133:
36:
1613:
In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze. Re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying. At the lower freezing point, the vapor
840:
These properties are colligative in systems where the solute is essentially confined to the liquid phase. Boiling point elevation (like vapor pressure lowering) is colligative for non-volatile solutes where the solute presence in the gas phase is negligible. Freezing point depression is colligative
192:
Only properties which result from the dissolution of a nonvolatile solute in a volatile liquid solvent are considered. They are essentially solvent properties which are changed by the presence of the solute. The solute particles displace some solvent molecules in the liquid phase and thereby reduce
1042:
The boiling point is the temperature at which there is equilibrium between liquid and gas phases. At the boiling point, the number of gas molecules condensing to liquid equals the number of liquid molecules evaporating to gas. Adding a solute dilutes the concentration of the liquid molecules and
828:
so that solvent molecules have less tendency to move to the gas or solid phases. As a result, liquid solutions slightly above the solvent boiling point at a given pressure become stable, which means that the boiling point increases. Similarly, liquid solutions slightly below the solvent freezing
260:
Colligative properties are studied mostly for dilute solutions, whose behavior may be approximated as that of an ideal solution. In fact, all of the properties listed above are colligative only in the dilute limit: at higher concentrations, the freezing point depression, boiling point elevation,
1478:
1581:
1007:
682:
1223:
1614:
pressure of the liquid is equal to the vapor pressure of the corresponding solid, and the chemical potentials of the two phases are equal as well. The equality of chemical potentials permits the evaluation of the cryoscopic constant as
384:
201:. This indicates that all colligative properties have a common feature, namely that they are related only to the number of solute molecules relative to the number of solvent molecules and not to the nature of the solute.
1720:, which allows the passage of solvent molecules but not of solute particles. If the two phases are at the same initial pressure, there is a net transfer of solvent across the membrane into the solution known as
281:
is the pressure exerted by a vapor in thermodynamic equilibrium with its solid or liquid state. The vapor pressure of a solvent is lowered when a non-volatile solute is dissolved in it to form a solution.
189:, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.
1689:
1303:
777:
550:
1377:
208:
1483:
909:
1983:
562:
193:
the concentration of solvent and increase its entropy, so that the colligative properties are independent of the nature of the solute. The word colligative is derived from the Latin
498:
1075:
418:
808:
is calculated with moles of solute i times initial moles and moles of solvent same as initial moles of solvent before dissociation. The measured colligative properties show that
296:
2052:
properties such as mass, which are the sums of properties of the constituent particles and therefore depend also on the composition (or molecular formula) of the solute, and
1365:
886:
806:
451:
1833:
1795:
1921:
2025:
1853:
712:
1716:
The osmotic pressure of a solution is the difference in pressure between the solution and the pure liquid solvent when the two are in equilibrium across a
1367:) of a pure solvent is lowered by the addition of a solute which is insoluble in the solid solvent, and the measurement of this difference is called
253:
which cannot be studied by other means. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of
2125:
1043:
reduces the rate of evaporation. To compensate for this and re-attain equilibrium, the boiling point occurs at a higher temperature.
261:
vapor pressure elevation or depression, and osmotic pressure are all dependent on the chemical nature of the solvent and the solute.
100:
72:
1617:
1231:
53:
899:
The boiling point of a pure solvent is increased by the addition of a non-volatile solute, and the elevation can be measured by
2046:
properties, which depend only on solute concentration and temperature and are independent of the nature of the solute particles
161:
in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for
727:
79:
2174:
2081:
17:
86:
2135:
1473:{\displaystyle \Delta T_{\rm {f}}=T_{\rm {f,{\text{solution}}}}-T_{\rm {f,{\text{pure solvent}}}}=-i\cdot K_{f}\cdot m}
503:
1576:{\displaystyle \Delta T_{\rm {f}}=T_{\rm {f,{\text{pure solvent}}}}-T_{\rm {f,{\text{solution}}}}=i\cdot K_{f}\cdot m}
1002:{\displaystyle \Delta T_{\rm {b}}=T_{\rm {b,{\text{solution}}}}-T_{\rm {b,{\text{pure solvent}}}}=i\cdot K_{b}\cdot m}
119:
677:{\displaystyle \Delta p=p_{\rm {A}}^{\star }-p=p_{\rm {A}}^{\star }(1-x_{\rm {A}})=p_{\rm {A}}^{\star }x_{\rm {B}}}
234:
For a given solute-solvent mass ratio, all colligative properties are inversely proportional to solute molar mass.
