942:. This decrease may be measured by chemical analysis in order to evaluate the transport numbers. Analysis of the anode compartment gives a second pair of values as a check, while there should be no change of concentrations in the central compartment unless diffusion of solutes has led to significant mixing during the time of the experiment and invalidated the results.
119:, less than half of the current is carried by the positively charged sodium ions (cations) and more than half is carried by the negatively charged chloride ions (anions) because the chloride ions are able to move faster, i.e., chloride ions have higher mobility than sodium ions. The sum of the transport numbers for all of the ions in solution always equals unity:
965:
The cation of the indicator electrolyte should not move faster than the cation whose transport number is to be determined, and it should have same anion as the principle electrolyte. Besides the principal electrolyte (e.g., HCl) is kept light so that it floats on indicator electrolyte.
637:. Measurement of the concentration changes in the anode and cathode compartments determines the transport numbers. The exact relationship depends on the nature of the reactions at the two electrodes. For the electrolysis of aqueous
1380:
583:
440:
628:
in 1853., and is based on observations of the changes in concentration of an electrolyte solution in the vicinity of the electrodes. In the
Hittorf method, electrolysis is carried out in a cell with three compartments:
359:
102:
1145:
596:) electrolytes with the transfer number of the ion near 1, concentration gradients do not develop. A constant electrolyte concentration is maintained during charge-discharge cycles. In case of
940:
1640:
M. Doyle, T. F. Fuller and J. Newman, "The importance of the lithium ion transference number in lithium/polymer cells." Electrochim Acta, 39, 2073 (1994) 10.1016/0013-4686(94)85091-7
1262:
962:. If a colored solution is used and the interface stays reasonably sharp, the speed of the moving boundary can be measured and used to determine the ion transference numbers.
251:
215:
163:
282:
844:
503:
472:
1464:
1437:
1410:
1175:
793:
728:
511:
of electrolyte. In practice the molar ionic conductivities are calculated from the measured ion transport numbers and the total molar conductivity. For the cation
600:
a more complete utilization of solid electroactive materials at high current densities is possible, even if the ionic conductivity of the electrolyte is reduced.
585:, and similarly for the anion. In solutions, where ionic complexation or associaltion are important, two different transport/transference numbers can be defined.
756:
693:
597:
1277:
514:
370:
1482:
of the distribution of ions comprising NMR-active nuclei (usually 1H, 19F, 7Li) in an electrochemical cells upon application of electric current
292:
1724:
Klett, Matilda; Giesecke, Marianne; Nyman, Andreas; Hallberg, Fredrik; Lindström, Rakel
Wreland; Lindbergh, Göran; Furó, István (2012).
1605:
1786:
53:
1081:
1506:
1271:
The EMF of transport concentration cell involves both the transport number of the cation and its activity coefficient:
1666:
1613:
1594:
1692:
999:(HCl(aq)) may be determined by electrolysis between a cadmium anode and an Ag-AgCl cathode. The anode reaction is
853:
588:
The practical importance of high (i.e. close to 1) transference numbers of the charge-shuttling ion (i.e. Li+ in
958:
in 1893. It depends on the movement of the boundary between two adjacent electrolytes under the influence of an
1700:
616:
involves measuring the speed of displacement of the boundary between two solutions due to an electric current.
