190:
198:
1377:
1303:
38:
986:
46:
384:
1298:{\displaystyle \Delta T_{\text{F}}={\frac {\Delta H_{T_{\text{F}}}^{\text{fus}}-2RT_{\text{F}}\cdot \ln a_{\text{liq}}-{\sqrt {2\Delta C_{p}^{\text{fus}}T_{\text{F}}^{2}R\cdot \ln a_{\text{liq}}+(\Delta H_{T_{\text{F}}}^{\text{fus}})^{2}}}}{2\left({\frac {\Delta H_{T_{\text{F}}}^{\text{fus}}}{T_{\text{F}}}}+{\frac {\Delta C_{p}^{\text{fus}}}{2}}-R\cdot \ln a_{\text{liq}}\right)}}.}
158:. The freezing-point depression prevents radiators from freezing in winter. Road salting takes advantage of this effect to lower the freezing point of the ice it is placed on. Lowering the freezing point allows the street ice to melt at lower temperatures, preventing the accumulation of dangerous, slippery ice. Commonly used
217:. This elevated concentration of solute decreases the freezing point of the water inside them, preventing the organism from freezing solid even as the water around them freezes, or as the air around them becomes very cold. Examples of organisms that produce antifreeze compounds include some species of
129:
result from a lowering of the chemical potential of the solvent in the presence of a solute. This lowering is an entropy effect. The greater randomness of the solution (as compared to the pure solvent) acts in opposition to freezing, so that a lower temperature must be reached, over a broader range,
124:
are equal. When a non-volatile solute is added to a volatile liquid solvent, the solution vapour pressure will be lower than that of the pure solvent. As a result, the solid will reach equilibrium with the solution at a lower temperature than with the pure solvent. This explanation in terms of vapor
142:
In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze (a lower concentration of solvent exists in a solution versus pure solvent). Re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing
300:
must be known, and the procedure is primarily useful for organic compounds using a nonpolar solvent. Cryoscopy is no longer as common a measurement method as it once was, but it was included in textbooks at the turn of the 20th century. As an example, it was still taught as a useful analytic
443:
1819:
Ge, Xinlei; Wang, Xidong (2009). "Calculations of
Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model".
979:
The simple relation above doesn't consider the nature of the solute, so it is only effective in a diluted solution. For a more accurate calculation at a higher concentration, for ionic solutes, Ge and Wang (2010) proposed a new equation:
143:
becomes equal to the rate of liquefying. The solute is not occluding or preventing the solvent from solidifying, it is simply diluting it so there is a reduced probability of a solvent making an attempt at freezing in any given moment.
1898:
Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (2008). "Correlation and
Prediction of Thermodynamic Properties of Some Complex Aqueous Electrolytes by the Modified Three-Characteristic-Parameter Correlation Model".
344:
is 3.9 °C·kg/mol. By melting lauric acid with the unknown substance, allowing it to cool, and recording the temperature at which the mixture freezes, the molar mass of the unknown compound may be determined.
1863:
Ge, Xinlei; Wang, Xidong; Zhang, Mei; Seetharaman, Seshadri (2007). "Correlation and
Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model".
193:
Pre-treating roads with salt relies on the warmer road surface to initially melt the snow and make a solution; Pre-treatment of bridges (which are colder than roads) does not typically work.
681:
146:
At the lower freezing point, the vapor 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.
340:
of an unknown substance via the freezing-point depression. The choice of lauric acid is convenient because the melting point of the pure compound is relatively high (43.8 °C). Its
189:
495:
370:
FPD measurements are also used in the dairy industry to ensure that milk has not had extra water added. Milk with a FPD of over 0.509 °C is considered to be unadulterated.
162:
can depress the freezing point of water to about −21 °C (−6 °F). If the road surface temperature is lower, NaCl becomes ineffective and other salts are used, such as
405:
620:
531:
1702:
563:
395:, the extent of freezing-point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant ("
1934:
Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (2008). "Correlation and
Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model".