68:
1929:
1732:
274:
1069:
of the solvent in the solution phase equals the chemical potential in the pure vapor phase above the solution.
177:, etc. The assumption that solution properties are independent of nature of solute particles is exact only for
57:
1218:{\displaystyle \mu _{A}(T_{b})=\mu _{A}^{\star }(T_{b})+RT\ln x_{A}\ =\mu _{A}^{\star }(g,1\,\mathrm {atm} ),}
463:
2277:
824:
Addition of solute to form a solution stabilizes the solvent in the liquid phase, and lowers the solvent's
1724:. The process stops and equilibrium is attained when the pressure difference equals the osmotic pressure.
389:
2272:
132:
1333:
834:
223:
1995:
As with the other colligative properties, this equation is a consequence of the equality of solvent
1727:
Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist
93:
1321:
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1341:
862:
850:
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782:
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218:
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2076:
Colligative properties of
Solutions" General Chemistry Mill Valley: Library of Congress, 2011.
1717:
1028:
714:, which represents the true number of solute particles for each formula unit. For example, the
1880:
1017:
692:
174:
1765:
237:
Measurement of colligative properties for a dilute solution of a non-ionized solute such as
1999:
of the two phases in equilibrium. In this case the phases are the pure solvent at pressure
1892:
1743:
of a dilute solution at constant temperature is directly proportional to its concentration.
151:
2010:
1838:
724:
dissociates into one Mg ion and two Cl ions, so that if ionization is complete, i = 3 and
379:{\displaystyle p=p_{\rm {A}}^{\star }x_{\rm {A}}+p_{\rm {B}}^{\star }x_{\rm {B}}+\cdots ,}
8:
1887:
1595:
2202:
1746:
The osmotic pressure of a solution is directly proportional to its absolute temperature.
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2236:
Logic, History, and the
Chemistry Textbook I. Does Chemistry Have a Logical Structure?
1996:
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T. Engel and P. Reid, Physical
Chemistry (Pearson Benjamin Cummings 2006) p.204-5
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1728:
813:
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212:
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properties, which depend further on the molecular structure of the given solute.
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for most solutes since very few solutes dissolve appreciably in solid solvents.
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1751:
1047:
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278:
182:
178:
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The osmotic pressure is proportional to the concentration of solute particles
888:) at which the vapor pressure of the liquid equals the external pressure. The
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154:
that depend on the ratio of the number of solute particles to the number of
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900:
27:
Properties of solutions that depend only on the number of solute particles
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are proportional to the lowering of vapor pressure in a dilute solution.
829:
point become stable meaning that the freezing point decreases. Both the
1310:
246:
1607:
186:
143:
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in solution, then the number of moles of solute is increased by the
460:
For a solution with a solvent (A) and one non-volatile solute (B),
35:
2035:
The word colligative (Latin: co, ligare) was introduced in 1891 by
1036:
250:
245:
in water or another solvent can lead to determinations of relative
170:
166:
158:
1061:
condition for liquid-vapor equilibrium. At the boiling point, the
273:
is a substance in a gaseous state at a temperature lower than its
1721:
242:
155:
1598:(equal to 1.86 °C kg/mol for the freezing point of water),
1606:
the molality (in mol/kg). This predicts the melting of ice by
1031:
of the solvent (equal to 0.512 °C kg/mol for water), and
2251:
Theory of
Solutions: A Knowledge of the Laws of Solutions ...