1054:
solution, it will rapidly be accelerated back to the boundary by the higher electric field; if a less mobile
1810:
1223:
1726:"Quantifying Mass Transport during Polarization in a Li Ion Battery Electrolyte by in Situ Li NMR Imaging"
1479:
224:
188:
125:
1805:
1531:
173:
1058:
ion diffuses into the HCl solution it will decelerate in the lower electric field and return to the
179:
At zero concentration, the limiting ion transport numbers may be expressed in terms of the limiting
1511:
260:
1516:
1065:
solution. Also the apparatus is constructed with the anode below the cathode, so that the denser
802:
1546:
625:
169:
481:
450:
955:
593:
589:
1714:, G. A. Lonergan and D. C. Pepper, J. Chem. Educ., 1965, 42 (2), p. 82. doi:10.1021/ed042p82
1768:
1677:
1556:
1491:
1442:
1415:
1388:
1153:
1022:
is added to make visible the boundary between the acidic HCl solution and the near-neutral
1014:) solution is formed near the anode and moves toward the cathode during the experiment. An
771:
608:
There are several experimental techniques for the determination of transport numbers. The
702:
8:
1551:
1015:
108:
1265:
741:
678:
638:
180:
1782:
1745:
1696:
1662:
1609:
1590:
1536:
1439:
are activities of HCl solutions of right and left hand electrodes, respectively, and
996:
1774:
1737:
1654:
1209:
1201:
1043:, and therefore a lower electric field to carry the same current. If a more mobile
1019:
1004:
761:
112:
32:
1541:
1526:
1375:{\displaystyle E_{\mathrm {T} }=-z{\frac {RT}{F}}\int _{I}^{II}t_{+}d\ln a_{+/-}}
116:
16:
Fraction of total electric current carried in an electrolyte by an ionic species
1711:
959:
612:
is based on measurements of ion concentration changes near the electrodes. The
1778:
1799:
1725:
1496:
578:{\displaystyle \lambda _{0}^{+}=t_{+}\cdot {\tfrac {\Lambda _{0}}{\nu ^{+}}}}
435:{\displaystyle t_{-}=\nu ^{-}\cdot {\frac {\lambda _{0}^{-}}{\Lambda _{0}}},}
354:{\displaystyle t_{+}=\nu ^{+}\cdot {\frac {\lambda _{0}^{+}}{\Lambda _{0}}}}
1749:
1582:
1501:
951:
508:
1075:
The cation transport number of the leading solution is then calculated as
176:
can arise from ions in a solution having different ion transport numbers.
36:
1629:
1741:
20:
1712:
Transport numbers and ionic mobilities by the moving boundary method
1473:
168:
The concept and measurement of transport number were introduced by
634:
1220:
This quantity can be calculated from the slope of the function
669:
and the anode reaction is the corresponding oxidation of Cu to
592:) is related to the fact, that in single-ion devices (such as
1521:
630:
1766:
1723:
107:
Differences in transport number arise from differences in
40:
1029:
solution. The boundary tends to remain sharp since the
507:
are the numbers of cations and anions respectively per
550:
1445:
1418:
1391:
1280:
1226:
1156:
1084:
856:
805:
774:
744:
705:
681:
517:
484:
453:
373:
295:
263:
227:
191:
128:
97:{\displaystyle t_{i}={\frac {I_{i}}{I_{\text{tot}}}}}
56:
1140:{\displaystyle t_{+}={\frac {z_{+}cLAF}{I\Delta t}}}
1458:
1431:
1404:
1374:
1256:
1169:
1139:
934:
838:
787:
750:
722:
697:coulombs of electricity leads to the reduction of
687:
577:
497:
466:
434:
353:
276:
245:
209:
157:
96:
1589:(8th ed. Oxford University Press, 2006) p.768-9
1474:Electrophoretic magnetic resonance imaging method
1797:
950:This method was developed by British physicists
1693:Principles and Applications of Electrochemistry
624:This method was developed by German physicist
1767:Friedman, H. L.; Franks, Felix, eds. (1973).
1695:D.R.Crow (4th ed., CRC Press 1994) p.165-169
665:ions, the cathode reaction is the reduction
1608:by Salvatore Califano (Springer 2012) p.61
1185:the distance moved by the boundary in time
935:{\displaystyle (1-t_{+})(Q/2F)=t_{-}(Q/2F)}
603:
1625:
1623:
1621:
945:
1770:Aqueous Solutions of Simple Electrolytes
1730:Journal of the American Chemical Society
799:flowing into the cathode compartment is
1618:
1033:HCl has a higher conductivity that the
1798:
1688:
1686:
1215:
995:For example, the transport numbers of
1630:http://lacey.se/science/transference/
1578:
1576:
1574:
1572:
1257:{\displaystyle E_{\mathrm {T} }=f(E)}
846:moles, so there is a net decrease of
1650:
1648:
1646:
850:in the cathode compartment equal to
1683:
1661:(Benjamin/Cummings 1982) p.276-280
1606:Pathways to Modern Chemical Physics
1268:, without or with ionic transport.
