln
1418:ln
1172:ln
38:uË
35:ÉË
3512:)
3508:(
3244:e
3237:t
3230:v
3016:e
3009:t
3002:v
2960:.
2938::
2864:.
2839:.
2825::
2817::
2790:.
2768:.
2728:.
2707:.
2703::
2697:8
2587:H
2534:H
2530:3
2518:3
2514:3
2506:3
2449:.
2439:i
2435:p
2429:i
2419:i
2415:x
2411:=
2408:p
2403:i
2400:,
2397:p
2387:i
2383:y
2354:i
2324:i
2321:,
2318:p
2305:(
2262:i
2258:y
2233:i
2207:i
2203:x
2179:,
2167:i
2163:p
2152:p
2146:i
2142:y
2135:=
2130:i
2126:x
2086:1
2080:x
2057:]
2054:1
2048:,
2045:0
2042:[
2036:x
2009:H
1979:T
1953:.
1950:)
1945:2
1941:x
1929:2
1925:x
1921:+
1916:1
1912:x
1900:1
1896:x
1892:(
1889:T
1886:R
1883:n
1880:=
1877:G
1831:.
1821:i
1817:p
1811:i
1807:x
1803:=
1798:i
1794:p
1763:.
1753:i
1749:f
1743:i
1739:x
1735:=
1730:i
1726:f
1699:.
1688:p
1677:i
1673:f
1661:T
1658:R
1655:+
1640:,
1637:i
1629:=
1614:,
1611:i
1583:i
1554:p
1531:i
1527:f
1499:,
1488:p
1482:i
1478:f
1466:T
1463:R
1460:+
1445:,
1442:i
1434:=
1429:i
1425:x
1415:T
1412:R
1409:+
1394:,
1391:i
1360:.
1350:,
1347:i
1339:=
1329:,
1326:i
1298:i
1270:i
1248:i
1244:x
1216:i
1188:,
1183:i
1179:x
1169:T
1166:R
1163:+
1153:i
1145:=
1140:i
1089:B
1085:x
1061:.
1056:B
1052:x
1048:)
1038:A
1034:p
1020:B
1016:p
1012:(
1009:+
999:A
995:p
991:=
986:B
982:x
971:B
967:p
963:+
960:)
955:B
951:x
944:1
941:(
931:A
927:p
923:=
920:p
894:.
889:B
885:x
874:B
870:p
866:+
861:A
857:x
846:A
842:p
838:=
835:p
810:B
806:p
783:A
779:p
758:p
695:.
690:B
686:x
675:A
671:p
667:=
664:)
659:A
655:x
648:1
645:(
635:A
631:p
627:=
624:p
611:A
607:p
603:=
600:p
576:,
571:A
567:x
556:A
552:p
548:=
545:p
508:+
503:B
499:n
495:+
490:A
486:n
477:+
472:B
468:n
457:B
453:p
449:+
444:A
440:n
429:A
425:p
417:=
414:p
388:.
382:+
377:B
373:x
362:B
358:p
354:+
349:A
345:x
334:A
330:p
326:=
323:p
289:i
267:i
263:x
242:i
211:i
207:p
186:i
160:i
156:p
130:i
126:x
115:i
111:p
107:=
102:i
98:p
47:/
44:z
41:l
32:r
29:Ë
26:/
22:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