237:), the molality is increased temporarily as a reaction to cold temperatures. In the case of the peeper frog, freezing temperatures trigger a large-scale breakdown of
710:
590:
766:
740:
125:
pressure is equivalent to the argument based on chemical potential, since the chemical potential of a vapor is logarithmically related to pressure. All of the
1657:
2319:
1418:
95:
of the solvent in the mixture is lower than that of the pure solvent, the difference between the two being proportional to the natural logarithm of the
1749:
348:
This is also the same principle acting in the melting-point depression observed when the melting point of an impure solid mixture is measured with a
1969:
Ge, Xinlei; Wang, Xidong (2009). "A Simple Two-Parameter
Correlation Model for Aqueous Electrolyte Solutions across a Wide Range of Temperatures†".
80:
that flows at a lower temperature than the silver pieces being joined), or the mixing of two solids such as impurities into a finely powdered drug.
367:, and the freezing point is often easier to measure with precision, which means measurements using the freezing-point depression are more precise.
107:(a mixture of salt and other compounds in water) to remain liquid at temperatures below 0 °C (32 °F), the freezing point of pure water.
268:= observe; "observe the cold") and relies on exact measurement of the freezing point. The degree of dissociation is measured by determining the
1782:
130:
before equilibrium between the liquid solution and solid solution phases is achieved. Melting point determinations are commonly exploited in
2021:
1512:
229:, which produces glycerol and other molecules to survive in frozen-over estuaries during the winter months. In other animals, such as the
359:
In principle, the boiling-point elevation and the freezing-point depression could be used interchangeably for this purpose. However, the
387:
Freezing temperature of seawater at different pressures and some substances as a function of salinity. See image description for source.
99:. In a similar manner, the chemical potential of the vapor above the solution is lower than that above a pure solvent, which results in
1688:
17:
154:
The phenomenon of freezing-point depression has many practical uses. The radiator fluid in an automobile is a mixture of water and
1706:
1364:, which typically requires 3 adjustable parameters. For the TCPC model, these parameters are available for many single salts.
91:. The resulting liquid solution or solid-solid mixture has a lower freezing point than the pure solvent or solid because the
170:
or a mixture of many. These salts are somewhat aggressive to metals, especially iron, so in airports safer media such as
1778:"Estimation of Freezing Point Depression, Boiling Point Elevation, and Vaporization Enthalpies of Electrolyte Solutions"
1729:
120:
The freezing point is the temperature at which the liquid solvent and solid solvent are at equilibrium, so that their
2066:
1761:
1614:
1495:
326:
716:, which is dependent on the properties of the solvent, not the solute. (Note: When conducting experiments, a higher
2014:
1664:
625:
289:. In this case, the molar mass of the solute must be known. The molar mass of a solute is determined by comparing
592:
of the solution, as the formula above results in a positive value given that all factors are positive. From the
2156:
2385:
2380:
2309:
451:
2239:
2007:
329:. The results obtained are in mol%, but the method has its place, where other methods of analysis fail.
2390:
2294:
438:{\displaystyle \Delta T_{f}\propto {\frac {\text{Moles of dissolved species}}{\text{Mass of solvent}}}}
245:
into the blood. With the formula below, freezing-point depression can be used to measure the degree of
2186:
197:
2171:
2106:
1388:
246:
205:
Freezing-point depression is used by some organisms that live in extreme cold. Such creatures have
595:
506:
2126:
1393:
622:
calculated using the formula above, the freezing point of the solution can then be calculated as
349:
100:
2224:
2219:
2076:
1398:
536:
364:
126:
61:
30:
This article is about the phenomenon caused by solutes. For the phenomenon in pure fluids, see
2324:
2304:
1531:
769:
269:
2038:
2030:
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869:
688:
568:
8:
2151:
2121:
713:
360:
341:
1641:
1845:
1468:
1413:
1322:
is the activity of the solvent in the solution (water activity for aqueous solution); Δ
751:
725:
209:
means through which they can produce a high concentration of various compounds such as
167:
92:
1563:
Treberg, J. R.; Wilson, C. E.; Richards, R. C.; Ewart, K. V.; Driedzic, W. R. (2002).
