424:
reactant or product. Although less common, we see from this expression that since the stoichiometric number can either be considered to be dimensionless or to have units of moles, conversely the extent of reaction can either be considered to have units of moles or to be a unitless mole fraction.
636:
Although in the example above the extent of reaction was positive since the system shifted in the forward direction, this usage implies that in general the extent of reaction can be positive or negative, depending on the direction that the system shifts from its initial composition.
1066:
1335:
1259:
828:
736:
939:
28:
is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It is usually denoted by the Greek letter
631:
87:
of the reactant A changes into B and C. This requires that all three mole numbers change according to the stoichiometry of the reaction, but they will not change by the same amounts. However, the extent of reaction
1183:
488:
947:
299:
1071:
In the above, we note that the stoichiometric number of a reactant is negative. Now when we know the extent, we can rearrange the equation and calculate the equilibrium amounts of B and C.
238:
193:
148:
386:
422:
359:
85:
329:
511:
106:
1265:
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759:
667:
1491:
849:
1419:
519:
108:
can be used to describe the changes on a common footing as needed. The change of the number of moles of A can be represented by the equation
1077:
438:
1061:{\displaystyle \xi _{equi}={\frac {\Delta n_{A}}{\nu _{A}}}={\frac {0.5\ {\text{mol}}-2\ {\text{mol}}}{-2}}=0.75\ {\text{mol}}}
1374:
432:. Considering finite changes instead of infinitesimal changes, one can write the equation for the extent of a reaction as
941:, and the equilibrium amount of A is 0.5 mol. We can calculate the extent of reaction in equilibrium from its definition
249:
838:
The extent of reaction is a useful quantity in computations with equilibrium reactions. Consider the reaction
1584:
493:
The extent of a reaction is generally defined as zero at the beginning of the reaction. Thus the change of
1579:
198:
153:
111:
1366:
1359:
364:
38:
390:
397:
334:
60:
307:
21:
496:
91:
8:
1520:
Vandezande, Jonathon E.; Vander Griend, Douglas A.; DeKock, Roger L. (August 23, 2013).
428:
The extent of reaction represents the amount of progress made towards equilibrium in a
17:
1370:
650:
646:
429:
1429:
1533:
1465:
1436:
1424:
1330:{\displaystyle n_{C}=0.75\ {\text{mol}}\times 3+0\ {\text{mol}}=2.25\ {\text{mol}}}
1254:{\displaystyle n_{B}=0.75\ {\text{mol}}\times 1+1\ {\text{mol}}=1.75\ {\text{mol}}}
823:{\displaystyle \Delta _{r}H=\left({\frac {\partial H}{\partial \xi }}\right)_{p,T}}
731:{\displaystyle \Delta _{r}G=\left({\frac {\partial G}{\partial \xi }}\right)_{p,T}}
745:
when applied to the oxidation-reduction reaction which generates the voltage of a
1521:
934:{\displaystyle n_{A}=2\ {\text{mol}},n_{B}=1\ {\text{mol}},n_{C}=0\ {\text{mol}}}
742:
1573:
1428:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
1453:
1440:
33:. The extent of reaction is usually defined so that it has units of amount (
746:
658:
34:
30:
626:{\displaystyle \xi _{equi}={\frac {n_{equi,i}-n_{initial,i}}{\nu _{i}}}}
513:
is the extent itself. Assuming that the system has come to equilibrium,
1537:
1469:
750:
654:
1519:
645:
The relation between the change in Gibbs reaction energy and
1178:{\displaystyle n_{equi,i}=\xi _{equi}\nu _{i}+n_{initial,i}}
483:{\displaystyle \Delta \xi ={\frac {\Delta n_{i}}{\nu _{i}}}}
1522:"Reaction Extrema: Extent of Reaction in General Chemistry"
749:. Analogously, the relation between the change in reaction
243:
The change in the extent of reaction is then defined as
1499:
Department of
Chemical Engineering, Bucknell University
1454:"The Use of Extent of Reaction in Introductory Courses"
1268:
1192:
1080:
950:
852:
762:
670:
522:
499:
441:
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367:
337:
310:
252:
201:
156:
114:
94:
63:
653:plotted against the extent of reaction at constant
1358:
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1177:
1060:
933:
822:
730:
625:
505:
482:
416:
380:
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323:
293:
232:
187:
142:
100:
79:
1571:
294:{\displaystyle d\xi ={\frac {dn_{i}}{\nu _{i}}}}
1356:
37:). It was introduced by the Belgian scientist
1452:Canagaratna, Sebastian C. (January 1, 2000).