2039:. Ostwald classified solute properties in three categories:
1228:
The asterisks indicate pure phases. This leads to the result
859:
of a liquid at a given external pressure is the temperature (
270:
1684:{\displaystyle K_{f}=RMT_{f}^{2}/\Delta _{\mathrm {fus} }H}
1298:{\displaystyle K_{b}=RMT_{b}^{2}/\Delta H_{\mathrm {vap} }}
238:
844:
1327:
772:{\displaystyle \Delta p=p_{\rm {A}}^{\star }x_{\rm {B}}}
684:, which is proportional to the mole fraction of solute.
264:
2013:
1932:
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137:
Freezing point depression and boiling point elevation
819:
60:. Unsourced material may be challenged and removed.
2203:"Van't Hoff's Laws of Osmotic Pressure - QS Study"
2019:
1977:
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544:
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412:
378:
1886:The osmotic pressure is then proportional to the
545:{\displaystyle p=p_{\rm {A}}^{\star }x_{\rm {A}}}
2259:
892:is the boiling point at a pressure equal to 1
2130:(3rd ed.). Addison-Wesley. p. 281.
289:, the equilibrium vapor pressure is given by
2234:W.B. Jensen, J. Chem. Educ. 75, 679 (1998)
1978:{\displaystyle \Pi ={\frac {nRTi}{V}}=cRTi}
2123:
2088:
1992:and is therefore a colligative property.
1797:, has as an analogue for ideal solutions
1197:
120:Learn how and when to remove this message
131:
2188:
2186:
14:
2260:
845:Boiling point elevation (ebullioscopy)
493:{\displaystyle p_{\rm {B}}^{\star }=0}
1328:Freezing point depression (cryoscopy)
2183:
2156:
2154:
2003:and the solution at total pressure (
1046:If the solution is assumed to be an
413:{\displaystyle p_{\rm {i}}^{\star }}
185:properties analogous to those of an
58:adding citations to reliable sources
29:
2163:Chemistry; Structure and Properties
2160:
1758:for gases. Similarly, the combined
1705:
265:Relative lowering of vapor pressure
249:, both for small molecules and for
209:Relative lowering of vapor pressure
181:, which are solutions that exhibit
24:
2014:
1933:
1863:is the number of moles of solute;
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1804:
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1205:
1202:
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607:
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519:
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457:of the component in the solution.
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312:
25:
2289:
2151:
204:Colligative properties include:
820:Boiling point and freezing point
34:
2240:
2114:(Benjamin/Cummings 1982), p.196
1602:is the van 't Hoff factor, and
812:is somewhat less than 3 due to
45:needs additional citations for
2228:
2219:
2195:
2124:Castellan, Gilbert W. (1983).
2117:
2101:
2096:Applications of Thermodynamics
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1480:(which can also be written as
1209:
1185:
1136:
1123:
1102:
1089:
639:
618:
13:
1:
2249:, Circulation 21, 808 (1960)
2062:
1875:is absolute temperature; and
424:component (i= A, B, ...) and
420:is the vapor pressure of the
2165:(Textbook.) (2nd ed.).
559:relative to pure solvent is
224:Depression of freezing point
7:
1360:{\displaystyle T_{\rm {f}}}
881:{\displaystyle T_{\rm {b}}}
801:{\displaystyle x_{\rm {B}}}
446:{\displaystyle x_{\rm {i}}}
10:
2294:
2074:McQuarrie, Donald, et al.
2030:
1828:{\displaystyle \Pi V=nRTi}
1709:
1331:
1057:can be evaluated from the
848:
219:Elevation of boiling point
1334:Freezing point depression
835:freezing point depression
2161:Tro, Nivaldo J. (2018).