1315:
is the normal freezing point of the pure solvent (273 K for water, for example);
325:
Freezing-point depression can also be used as a purity analysis tool when analyzed by
2329:
2288:
2191:
1986:
1951:
1916:
1880:
1837:
1801:
1757:
1725:
1682:
1610:
1588:
1564:
1539:
1491:
1472:
1460:
1376:
183:
175:
131:
69:
1849:
772:(number of ion particles per formula unit of solute, e.g. i = 2 for NaCl, 3 for BaCl
2264:
2259:
2091:
2051:
1978:
1943:
1908:
1872:
1829:
1791:
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1357:
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353:
163:
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2131:
2116:
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2096:
2061:
396:
159:
65:
1346:
is the difference between the heat capacities of the liquid and solid phases at
201:
Dissolved solutes prevent sap and other fluids in trees from freezing in winter.
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2254:
2244:
2161:
2056:
2046:
1745:
1408:
392:
179:
171:
121:
87:, while the original substance present in larger quantity is thought of as the
83:
In all cases, the substance added/present in smaller amounts is considered the
1833:
49:
Freezing point depression is responsible for keeping ice cream soft below 0°C.
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2344:
2181:
2141:
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1990:
1955:
1920:
1884:
1841:
1805:
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1372:
The freezing point of ethanol water mixture is shown in the following graph.
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230:
226:
96:
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2201:
2196:
1592:
1443:"Controlling the hardness of ice cream, gelato and similar frozen desserts"
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31:
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333:
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1361:
882:
337:
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155:
73:
37:
27:
Drop in freezing temperature of a solvent due to the addition of solute
1982:
1947:
1912:
1876:
1796:
1777:
1513:"Salt Doesn't Melt Ice—Here's How It Makes Winter Streets Safer"
1486:
Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002).
2359:
2314:
2229:
1999:
720:
value makes it easier to observe larger drops in the freezing point.)
206:
104:
64:
substance is added. Examples include adding salt into water (used in
72:), alcohol in water, ethylene or propylene glycol in water (used in
2176:
743:
238:
214:
210:
57:
45:
2279:
2081:
2071:
1403:
908:
843:
830:
533:
is the decrease in freezing point, defined as the freezing point
352:
since melting and freezing points both refer to the liquid-solid
242:
241:
in the frog's liver and subsequent release of massive amounts of
88:
383:
134:
to aid in identifying substances and to ascertain their purity.
947:
806:
218:
84:
2101:
960:
41:
Workers spreading salt from a salt truck for deicing the road
222:
1756:(5 ed.), Sweden: John Wiley & Sons, p. 202,
1562:
56:
is a drop in the maximum temperature at which a substance
1332:
is the enthalpy change of fusion of the pure solvent at
76:
in cars), adding copper to molten silver (used to make
1862:
1485:
989:
754:
728:
691:
628:
598:
571:
539:
509:
454:
408:
2320:
List of boiling and freezing information of solvents
1419:
List of boiling and freezing information of solvents
296:with the amount of solute dissolved. In this case,
137:
1724:(4th ed.). Freeman. p. C17 (Table 7.2).
1297:
760:
734:
704:
675:
614:
584:
557:
525:
489:
437:
253:of the solute. This kind of measurement is called
1626:BIOETYMOLOGY – Biomedical Terms of Greek Origin.
1490:(8th ed.). Prentice-Hall. pp. 557–558.