992:and the principal electrolyte HCl.
13:
1569:
1507:Einstein relation (kinetic theory)
1287:
1233:
1128:
553:
418:
340:
265:
14:
1822:
1760:
1643:
673:. At the cathode, the passage of
619:
795:of the current, the quantity of
246:{\displaystyle \lambda _{0}^{-}}
210:{\displaystyle \lambda _{0}^{+}}
158:{\displaystyle \sum _{i}t_{i}=1}
1678:Electrochemistry Dictionary - H
31:, is the fraction of the total
1717:
1705:
1671:
1634:
1599:
1251:
1245:
1072:solution forms at the bottom.
929:
912:
896:
879:
876:
857:
833:
816:
1:
277:{\displaystyle \Lambda _{0}}
7:
1773:. Boston, MA: Springer US.
1485:
1466:is the transport number of
839:{\displaystyle t_{+}(Q/2F)}
10:
1827:
1480:magnetic resonance imaging
1196:the cross-sectional area,
1779:10.1007/978-1-4684-2955-8
1532:Liquid junction potential
1478:This method is based on
174:Liquid junction potential
1562:
1512:Electrochemical kinetics
604:Experimental measurement
498:{\displaystyle \nu ^{-}}
467:{\displaystyle \nu ^{+}}
1517:Ion selective electrode
1547:Supporting electrolyte
1460:
1433:
1406:
1376:
1258:
1177:is the cation charge,
1171:
1141:
1047:ion diffuses into the
946:Moving boundary method
936:
840:
789:
768:ions carry a fraction
752:
724:
689:
667:Cu(aq) + 2 e → Cu(s)
648:) as an example, with
626:Johann Wilhelm Hittorf
614:moving boundary method
579:
499:
468:
436:
355:
278:
247:
211:
170:Johann Wilhelm Hittorf
159:
98:
1585:and Julio de Paula,
1461:
1459:{\displaystyle t_{M}}
1434:
1432:{\displaystyle a_{1}}
1407:
1405:{\displaystyle a_{2}}
1377:
1259:
1172:
1170:{\displaystyle z_{+}}
1142:
956:William Cecil Dampier
937:
841:
790:
788:{\displaystyle t_{+}}
753:
725:
690:
594:lithium-ion batteries
590:lithium-ion batteries
580:
500:
469:
437:
356:
279:
248:
212:
160:
111:. For example, in an
99:
1492:Activity coefficient
1443:
1416:
1389:
1278:
1224:
1154:
1082:
977:is less mobile than
973:serves best because
854:
803:
772:
742:
723:{\displaystyle Q/2F}
703:
679:
515:
482:
451:
371:
293:
261:
255:), and electrolyte (
225:
189:
181:molar conductivities
126:
54:
25:ion transport number
1811:Physical quantities
1736:(36): 14654–14657.
1552:Thermogalvanic cell
1334:
1266:concentration cells
1216:Concentration cells
1181:the concentration,
1016:acid-base indicator
532:
416:
338:
242:
206:
109:electrical mobility
29:transference number
1680:Corrosion Doctors.
1659:Physical Chemistry
1587:Physical Chemistry
1456:
1429:
1402:
1372:
1317:
1254:
1167:
1137:
1035:indicator solution
985:is common to both
932:
836:
785:
748:
720:
685:
639:copper(II) sulfate
575:
573:
518:
495:
464:
432:
402:
351:
324:
274:
243:
228:
207:
192:
172:in the year 1853.