1322:enthalpy of vaporization
150:are those properties of
69:"Colligative properties"
1750:These are analogous to
851:Boiling point elevation
831:boiling point elevation
2021:
1979:
1917:
1849:
1829:
1791:
1790:{\displaystyle PV=nRT}
1731:and the Dutch chemist
1718:semipermeable membrane
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1577:
1474:
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1299:
1219:
1029:ebullioscopic constant
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882:
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708:
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414:
380:
165:of a solution such as
148:colligative properties
139:
2022:
1980:
1918:
1916:{\displaystyle c=n/V}
1855:is osmotic pressure;
1850:
1830:
1792:
1710:Further information:
1698:is the solvent molar
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1578:
1475:
1362:
1320:is the solvent molar
1300:
1220:
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175:normality (chemistry)
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2225:Engel and Reid p.207
2169:. pp. 563–566.
2020:{\displaystyle \Pi }
2011:
1930:
1893:
1848:{\displaystyle \Pi }
1839:
1801:
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1618:
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1371:. It is found that
1342:
1338:The freezing point (
1232:
1076:
910:
903:. It is found that
890:normal boiling point
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54:improve this article
18:Colligative property
2278:Amount of substance
1997:chemical potentials
1888:molar concentration
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1596:cryoscopic constant
1309:, M is the solvent
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555:The vapor pressure
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2127:Physical Chemistry
2112:Physical Chemistry
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1881:Van 't Hoff factor
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1663:
1658:
1652:
1647:
1643:
1639:
1636:
1633:
1628:
1624:
1590:
1585:
1584:
1572:
1569:
1564:
1560:
1556:
1553:
1550:
1539:
1536:
1531:
1527:
1516:
1513:
1508:
1504:
1498:
1493:
1489:
1469:
1466:
1461:
1457:
1453:
1450:
1447:
1444:
1433:
1430:
1425:
1421:
1410:
1407:
1402:
1398:
1392:
1387:
1383:
1353:
1348:
1332:Main article:
1329:
1326:
1317:
1291:
1288:
1285:
1280:
1276:
1272:
1266:
1261:
1257:
1253:
1250:
1247:
1242:
1238:
1226:
1225:
1214:
1211:
1207:
1204:
1201:
1196:
1193:
1190:
1187:
1182:
1177:
1173:
1169:
1161:
1157:
1153:
1150:
1147:
1144:
1141:
1138:
1133:
1129:
1125:
1120:
1115:
1111:
1107:
1104:
1099:
1095:
1091:
1086:
1082:
1066:
1054:
1048:ideal solution
1024:
1010:
1009:
998:
995:
990:
986:
982:
979:
976:
965:
962:
957:
953:
942:
939:
934:
930:
924:
919:
915:
874:
869:
849:Main article:
846:
843:
821:
818:
794:
789:
765:
760:
754:
748:
743:
739:
736:
733:
720:
703:
687:If the solute
670:
665:
659:
653:
648:
644:
641:
635:
630:
626:
623:
620:
615:
609:
604:
600:
597:
594:
589:
583:
578:
574:
571:
568:
538:
533:
527:
521:
516:
512:
509:
489:
486:
481:
475:
470:
439:
434:
407:
401:
396:
375:
372:
369:
363:
358:
352:
346:
341:
337:
331:
326:
320:
314:
309:
305:
302:
287:ideal solution
279:Vapor Pressure
275:critical point
266:
263:
257:taking place.