2372:
1356:The solvent activity can be calculated from the
1783:Industrial & Engineering Chemistry Research
1339:, which is 333.6 J/g for water at 273 K; Δ
60:, caused when a smaller amount of another, non-
1933:
1897:
1744:
2015:
1927:
1891:
1569:: initiation and subsequent suppression 6353"
565:of the pure solvent minus the freezing point
1962:
1769:
974:
676:{\displaystyle T_{f}=T_{f}^{0}-\Delta T_{f}}
103:. Freezing-point depression is what causes
2022:
2008:
1971:Journal of Chemical & Engineering Data
1936:Journal of Chemical & Engineering Data
1901:Journal of Chemical & Engineering Data
1865:Journal of Chemical & Engineering Data
1856:
1609:, 2005, Thomson Brooks/Cole, Belmont, CA,
1607:Animal Physiology: From Genes to Organisms
1375:
1795:
1454:
746:(moles of solute per kilogram of solvent)
1565:"The freeze-avoidance response of smelt
382:
196:
188:
115:
44:
36:
780:Some values of the cryoscopic constant
14:
2373:
2029:
1968:
1818:
1775:
1719:
1687:: CS1 maint: archived copy as title (
378:
2003:
1639:
490:{\displaystyle \Delta T_{f}=K_{f}bi}
1703:"Freezing Point Depression of Milk"
1573:The Journal of Experimental Biology
1529:
1510:
1353:, which is 2.11 J/(g·K) for water.
24:
1367:
1235:
1191:
1141:
1080:
1009:
990:
660:
599:
510:
455:
409:
356:(albeit in different directions).
320:
25:
2402:
1776:Ge, Xinlei; Wang, Xidong (2009).
1504:
391:If the solution is treated as an
327:differential scanning calorimetry
1705:. Dairy UK. 2014. Archived from
1530:Ray, C. Claiborne (2002-02-05).
138:Due to concentration and entropy
1812:
1738:
1713:
1695:
336:may be used to investigate the
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1633:
1620:
1599:
1556:
1523:
1479:
1435:
1167:
1138:
110:
13:
1:
1822:Journal of Solution Chemistry
1429:
2310:Inorganic nonaqueous solvent
1630:. bioetymology.blogspot.com.
615:{\displaystyle \Delta T_{f}}
526:{\displaystyle \Delta T_{f}}
303:Practical Organic Chemistry
7:
1646:. London: MacMillan and Co.
1643:Practical Organic Chemistry
1447:Food Science and Technology
1382:
315:Beckmann freezing apparatus
10:
2407:
2295:Acid dissociation constant
428:Moles of dissolved species
373:
29:
2278:
2210:
2140:
2037:
1834:10.1007/s10953-009-9433-0
1640:Cohen, Julius B. (1910).
975:For concentrated solution
558:{\displaystyle T_{f}^{0}}
282:and then comparing it to
54:Freezing-point depression
18:Freezing point depression
1754:SI Chemical Data 5th ed.
1389:Melting-point depression
2260:Solubility table (data)
2127:Apparent molar property
1585:10.1242/jeb.205.10.1419
1394:Boiling-point elevation
1308:In the above equation,
787:for selected solvents:
350:melting-point apparatus
149:
101:boiling-point elevation
2225:Total dissolved solids
2220:Solubility equilibrium
2145:and related quantities
1720:Atkins, P. W. (1990).
1399:Colligative properties
1299:
762:
736:
706:
677:
616:
586:
559:
527:
491:
439:
388:
365:ebullioscopic constant
313:is determined using a
305:of 1910, in which the
202:
194:
127:colligative properties
50:
42:
2325:Partition coefficient
2305:Polar aprotic solvent
1456:10.1002/fsat.3510_3.x
1300:
763:
737:
707:
705:{\displaystyle K_{f}}
678:
617:
587:
585:{\displaystyle T_{f}}
560:
528:
492:
440:
386:
301:procedure in Cohen's
275:by first determining
200:
192:
116:Using vapour pressure
48:
40:
2240:Enthalpy of solution
2167:Volume concentration
2162:Number concentration
1605:L. Sherwood et al.,
1579:(Pt 10): 1419–1427.