155:
138:
94:
27:, also called the
1788:978-1-4684-2957-2
1742:10.1021/ja305461j
1657:and Meiser J.H.,
1557:van't Hoff factor
1537:Solvated electron
1315:
1135:
997:hydrochloric acid
751:{\displaystyle F}
688:{\displaystyle Q}
598:porous electrodes
572:
427:
349:
129:
92:
89:
1818:
1806:Electrochemistry
1792:
1754:
1753:
1721:
1715:
1709:
1703:
1690:
1681:
1675:
1669:
1652:
1641:
1638:
1632:
1627:
1616:
1603:
1597:
1580:
1469:
1465:
1463:
1462:
1457:
1455:
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1438:
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1291:
1290:
1263:
1261:
1260:
1255:
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1237:
1236:
1210:electric current
1207:
1202:Faraday constant
1199:
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1191:
1184:
1180:
1176:
1174:
1173:
1168:
1166:
1165:
1146:
1144:
1143:
1138:
1136:
1134:
1123:
1110:
1109:
1099:
1094:
1093:
1071:
1064:
1057:
1053:
1046:
1042:
1031:leading solution
1028:
1020:bromophenol blue
1013:
1005:cadmium chloride
1002:
991:
984:
980:
976:
972:
941:
939:
938:
933:
922:
911:
910:
889:
875:
874:
849:
845:
843:
842:
837:
826:
815:
814:
798:
794:
792:
791:
786:
784:
783:
767:
762:Faraday constant
759:
757:
755:
754:
749:
735:
731:
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726:
721:
713:
696:
694:
692:
691:
686:
672:
668:
664:
662:
661:
658:
651:
647:
584:
582:
581:
576:
574:
571:
570:
561:
560:
551:
545:
544:
531:
526:
506:
504:
502:
501:
496:
494:
493:
475:
473:
471:
470:
465:
463:
462:
441:
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426:
425:
415:
410:
401:
396:
395:
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382:
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357:
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350:
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332:
323:
318:
317:
305:
304:
285:
283:
281:
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273:
272:
254:
252:
250:
249:
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241:
236:
218:
216:
214:
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208:
205:
200:
164:
162:
161:
156:
148:
147:
137:
113:aqueous solution
103:
101:
100:
95:
93:
91:
90:
87:
81:
80:
71:
66:
65:
46:
33:electric current
1826:
1825:
1821:
1820:
1819:
1817:
1816:
1815:
1796:
1795:
1789:
1763:
1758:
1757:
1722:
1718:
1710:
1706:
1691:
1684:
1676:
1672:
1653:
1644:
1639:
1635:
1628:
1619:
1604:
1600:
1581:
1570:
1565:
1542:Solvation shell
1527:Law of dilution
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1227:
1225:
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1221:
1218:
1205:
1197:
1193:
1186:
1182:
1178:
1161:
1157:
1155:
1152:
1151:
1124:
1105:
1101:
1100:
1098:
1089:
1085:
1083:
1080:
1079:
1070:
1066:
1063:
1059:
1055:
1052:
1048:
1044:
1041:
1037:
1027:
1023:
1012:
1008:
1001:Cd → Cd + 2 e
1000:
990:
986:
982:
978:
974:
971:
967:
948:
918:
906:
902:
885:
870:
866:
855:
852:
851:
847:
822:
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333:
328:
322:
313:
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290:
268:
264:
262:
259:
258:
256:
237:
232:
226:
223:
222:
220:
201:
196:
190:
187:
186:
184:
183:of the cation (
143:
139:
133:
127:
124:
123:
117:sodium chloride
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82:
76:
72:
70:
61:
57:
55:
52:
51:
44:
17:
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11:
5:
1824:
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1808:
1794:
1793:
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1761:External links
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1497:Born equation
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1190:
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1158:
1131:
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1120:
1117:
1114:
1111:
1106:
1102:
1095:
1090:
1086:
1078:
1077:
1076:
1073:
1036:
1032:
1021:
1017:
1006:
998:
993:
963:
961:
957:
953:
943:
926:
923:
919:
915:
907:
903:
899:
893:
890:
886:
882:
871:
867:
863:
860:
830:
827:
823:
819:
811:
807:
780:
776:
763:
745:
717:
714:
710:
706:
682:
640:
636:
632:
627:
617:
615:
611:
601:
599:
595:
591:
586:
567:
563:
557:
546:
541:
537:
533:
528:
523:
519:
510:
490:
486:
459:
455:
429:
422:
412:
407:
403:
397:
392:
388:
384:
379:
375:
367:
366:
365:
344:
334:
329:
325:
319:
314:
310:
306:
301:
297:
289:
288:
287:
269:
238:
233:
229:
202:
197:
193:
182:
177:
175:
171:
152:
149:
144:
140:
134:
130:
122:
121:
120:
118:
114:
110:
83:
77:
73:
67:
62:
58:
50:
49:
48:
42:
38:
34:
30:
26:
22:
1769:
1733:
1729:
1719:
1707:
1673:
1658:
1655:Laidler K.J.