232:
231:
226:
221:
216:
199:bound together
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
2290:
2279:
2276:
2274:
2271:
2269:
2266:
2265:
2263:
2252:
2248:
2243:
2237:
2231:
2222:
2208:
2204:
2198:
2189:
2187:
2178:
2172:
2168:
2164:
2157:
2155:
2139:
2133:
2129:
2128:
2120:
2113:
2109:
2104:
2097:
2091:
2085:
2083:
2079:
2071:
2067:
2057:
2054:
2051:
2048:
2045:
2042:
2041:
2040:
2038:
2028:
2006:
2002:
1998:
1993:
1991:
1972:
1969:
1966:
1963:
1960:
1955:
1951:
1948:
1945:
1942:
1936:
1926:
1925:
1924:
1910:
1906:
1902:
1899:
1896:
1889:
1884:
1882:
1878:
1874:
1870:
1867:is the molar
1866:
1862:
1858:
1822:
1819:
1816:
1813:
1810:
1807:
1784:
1781:
1778:
1775:
1772:
1769:
1761:
1760:ideal gas law
1757:
1756:Charles's law
1753:
1745:
1742:
1738:
1737:
1736:
1734:
1730:
1725:
1723:
1719:
1713:
1703:
1701:
1697:
1678:
1656:
1650:
1645:
1641:
1637:
1634:
1631:
1626:
1622:
1611:
1609:
1605:
1601:
1597:
1593:
1570:
1567:
1562:
1558:
1554:
1551:
1548:
1537:
1529:
1525:
1514:
1506:
1502:
1491:
1467:
1464:
1459:
1455:
1451:
1448:
1445:
1442:
1431:
1423:
1419:
1408:
1400:
1396:
1385:
1374:
1373:
1372:
1370:
1346:
1335:
1325:
1323:
1316:
1312:
1308:
1278:
1270:
1264:
1259:
1255:
1251:
1248:
1245:
1240:
1236:
1212:
1194:
1191:
1188:
1180:
1175:
1171:
1167:
1159:
1155:
1151:
1148:
1145:
1142:
1139:
1131:
1127:
1118:
1113:
1109:
1105:
1097:
1093:
1084:
1080:
1072:
1071:
1070:
1064:
1060:
1059:thermodynamic
1053:
1049:
1044:
1040:
1038:
1034:
1030:
1023:
1019:
1015:
996:
993:
988:
984:
980:
977:
974:
963:
955:
951:
940:
932:
928:
917:
906:
905:
904:
902:
897:
895:
891:
867:
858:
857:boiling point
852:
842:
838:
836:
832:
827:
817:
815:
811:
787:
758:
752:
741:
737:
734:
723:
717:
701:
694:
690:
685:
663:
657:
646:
642:
628:
624:
621:
613:
602:
598:
595:
592:
587:
576:
572:
569:
558:
553:
531:
525:
514:
510:
507:
487:
484:
479:
468:
458:
456:
455:mole fraction
432:
423:
405:
394:
373:
370:
367:
356:
350:
339:
335:
324:
318:
307:
303:
300:
292:
288:
283:
280:
276:
272:
262:
258:
256:
252:
248:
244:
240:
235:
230:
227:
225:
222:
220:
217:
214:
210:
207:
206:
205:
202:
200:
196:
190:
188:
184:
183:thermodynamic
180:
176:
172:
168:
164:
163:concentration
160:
157:
153:
149:
145:
138:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
2250:
2242:
2235:
2230:
2221:
2210:. Retrieved
2206:
2197:
2162:
2141:. Retrieved
2126:
2119:
2111:
2108:K.J. Laidler
2103:
2095:
2090:
2075:
2070:
2055:
2049:
2043:
2034:
2004:
2000:
1994:
1989:
1987:
1885:
1876:
1872:
1869:gas constant
1864:
1860:
1856:
1749:
1726:
1715:
1695:
1612:
1603:
1599:
1588:
1586:
1519:pure solvent
1436:pure solvent
1368:
1337:
1314:
1227:
1051:
1045:
1041:
1032:
1021:
1013:
1011:
968:pure solvent
901:ebullioscopy
898:
889:
854:
839:
823:
809:
686:
556:
554:
459:
421:
291:Raoult's law
284:
268:
259:
255:dissociation
247:molar masses
236:
233:
213:Raoult's law
203:
198:
194:
191:
147:
141:
136:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
2207:qsstudy.com
2044:colligative
1752:Boyle's law
689:dissociates
2262:Categories
2247:H.W. Smith
2212:2022-03-08
2094:KL Kapoor
2063:References
1691:, where Δ
1311:molar mass
1020:as above,
195:colligatus
80:newspapers
2268:Solutions
2015:Π
1934:Π
1843:Π
1805:Π
1662:Δ
1608:road salt
1568:⋅
1555:⋅
1526:−
1488:Δ
1465:⋅
1452:⋅
1446:−
1420:−
1382:Δ
1369:cryoscopy
1275:Δ
1181:⋆
1172:μ
1152:
1119:⋆
1110:μ
1081:μ
994:⋅
981:⋅
952:−
914:Δ
753:⋆
732:Δ
658:⋆
625:−
614:⋆
593:−
588:⋆
567:Δ
526:⋆
480:⋆
406:⋆
371:⋯
351:⋆
319:⋆
187:ideal gas
159:particles
152:solutions
144:chemistry
2098:Volume 3
2050:additive
1923:, since
1835:, where
1542:solution
1413:solution
1037:molality
945:solution
833:and the
779:, where
557:lowering
251:polymers
197:meaning
171:molality
167:molarity
110:May 2010
2143:20 July
2031:History
1879:is the
1722:osmosis
1594:is the
1035:is the
1027:is the
1016:is the
453:is the
285:For an
243:glucose
156:solvent
94:scholar
2173:
2134:
2080:
1165:
386:where
96:
89:
82:
75:
67:
1587:Here
1313:and Δ
1012:Here
271:vapor
101:JSTOR
87:books
2171:ISBN
2145:2019
2132:ISBN
2078:ISBN
1754:and
1739:The
855:The
719:MgCl
500:and
422:pure
239:urea
73:news
2027:).