987:
870:Carbon tetrachloride
752:
726:
689:
626:
596:
569:
537:
507:
452:
406:
2386:Chemical properties
2381:Amount of substance
2152:Molar concentration
2122:Dilution (equation)
1517:Scientific American
1252:
1215:
1165:
1112:
1097:
1033:
796:Freezing point (°C)
714:cryoscopic constant
656:
554:
379:For dilute solution
363:is larger than the
361:cryoscopic constant
342:cryoscopic constant
332:In the laboratory,
235:Pseudacris crucifer
2192:Isotopic abundance
2157:Mass concentration
2031:Chemical solutions
1722:Physical Chemistry
1617:, p. 691–692.
1536:The New York Times
1414:Frigorific mixture
1295:
1238:
1194:
1144:
1098:
1083:
1012:
770:van 't Hoff factor
758:
732:
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642:
612:
582:
555:
540:
523:
487:
435:
389:
270:van 't Hoff factor
203:
195:
186:are used instead.
168:magnesium chloride
93:chemical potential
51:
43:
2391:Phase transitions
2368:
2367:
1983:10.1021/je800483q
1948:10.1021/je700446q
1913:10.1021/je7006499
1877:10.1021/je060451k
1797:10.1021/ie900434h
1488:General Chemistry
1290:
1281:
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1213:
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1031:
1024:
1000:
972:
971:
761:{\displaystyle i}
735:{\displaystyle b}
433:
432:
429:
184:potassium acetate
176:potassium formate
132:organic chemistry
16:(Redirected from
2398:
2265:Solubility chart
2092:Phase separation
2052:Aqueous solution
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2017:
2010:
2001:
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1995:
1994:
1966:
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1959:
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1828:(9): 1097–1117.
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1750:Findlay, Tristan
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1663:. Archived from
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1597:
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1511:Pollock, Julie.
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354:phase transition
164:calcium chloride
66:ice cream makers
21:
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2235:Solvation shell
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2144:
2136:
2132:Miscibility gap
2117:Serial dilution
2112:Supersaturation
2062:Buffer solution
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2028:
1998:
1967:
1963:
1932:
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1746:Aylward, Gordon
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1658:"Archived copy"
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1368:Ethanol example
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321:Laboratory uses
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160:sodium chloride
156:ethylene glycol
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122:vapor pressures
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35:
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5:
2404:
2394:
2393:
2388:
2383:
2366:
2365:
2363:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2302:
2300:Protic solvent
2297:
2292:
2284:
2282:
2276:
2275:
2273:
2272:
2267:
2262:
2257:
2252:
2247:
2245:Lattice energy
2242:
2237:
2232:
2227:
2222:
2216:
2214:
2208:
2207:
2205:
2204:
2199:
2194:
2189:
2184:
2179:
2174:
2169:
2164:
2159:
2154:
2148:
2146:
2138:
2137:
2135:
2134:
2129:
2124:
2119:
2114:
2109:
2104:
2099:
2097:Eutectic point
2094:
2089:
2084:
2079:
2074:
2069:
2064:
2059:
2057:Solid solution
2054:
2049:
2047:Ideal solution
2043:
2041:
2035:
2034:
2027:
2026:
2019:
2012:
2004:
1997:
1996:
1977:(2): 179–186.
1961:
1942:(1): 149–159.
1926:
1907:(4): 950–958.
1890:
1871:(2): 538–547.
1855:
1811:
1768:
1762:
1737:
1731:978-0716720737
1730:
1712:
1709:on 2014-02-23.
1694:
1649:
1632:
1619:
1598:
1567:Osmerus mordax
1555:
1522:
1503:
1496:
1478:
1449:. 2021-03-18.