1558:Lisý, Ján Mikuláš; Valko, Ladislav (1979).
1492:"Extent of Reaction or Events of Reaction?"
1451:
1390:Lisý, Ján Mikuláš; Valko, Ladislav (1979).
753:and enthalpy can be defined. For example,
1557:
1389:
1352:
1350:
1489:
1357:Atkins, Peter; de Paula, Julio (2006).
1572:
1404:
1347:
1560:Príklady a úlohy z fyzikálnej chémie
1392:Príklady a úlohy z fyzikálnej chémie
649:can be defined as the slope of the
331:denotes the number of moles of the
13:
1425:Compendium of Chemical Terminology
976:
795:
787:
764:
703:
695:
672:
454:
442:
14:
1596:
57:Suppose an infinitesimal amount
1551:
1513:
1483:
1445:
1413:
1398:
1383:
846:where the initial amounts are
233:{\displaystyle dn_{C}=+3d\xi }
188:{\displaystyle dn_{B}=+2d\xi }
1:
1526:Journal of Chemical Education
1340:
143:{\displaystyle dn_{A}=-d\xi }
44:
640:
7:
10:
1601:
833:
741:This formula leads to the
1405:Ulický, Ladislav (1983).
195:, and the change of C is
1490:Hanyak, Jr., Michael E.
381:{\displaystyle \nu _{i}}
361:reactant or product and
1441:10.1351/goldbook.S06025
1430:stoichiometric number,
1407:Chemický náučný slovník
1365:(8 ed.). p.
1331:
1255:
1179:
1062:
935:
824:
732:
627:
507:
484:
418:
417:{\displaystyle i^{th}}
382:
355:
354:{\displaystyle i^{th}}
325:
295:
234:
189:
144:
102:
81:
80:{\displaystyle dn_{i}}
49:Consider the reaction
1332:
1256:
1180:
1063:
936:
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733:
628:
508:
485:
419:
391:stoichiometric number
383:
356:
326:
324:{\displaystyle n_{i}}
296:
235:
190:
150:, the change of B is
145:
103:
82:
1585:Analytical chemistry
1266:
1190:
1078:
948:
850:
760:
668:
520:
506:{\displaystyle \xi }
497:
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365:
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308:
250:
199:
154:
112:
101:{\displaystyle \xi }
92:
61:
22:chemical engineering
39:Théophile de Donder
1580:Physical chemistry
1361:Physical chemistry
1327:
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728:
623:
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26:extent of reaction
18:physical chemistry
1538:10.1021/ed400069d
1376:978-0-7167-8759-4
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430:chemical reaction
289:
1592:
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1549:
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1544:
1532:(9): 1177–1179.
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1511:
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1470:10.1021/ed077p52
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194:
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169:
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149:
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127:
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107:
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75:
1600:
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1502:
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1488:
1484:
1474:
1472:
1450:
1446:
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1384:
1377:
1355:
1348:
1343:
1322:
1308:
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1232:
1212:
1197:
1193:
1191:
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1132:
1128:
1113:
1109:
1085:
1081:
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983:
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743:Nernst equation
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47:
12:
11:
5:
1598:
1588:
1587:
1582:
1566:
1565:
1562:. p. 593.
1550:
1512:
1482:
1444:
1412:
1409:. p. 313.
1397:
1394:. p. 593.