1693:fus
1318:vap
894:atm
293:as
241:or
142:In
56:by
2264::
2205:.
2185:^
2153:^
2007:+
1990:ci
1883:.
1762:,
1735::
1702:.
1610:.
1324:.
1149:ln
1050:,
896:.
816:.
552:.
277:.
269:A
173:,
169:,
146:,
2215:.
2179:.
2147:.
2084:.
2005:P
2001:P
1973:i
1970:T
1967:R
1964:c
1961:=
1956:V
1952:i
1949:T
1946:R
1943:n
1937:=
1911:V
1907:/
1903:n
1900:=
1897:c
1877:i
1873:T
1865:R
1861:n
1857:V
1823:i
1820:T
1817:R
1814:n
1811:=
1808:V
1785:T
1782:R
1779:n
1776:=
1773:V
1770:P
1696:H
1679:H
1673:s
1670:u
1667:f
1657:/
1651:2
1646:f
1642:T
1638:M
1635:R
1632:=
1627:f
1623:K
1604:m
1600:i
1591:f
1589:K
1583:)
1571:m
1563:f
1559:K
1552:i
1549:=
1538:,
1535:f
1530:T
1515:,
1512:f
1507:T
1503:=
1497:f
1492:T
1468:m
1460:f
1456:K
1449:i
1443:=
1432:,
1429:f
1424:T
1409:,
1406:f
1401:T
1397:=
1391:f
1386:T
1352:f
1347:T
1315:H
1290:p
1287:a
1284:v
1279:H
1271:/
1265:2
1260:b
1256:T
1252:M
1249:R
1246:=
1241:b
1237:K
1213:,
1210:)
1206:m
1203:t
1200:a
1195:1
1192:,
1189:g
1186:(
1176:A
1168:=
1160:A
1156:x
1146:T
1143:R
1140:+
1137:)
1132:b
1128:T
1124:(
1114:A
1106:=
1103:)
1098:b
1094:T
1090:(
1085:A
1067:A
1065:μ
1055:b
1052:K
1033:m
1025:b
1022:K
1014:i
997:m
989:b
985:K
978:i
975:=
964:,
961:b
956:T
941:,
938:b
933:T
929:=
923:b
918:T
873:b
868:T
810:i
793:B
788:x
764:B
759:x
747:A
742:p
738:=
735:p
721:2
702:i
669:B
664:x
652:A
647:p
643:=
640:)
634:A
629:x
622:1
619:(
608:A
603:p
599:=
596:p
582:A
577:p
573:=
570:p
537:A
532:x
520:A
515:p
511:=
508:p
488:0
485:=
474:B
469:p
438:i
433:x
400:i
395:p
374:,
368:+
362:B
357:x
345:B
340:p
336:+
330:A
325:x
313:A
308:p
304:=
301:p
215:)
211:(
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
