594:
77:
occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured van 't Hoff factor to be less than that predicted in an ideal solution. The deviation for the
668:
is the actual number of particles in solution after dissociation divided by the number of formula units initially dissolved in solution and means the number of particles per formula unit of the solute when a solution is dilute.
551:
434:
220:
281:
338:
147:
127:
580:
310:
708:
249:
358:
167:
476:
802:
50:. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the
829:
378:
778:
27:
824:
819:
175:
129:. There is a simple relationship between this parameter and the van 't Hoff factor. If a fraction
47:
744:
106:
739:
254:
43:
724:
719:
31:
323:
132:
112:
65:
dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a
559:
289:
684:
8:
754:
678:
228:
626:
in benzene, so that the number of solute particles is half the number of acid molecules.
796:
646:
642:
369:
343:
152:
105:
The degree of dissociation is the fraction of the original solute molecules that have
784:
774:
623:
440:
365:
78:
van 't Hoff factor tends to be greatest where the ions have multiple charges.
35:
734:
729:
638:
611:
556:
For association in the absence of dissociation, the van 't Hoff factor is:
546:{\displaystyle i=1-\left(1-{\frac {1}{2}}\right)\alpha =1-{\frac {\alpha }{2}}.}
286:
For dissociation in the absence of association, the van 't Hoff factor is:
70:
62:
39:
788:
813:
598:
51:
768:
619:
66:
615:
593:
444:
55:
630:
90:
82:
652:
When solute particles neither dissociate nor associate in solution,
94:
86:
74:
470:
2 moles of acetic acid associate to form 1 mole of dimer, so that
58:
dissolved in water, the van 't Hoff factor is essentially 1.
749:
657:
448:
429:{\displaystyle i=1-\left(1-{\frac {1}{n}}\right)\alpha .}
54:
of a substance as calculated from its mass. For most non-
687:
562:
479:
381:
346:
326:
292:
257:
231:
178:
155:
135:
115:
702:
672:
597:Dimerization of a carboxylic acid by formation of
574:
545:
428:
352:
332:
304:
275:
243:
225:For example, the dissociation KCl ⇌ K + Cl yields
214:
161:
141:
121:
773:(Fifth ed.). Hoboken, NJ. pp. 613–614.
360:moles of solute associate to form one mole of an
811:
109:. It is usually indicated by the Greek symbol
606:When solute particles associate in solution,
585:
30:) is a measure of the effect of a solute on
801:: CS1 maint: location missing publisher (
592:
812:
100:
770:Chemistry : A Molecular Approach
315:
677:This quantity can be related to the
766:
69:of the substance. This is true for
13:
14:
841:
215:{\displaystyle i=1+\alpha (n-1).}
673:Relation to osmotic coefficient
149:of the solute dissociates into
206:
194:
1:
760:
610:is less than 1. For example,
830:Jacobus Henricus van 't Hoff
28:Jacobus Henricus van 't Hoff
7:
713:
276:{\displaystyle i=1+\alpha }
26:(named after Dutch chemist
10:
846:
586:Physical significance of
320:Similarly, if a fraction
48:freezing-point depression
767:Tro, Nivaldo J. (2020).
745:Dissociation (chemistry)
637:is greater than 1 (e.g.
21:van 't Hoff factor
16:Measure of solute effect
601:(shown as dotted lines)
333:{\displaystyle \alpha }
142:{\displaystyle \alpha }
122:{\displaystyle \alpha }
44:boiling-point elevation
38:, relative lowering in
725:Thermodynamic activity
720:Colligative properties
704:
629:When solute particles
602:
576:
575:{\displaystyle i<1}
547:
430:
354:
334:
306:
305:{\displaystyle i>1}
277:
245:
216:
163:
143:
123:
73:only, as occasionally
32:colligative properties
825:Dimensionless numbers
705:
596:
577:
548:
431:
355:
335:
307:
278:
246:
217:
164:
144:
124:
740:Van 't Hoff equation
703:{\displaystyle i=ng}
685:
681:g by the relation:
560:
477:
379:
344:
324:
290:
255:
229:
176:
153:
133:
113:
755:Osmotic coefficient
679:osmotic coefficient
618:(ethanoic acid) or
244:{\displaystyle n=2}
101:Dissociated solutes
820:Physical chemistry
700:
647:magnesium chloride
643:potassium chloride
603:
572:
543:
426:
350:
330:
316:Associated solutes
302:
273:
241:
212:
159:
139:
119:
780:978-0-13-498889-4
538:
511:
413:
353:{\displaystyle n}
162:{\displaystyle n}
81:The factor binds
837:
806:
800:
792:
709:
707:
706:
701:
667:
655:
636:
612:carboxylic acids
609:
589:
581:
579:
578:
573:
552:
550:
549:
544:
539:
531:
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406:
359:
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274:
250:
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242:
221:
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218:
213:
168:
166:
165:
160:
148:
146:
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140:
128:
126:
125:
120:
36:osmotic pressure
24:
845:
844:
840:
839:
838:
836:
835:
834:
810:
809:
794:
793:
781:
763:
735:Law of dilution
716:
686:
683:
682:
675:
665:
656:equals 1 (e.g.