1433:
1431:
1428:
1427:
1426:
1421:
1416:
1411:
1409:Eutectic point
1406:
1401:
1396:
1391:
1384:
1381:
1369:
1366:
1350:
1343:
1336:
1328:
1326:
1319:
1312:
1306:
1305:
1294:
1287:
1277:
1273:
1270:
1267:
1264:
1261:
1256:
1245:
1241:
1237:
1231:
1220:
1202:
1197:
1193:
1186:
1182:
1173:
1169:
1152:
1147:
1143:
1140:
1137:
1128:
1124:
1121:
1118:
1115:
1110:
1101:
1090:
1086:
1082:
1079:
1074:
1065:
1061:
1058:
1055:
1046:
1042:
1039:
1036:
1020:
1015:
1011:
1005:
996:
992:
976:
973:
970:
969:
966:
963:
957:
956:
953:
950:
944:
943:
940:
937:
931:
930:
927:
924:
918:
917:
914:
911:
905:
904:
901:
898:
892:
891:
888:
885:
879:
878:
875:
872:
866:
865:
862:
859:
853:
852:
849:
846:
840:
839:
836:
833:
827:
826:
823:
820:
814:
813:
802:
797:
794:
784:
778:
777:
773:
757:
747:
731:
721:
699:
695:
684:
670:
666:
662:
659:
654:
649:
645:
641:
636:
632:
609:
605:
601:
579:
575:
552:
547:
543:
520:
516:
512:
498:
497:
486:
483:
478:
474:
470:
465:
461:
457:
446:
445:
424:
419:
415:
411:
393:ideal solution
380:
377:
375:
372:
322:
319:
293:
286:
279:
180:sodium acetate
172:sodium formate
151:
148:
139:
136:
117:
114:
112:
109:
70:de-icing roads
26:
9:
6:
4:
3:
2:
2403:
2392:
2389:
2387:
2384:
2382:
2379:
2378:
2376:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2290:
2286:
2285:
2283:
2281:
2277:
2271:
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2236:
2233:
2231:
2228:
2226:
2223:
2221:
2218:
2217:
2215:
2213:
2209:
2203:
2200:
2198:
2195:
2193:
2190:
2188:
2187:Mass fraction
2185:
2183:
2182:Mole fraction
2180:
2178:
2175:
2173:
2170:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2149:
2147:
2143:
2142:Concentration
2139:
2133:
2130:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2087:Phase diagram
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2068:
2067:Flory–Huggins
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2044:
2042:
2040:
2036:
2032:
2025:
2020:
2018:
2013:
2011:
2006:
2005:
2002:
1992:
1988:
1984:
1980:
1976:
1972:
1965:
1957:
1953:
1949:
1945:
1941:
1937:
1930:
1922:
1918:
1914:
1910:
1906:
1902:
1894:
1886:
1882:
1878:
1874:
1870:
1866:
1859:
1851:
1847:
1843:
1839:
1835:
1831:
1827:
1823:
1815:
1807:
1803:
1798:
1793:
1789:
1785:
1784:
1779:
1772:
1765:
1763:0-470-80044-5
1759:
1755:
1751:
1747:
1741:
1733:
1727:
1723:
1716:
1708:
1704:
1698:
1690:
1684:
1670:on 2020-08-03
1666:
1659:
1653:
1645:
1644:
1636:
1629:
1623:
1616:
1615:0-534-55404-0
1612:
1608:
1602:
1594:
1590:
1586:
1582:
1578:
1574:
1570:
1568:
1559:
1545:
1541:
1537:
1533:
1526:
1518:
1514:
1507:
1499:
1497:0-13-014329-4
1493:
1489:
1482:
1474:
1470:
1466:
1462:
1457:
1452:
1448:
1444:
1438:
1434:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1386:
1380:
1378:
1373:
1365:
1363:
1359:
1354:
1349:
1342:
1335:
1325:
1318:
1311:
1292:
1285:
1275:
1271:
1268:
1265:
1262:
1259:
1254:
1243:
1239:
1229:
1218:
1200:
1195:
1184:
1180:
1171:
1150:
1145:
1135:
1126:
1122:
1119:
1116:
1113:
1108:
1099:
1088:
1084:
1077:
1072:
1063:
1059:
1056:
1053:
1044:
1040:
1037:
1034:
1018:
1013:
1003:
994:
983:
982:
981:
967:
964:
962:
959:
958:
954:
951:
949:
946:
945:
941:
938:
936:
933:
932:
928:
925:
923:
920:
919:
915:
912:
910:
907:
906:
902:
899:
897:
894:
893:
889:
886:
884:
881:
880:
876:
873:
871:
868:
867:
863:
860:
858:
855:
854:
850:
847:
845:
842:
841:
837:
834:
832:
829:
828:
824:
821:
819:
816:
815:
812:
808:
801:
798:
795:
792:
791:
788:
783:
771:
755:
748:
745:
729:
722:
719:
715:
697:
693:
685:
668:
664:
657:
652:
647:
643:
639:
634:
630:
607:
603:
577:
573:
550:
545:
541:
518:
514:
503:
502:
501:
484:
481:
476:
472:
468:
463:
459:
448:
447:
422:
417:
413:
402:
401:
400:
398:
394:
385:
371:
368:
366:
362:
357:
355:
351:
346:
343:
339:
335:
330:
328:
318:
316:
312:
308:
304:
299:
292:
285:
278:
274:
271:
267:
263:
260:
256:
252:
248:
244:
240:
236:
232:
231:spring peeper
228:
227:rainbow smelt
224:
220:
216:
212:
208:
199:
191:
187:
185:
181:
177:
173:
169:
165:
161:
157:
147:
144:
135:
133:
128:
123:
108:
106:
102:
98:
97:mole fraction
94:
90:
86:
81:
79:
75:
71:
67:
63:
59:
55:
47:
39:
33:
19:
2250:Raoult's law
2202:Ternary plot
2197:Mixing ratio
1974:
1970:
1964:
1939:
1935:
1929:
1904:
1900:
1893:
1868:
1864:
1858:
1825:
1821:
1814:
1790:(10): 5123.
1787:
1781:
1771:
1753:
1740:
1721:
1715:
1707:the original
1697:
1672:. Retrieved
1665:the original
1652:
1642:
1635:
1622:
1606:
1601:
1576:
1572:
1566:
1558:
1547:. Retrieved
1535:
1525:
1516:
1506:
1487:
1481:
1446:
1437:
1424:Snow removal
1374:
1371:
1360:or modified
1358:Pitzer model
1355:
1347:
1340:
1333:
1323:
1316:
1309:
1307:
978:
799:
781:
779:
717:
499:
390:
369:
358:
347:
331:
324:
314:
302:
297:
290:
283:
276:
272:
265:
261:
254:
247:dissociation
234:
225:such as the
204:
153:
145:
141:
119:
82:
53:
52:
32:supercooling
2355:Lyonium ion
2270:Miscibility
2255:Henry's law
1532:"Q & A"
935:Naphthalene
922:Ethyl ether
896:Cyclohexane
818:Acetic acid
334:lauric acid
311:naphthalene
111:Explanation
2375:Categories
2350:Amphiphile
2345:Lipophilic
2340:Hydrophile
2335:Hydrophobe
2212:Solubility
2107:Saturation
2077:Suspension
1674:2019-07-08
1549:2022-02-10
1430:References
1362:TCPC model
883:Chloroform
399:'s Law").