1382:
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1125:
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1119:
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1103:
1100:
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1040:
1037:
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1021:
1010:
1004:
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993:
986:
982:
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972:
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964:
961:
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922:
919:
914:
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906:
895:
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879:
868:
865:
860:
856:
844:
843:
835:
832:
831:
830:
817:
814:
811:
806:
800:
797:
792:
789:
783:
778:
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770:
766:
739:
738:
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722:
719:
714:
708:
705:
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683:
678:
674:
642:
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633:
618:
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55:
54:
46:
43:
9:
6:
4:
3:
2:
1597:
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1578:
1577:
1575:
1561:
1554:
1539:
1535:
1531:
1527:
1523:
1516:
1500:
1493:
1486:
1471:
1467:
1463:
1459:
1458:J. Chem. Educ
1455:
1448:
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1217:
1206:
1203:
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1194:
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1167:
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1138:
1133:
1129:
1123:
1120:
1117:
1114:
1110:
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1101:
1098:
1095:
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1086:
1082:
1074:
1073:
1072:
1047:
1044:
1038:
1035:
1022:
1019:
1008:
1002:
995:
991:
984:
980:
970:
965:
962:
959:
956:
952:
944:
943:
942:
920:
917:
912:
908:
904:
893:
890:
885:
881:
877:
866:
863:
858:
854:
842:2 A ⇌ B + 3 C
841:
840:
839:
815:
812:
809:
804:
798:
790:
781:
776:
773:
768:
756:
755:
754:
752:
748:
744:
723:
720:
717:
712:
706:
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689:
684:
681:
676:
664:
663:
662:
660:
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652:
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616:
612:
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602:
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587:
584:
581:
577:
573:
568:
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562:
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531:
528:
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514:
500:
473:
469:
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426:
409:
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402:
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369:
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339:
316:
312:
284:
280:
273:
269:
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259:
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227:
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210:
206:
202:
182:
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165:
161:
157:
137:
134:
131:
128:
123:
119:
115:
95:
72:
68:
64:
53:A ⇌ 2 B + 3 C
52:
51:
50:
42:
40:
36:
32:
27:
23:
19:
1559:
1553:
1541:. Retrieved
1529:
1525:
1515:
1503:. Retrieved
1498:
1485:
1473:. Retrieved
1461:
1457:
1447:
1431:
1423:
1415:
1406:
1400:
1391:
1385:
1360:
1070:
845:
837:
747:voltaic cell
740:
651:Gibbs energy
647:Gibbs energy
644:
635:
492:
427:
389:
303:
242:
56:
48:
25:
15:
659:temperature
1574:Categories
1341:References
45:Definition
1464:(1): 52.
1294:×
1218:×
1130:ν
1111:ξ
1036:−
1020:−
992:ν
977:Δ
953:ξ
799:ξ
796:∂
788:∂
765:Δ
707:ξ
704:∂
696:∂
673:Δ
641:Relations
613:ν
574:−
525:ξ
501:ξ
470:ν
455:Δ
446:ξ
443:Δ
370:ν
281:ν
257:ξ
228:ξ
183:ξ
138:ξ
132:−
96:ξ
751:enthalpy
655:pressure
1543:10 July
834:Example
394:of the
388:is the
1501:. 2014
1373:
1320:
1306:
1286:
1244:
1230:
1210:
1051:
1026:
1012:
924:
897:
870:
304:where
1505:3 May
1495:(PDF)
1475:3 May
1420:IUPAC
35:moles
1545:2021
1507:2021
1477:2021
1371:ISBN
1317:2.25
1283:0.75
1241:1.75
1207:0.75
1048:0.75
657:and
20:and
1534:doi
1466:doi
1437:doi
1435:".
1367:201
1324:mol
1310:mol
1290:mol
1248:mol
1234:mol
1214:mol
1055:mol
1030:mol
1016:mol
1009:0.5
928:mol
901:mol
874:mol
240:.
16:In
1576::
1530:90
1528:.
1524:.
1497:.
1462:77
1460:.
1456:.
1422:,
1369:.
1349:^
661:.
41:.
24:,
1547:.
1536::
1509:.
1479:.
1468::
1439::
1432:ν
1379:.
1314:=
1303:0
1300:+
1297:3
1280:=
1275:C
1271:n
1238:=
1227:1
1224:+
1221:1
1204:=
1199:B
1195:n
1171:i
1168:,
1165:l
1162:a
1159:i
1156:t
1153:i
1150:n
1147:i
1143:n
1139:+
1134:i
1124:i
1121:u
1118:q
1115:e
1107:=
1102:i
1099:,
1096:i
1093:u
1090:q
1087:e
1083:n
1045:=
1039:2
1023:2
1003:=
996:A
985:A
981:n
971:=
966:i
963:u
960:q
957:e
921:0
918:=
913:C
909:n
905:,
894:1
891:=
886:B
882:n
878:,
867:2
864:=
859:A
855:n
816:T
813:,
810:p
805:)
791:H
782:(
777:=
774:H
769:r
724:T
721:,
718:p
713:)
699:G
690:(
685:=
682:G
677:r
617:i
606:i
603:,
600:l
597:a
594:i
591:t
588:i
585:n
582:i
578:n
569:i
566:,
563:i
560:u
557:q
554:e
550:n
543:=
538:i
535:u
532:q
529:e
474:i
463:i
459:n
449:=
410:h
407:t
403:i
374:i
347:h
344:t
340:i
317:i
313:n
285:i
274:i
270:n
266:d
260:=
254:d
225:d
222:3
219:+
216:=
211:C
207:n
203:d
180:d
177:2
174:+
171:=
166:B
162:n
158:d
135:d
129:=
124:A
120:n
116:d
73:i
69:n
65:d
31:ξ
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