653:
639:sodium chloride
634:
607:
591:
587:
561:
558:
557:
530:
503:
496:
492:
478:
475:
474:
466:
462:
458:
405:
398:
394:
380:
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376:
345:
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341:
325:
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321:
318:
291:
288:
287:
256:
253:
252:
230:
227:
226:
177:
174:
173:
154:
151:
150:
134:
131:
130:
114:
111:
110:
103:
71:ideal solutions
63:ionic compounds
22:
17:
12:
11:
5:
843:
833:
832:
827:
822:
808:
807:
779:
762:
759:
758:
757:
752:
747:
742:
737:
732:
727:
722:
715:
712:
699:
696:
693:
690:
674:
671:
662:
661:
650:
627:
599:hydrogen bonds
590:
584:
571:
568:
565:
554:
553:
542:
537:
534:
529:
526:
523:
520:
516:
510:
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491:
488:
485:
482:
468:
467:
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460:
456:
437:
436:
425:
422:
418:
412:
409:
404:
401:
397:
393:
390:
387:
384:
372:, etc.), then
349:
329:
317:
314:
301:
298:
295:
272:
269:
266:
263:
260:
251:ions, so that
240:
237:
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222:
211:
208:
205:
202:
199:
196:
193:
190:
187:
184:
181:
158:
138:
118:
102:
99:
40:vapor pressure
15:
9:
6:
4:
3:
2:
842:
831:
828:
826:
823:
821:
818:
817:
815:
804:
798:
790:
786:
782:
776:
772:
771:
765:
764:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
721:
718:
717:
711:
697:
694:
691:
688:
680:
670:
664:The value of
659:
651:
648:
644:
640:
633:in solution,
632:
628:
625:
621:
617:
613:
605:
604:
600:
595:
583:
569:
566:
563:
540:
535:
532:
527:
524:
521:
518:
514:
508:
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500:
497:
493:
489:
486:
483:
480:
473:
472:
471:
454:
453:
452:
450:
446:
442:
423:
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416:
410:
407:
402:
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395:
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388:
385:
382:
375:
374:
373:
371:
367:
363:
347:
327:
313:
299:
296:
293:
284:
270:
267:
264:
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258:
238:
235:
232:
209:
203:
200:
197:
191:
188:
185:
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179:
172:
171:
170:
156:
136:
116:
108:
98:
96:
92:
88:
84:
79:
76:
72:
68:
64:
59:
57:
53:
52:concentration
49:
45:
41:
37:
33:
29:
25:
769:
730:Raoult's law
676:
663:
620:benzoic acid
555:
469:
441:dimerisation
438:
361:
319:
285:
224:
104:
80:
67:formula unit
60:
56:electrolytes
20:
18:
616:acetic acid
445:acetic acid
169:ions, then
107:dissociated
75:ion pairing
814:Categories
789:1048659501
761:References
660:in water).
649:in water).
645:in water,
641:in water,
631:dissociate
459:COOH ⇌ (CH
91:osmolality
83:osmolarity
797:cite book
533:α
528:−
519:α
501:−
490:−
421:α
403:−
392:−
328:α
271:α
201:−
192:α
137:α
117:α
61:For most
714:See also
614:such as
439:For the
95:molality
87:molarity
34:such as
750:Osmosis
658:glucose
449:benzene
787:
777:
624:dimers
370:trimer
364:-mer (
622:form
463:COOH)
366:dimer
803:link
785:OCLC
775:ISBN
567:<
455:2 CH
297:>
89:and
46:and
19:The
447:in
443:of
340:of
93:to
85:to
816::
799:}}
795:{{
783:.
710:.
582:.
451::
368:,
312:.
283:.
97:.
42:,
805:)
791:.
698:g
695:n
692:=
689:i
666:i
654:i
635:i
608:i
588:i
570:1
564:i
541:.
536:2
525:1
522:=
515:)
509:2
506:1
498:1
494:(
487:1
484:=
481:i
465:2
461:3
457:3
424:.
417:)
411:n
408:1
400:1
396:(
389:1
386:=
383:i
362:n
348:n
300:1
294:i
268:+
265:1
262:=
259:i
239:2
236:=
233:n
210:.
207:)
204:1
198:n
195:(
189:+
186:1
183:=
180:i
157:n
23:i
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