338:molar mass
307:molar mass
251:molar mass
74:antifreeze
2360:Lyate ion
2315:Solvation
2230:Solvation
2172:Normality
1991:0021-9568
1956:0021-9568
1921:0021-9568
1885:0021-9568
1842:0095-9782
1806:0888-5885
1628:cryoscopy
1544:0362-4331
1473:243583017
1465:1475-3324
1272:
1266:⋅
1260:−
1236:Δ
1192:Δ
1142:Δ
1123:
1117:⋅
1081:Δ
1073:−
1060:
1054:⋅
1035:−
1010:Δ
991:Δ
661:Δ
658:−
600:Δ
511:Δ
456:Δ
423:∝
410:Δ
255:cryoscopy
105:sea water
2330:Polarity
2289:Category
2177:Molality
2039:Solution
1850:96186176
1752:(2002),
1683:cite web
1593:11976353
1383:See also
793:Compound
744:molality
264:= cold,
239:glycogen
221:-living
215:glycerol
211:sorbitol
68:and for
62:volatile
2280:Solvent
2082:Colloid
2072:Mixture
1404:Deicing
909:Ethanol
844:Camphor
831:Benzene
768:is the
742:is the
500:where:
397:Blagden
374:Formula
249:or the
243:glucose
207:evolved
89:solvent
58:freezes
1989:
1954:
1919:
1883:
1848:
1840:
1804:
1760:
1728:
1613:
1591:
1542:
1494:
1471:
1463:
948:Phenol
926:−116.2
913:−114.6
712:, the
287:solute
266:scopos
233:frog (
219:arctic
182:, and
85:solute
78:solder
2102:Alloy
1846:S2CID
1668:(PDF)
1661:(PDF)
1469:S2CID
968:1.86
961:Water
955:7.27
929:1.79
916:1.99
903:20.2
890:4.68
887:−63.5
851:39.7
848:179.8
838:5.12
825:3.90
259:Greek
1987:ISSN
1952:ISSN
1917:ISSN
1881:ISSN
1838:ISSN
1802:ISSN
1758:ISBN
1726:ISBN
1689:link
1611:ISBN
1589:PMID
1540:ISSN
1492:ISBN
1461:ISSN
942:6.9
939:80.2
864:3.8
861:−112
822:16.6
809:⋅kg/
262:cryo
223:fish
213:and
150:Uses
1979:doi
1944:doi
1909:doi
1873:doi
1830:doi
1792:doi
1581:doi
1577:205
1451:doi
1320:liq
1280:liq
1249:fus
1212:fus
1162:fus
1131:liq
1094:fus
1068:liq
1030:fus
900:6.4
877:30
874:−23
835:5.5
811:mol
805:in
309:of
2377::
1985:.
1975:54
1973:.
1950:.
1940:53
1938:.
1915:.
1905:53
1903:.
1879:.
1869:52
1867:.
1844:.
1836:.
1826:38
1824:.
1800:.
1788:48
1786:.
1780:.
1748:;
1685:}}
1681:{{
1587:.
1575:.
1571:.
1538:.
1534:.
1515:.
1467:.
1459:.
1445:.
1269:ln
1120:ln
1057:ln
952:41
776:).
317:.
178:,
174:,
166:,
2291:)
2287:(
2023:e
2016:t
2009:v
1993:.
1981::
1958:.
1946::
1923:.
1911::
1887:.
1875::
1852:.
1832::
1808:.
1794::
1734:.
1691:)
1677:.
1595:.
1583::
1552:.
1519:.
1500:.
1475:.
1453::
1351:F
1348:T
1344:p
1341:C
1337:F
1334:T
1329:F
1327:T
1324:H
1317:a
1313:F
1310:T
1293:.
1286:)
1276:a
1263:R
1255:2
1244:p
1240:C
1230:+
1223:F
1219:T
1205:F
1201:T
1196:H
1185:(
1181:2
1172:2
1168:)
1155:F
1151:T
1146:H
1139:(
1136:+
1127:a
1114:R
1109:2
1104:F
1100:T
1089:p
1085:C
1078:2
1064:a
1049:F
1045:T
1041:R
1038:2
1023:F
1019:T
1014:H
1004:=
999:F
995:T
965:0
807:K
803:f
800:K
785:f
782:K
774:2
756:i
730:b
718:k
698:f
694:K
683:.
669:f
665:T
653:0
648:f
644:T
640:=
635:f
631:T
608:f
604:T
578:f
574:T
551:0
546:f
542:T
519:f
515:T
485:i
482:b
477:f
473:K
469:=
464:f
460:T
418:f
414:T
298:i
294:B
291:m
284:m
280:B
277:m
273:i
257:(
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