1636:
1601:
1586:
1583:Peter Atkins
1502:Debye length
1477:
1384:
1270:
1219:
1188:
1149:
1074:
1034:
1030:
994:
964:
954:in 1886 and
952:Oliver Lodge
949:
764:. Since the
623:
613:
609:
607:
587:
509:formula unit
444:
363:
178:
167:
106:
28:
24:
18:
39:by a given
37:electrolyte
1800:Categories
1701:0748743782
1003:so that a
219:), anion (
1368:−
1352:
1319:∫
1297:−
1129:Δ
908:−
864:−
732:moles of
564:ν
554:Λ
547:⋅
520:λ
491:−
487:ν
456:ν
419:Λ
413:−
404:λ
398:⋅
393:−
389:ν
380:−
341:Λ
326:λ
320:⋅
311:ν
266:Λ
239:−
230:λ
194:λ
131:∑
21:chemistry
1750:22900791
1486:See also
1018:such as
736:, where
43:species
1264:of two
760:is the
758:
738:
730:
699:
695:
675:
635:cathode
505:
478:
474:
447:
284:
257:
253:
221:
217:
185:
1785:
1748:
1699:
1665:
1612:
1593:
1385:where
1204:, and
1150:where
650:Cu(aq)
445:where
1563:Notes
1522:ITIES
631:anode
364:and
41:ionic
1783:ISBN
1746:PMID
1697:ISBN
1663:ISBN
1610:ISBN
1591:ISBN
1412:and
1208:the
1200:the
1067:CdCl
1060:CdCl
1049:CdCl
1038:CdCl
1024:CdCl
1009:CdCl
987:CdCl
981:and
968:CdCl
663:(aq)
652:and
643:CuSO
476:and
1775:doi
1738:doi
1734:134
286:):
115:of
88:tot
19:In
1802::
1781:.
1744:.
1732:.
1728:.
1685:^
1645:^
1620:^
1571:^
1470:.
1468:Cl
1349:ln
1212:.
1192:,
1056:Cd
983:Cl
975:Cd
848:Cu
797:Cu
766:Cu
734:Cu
671:Cu
657:2−
654:SO
47::
23:,
1791:.
1777::
1752:.
1740::
1452:M
1448:t
1425:1
1421:a
1398:2
1394:a
1364:/
1360:+
1356:a
1346:d
1341:+
1337:t
1331:I
1328:I
1323:I
1313:F
1309:T
1306:R
1300:z
1294:=
1288:T
1283:E
1252:)
1249:E
1246:(
1243:f
1240:=
1234:T
1229:E
1206:I
1198:F
1194:A
1189:t
1187:Δ
1183:L
1179:c
1163:+
1159:z
1132:t
1126:I
1121:F
1118:A
1115:L
1112:c
1107:+
1103:z
1096:=
1091:+
1087:t
1069:2
1062:2
1051:2
1045:H
1040:2
1026:2
1011:2
1007:(
989:2
979:H
970:2
930:)
927:F
924:2
920:/
916:Q
913:(
904:t
900:=
897:)
894:F
891:2
887:/
883:Q
880:(
877:)
872:+
868:t
861:1
858:(
834:)
831:F
828:2
824:/
820:Q
817:(
812:+
808:t
781:+
777:t
746:F
718:F
715:2
711:/
707:Q
683:Q
660:4
645:4
641:(
568:+
558:0
542:+
538:t
534:=
529:+
524:0
460:+
430:,
423:0
408:0
385:=
376:t
345:0
335:+
330:0
315:+
307:=
302:+
298:t
270:0
234:0
203:+
198:0
153:1
150:=
145:i
141:t
135:i
84:I
78:i
74:I
68:=
63:i
59:t
45:i
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