869:
middle oxidation state will either be in a âhillâ or in a âvalleyâ shape. A hill is formed when the left slope is steeper than the right, and a valley is formed when the right slope is steeper than the left. An oxidation state that is on âtop of the hillâ tends to favor disproportionation into the adjacent oxidation states. The adjacent oxidation states, however, will favor comproportionation if the middle oxidation state is in the âbottom of a valleyâ. By
343:
882:
34:
283:
axis of the Frost diagram. Oxidation states are unitless and are also scaled in positive and negative integers. Most often, the Frost diagram displays oxidation state in increasing order, but in some cases it is displayed in decreasing order. The neutral species of the pure element with a free energy
973:
The Frost diagram is also a useful tool for comparing the trends of standard potentials (slope) of acidic and basic solutions. The pure, neutral element transitions to different compounds depending whether the species is in acidic and basic pHs. Though the value and amount of oxidation states remain
868:
Using a Frost diagram, one can predict whether one oxidation state would undergo disproportionation, or two oxidation states would undergo comproportionation. Looking at two slopes among a set of three oxidation states on the diagram, assuming the two standard potentials (slopes) are not equal, the
303:
between two oxidation states. In other words, the steepness of the line shows the tendency for those two reactants to react and to form the lowest-energy product. There is a possibility of having either a positive or a negative slope. A positive slope between two species indicates a tendency for an
982:
Arthur Frost stated in his own original publication that there may be potential criticism for his Frost diagram. He predicts that âthe slopes may not be as easily or accurately recognized as they are the direct numerical values of the oxidation potentials â. Many inorganic chemists use both the
983:
Latimer and Frost diagrams in tandem, using the
Latimer for quantitative data, and then converting those data into a Frost diagram for visualization. Frost suggested that the numerical values of standard potentials could be added next to the slopes to provide supplemental information.
873:, drawing the line between the oxidation state to the left and the one to the right and seeing if the species lies above or below this line is a quick way to determine concavity/convexity (concavity would indicate comproportionation, for example).
1015:
However, in some textbooks the Frost diagram of an element may be confusing for the reader, because the redox potential depends on pH and some notations, or conventions, may differ from the standard conditions and be unclear.
271:
axis of the graph displays the free energy. Increasing stability (lower free energy) is lower on the graph, so the higher free energy and higher on the graph a species of an element is, the more unstable and reactive it is.
1080:), while also discussing redox processes occurring in a basic-solution. To attempt to overcome the problem, in the Phillips and Williams Inorganic Chemistry textbook, however, the reduction potentials for
1143:
value (0 or 14) for which the Frost diagrams have been constructed, or even better, to present both curves (for pH 0 and 14) on the same diagram to put in evidence the effect of pH on the
962:
exchanged. Electrons are always exchanged in electrochemistry, but not necessarily protons. If there is no proton exchange in the reaction equilibrium, the reaction is said to be
1354:
802:
is the opposite reaction, in which two equivalents of an element, identical in oxidation state, react to form two products with differing oxidation states.
974:
unchanged, the free energies can vary greatly. The Frost diagram allows the superimposition of acidic and basic graphs for easy and convenient comparison.
594:
413:: as not all chemical species are necessarily indicated on a given Frost diagram, these diagrams can easily exhibit significant differences:
1139:
So, to avoid confusion for the reader, it is important to use clear conventions and notations, and to also systematically indicate the
1084:
solutions are calculated with non-standard conditions and unusual conventions ( = 1 M, pH = 14) according to the following formula:
259:° = 0 value is usually the neutral species of the pure element. The Frost diagram normally shows free-energy values above and below
279:(sometimes also called oxidation number as on the x axis of two illustrating figures on this page) of the species is shown on the
1069:
Some textbooks present the reduction potentials calculated under standard conditions, so with = 1 M (pH = 0, acid-solution),
620:
A species located above the line between two surrounding species (thus shown at the top of a peak), is unstable and prone to
684:) are both located at the top of a peak and so can easily disproportionate towards the two more stable surrounding species:
158:, who originally invented it as a way to "show both free energy and oxidation potential data conveniently" in a 1951 paper.
987:
434:), also a quite unstable compound and the next Frost diagram for nitrogen, here below, does not present the azide species.
89:
304:
oxidation reaction, while a negative slope between two species indicates a tendency for reduction. For example, if the
970:
in question change oxidation states are the same whatever the pH conditions under which the procedure is carried out.
1039:
334:
is 4/2 = 2, yielding a standard potential of +2. The stability of any terms can be similarly found by this graph.
1386:
790:
In regards to electrochemical reactions, two main types of reactions can be visualized using the Frost diagram.
1038:
anions released in solution during reduction, or at the contrary consumed by oxidation reactions, according to
966:. This means that the values for the electrochemical potential rendered in a redox half-reaction, whereby the
74:
624:(ââ), while a species located below the line joining two surrounding species (thus shown in a dip) lies in a
1031:
870:
148:
439:
The slope of the line between any two points on a Frost diagram gives the standard reduction potential,
178:
167:
80:. The Frost diagram allows easier comprehension of these reduction potentials than the earlier-designed
1296:
MartĂnez de
Illarduya, JesĂșs M.; Villafane, Fernando (June 1994). "A Warning for Frost Diagram Users".
1305:
1265:
1147:
606:
601:
than nitrate, the Gibbs free energy of the half-reaction for nitrate reduction is more important (â
20:
1348:
1023:
1007:
799:
791:
633:
621:
404:
300:
232:
153:
1340:
25:
1164:
316:
185:
62:
1313:
1273:
1206:
1159:
1081:
990:, Martinez de Ilarduya and Villafañe (1994) warn users of Frost diagrams to be aware of the
967:
712:
197:
130:
54:
1043:
795:
598:
276:
174:
81:
66:
58:
1309:
1269:
342:
1333:
1055:
922:
917:
640:
374:
881:
1380:
660:
625:
387:
382:
252:
77:
590:
84:, because the âlack of additivity of potentialsâ was confusing. The free energy Î
1371:
994:
conditions (acid or basic) considered to construct the diagrams. Frost diagrams
73:, so this parameter also must be included. The free energy is determined by the
701:
504:° determined for their respective half-reactions of reduction towards gaseous
288:° = 0) also has an oxidation state equal to zero. However, the energy of some
978:
Possible confusion related to non-standard conventions / pH used in textbooks
959:
423:
418:
309:
305:
289:
38:
33:
886:
685:
614:
447:
347:
228:
1210:
951:
482:
478:
458:
264:
1317:
1278:
1253:
16:
Graph showing the free energy vs oxidation state of a chemical species
1197:
Frost, Arthur (1951). "Oxidation
PotentialâFree Energy Diagrams".
1144:
1027:
904:
899:
880:
798:, combine to form a product with an intermediate oxidation state.
749:
360:
355:
296:
193:
32:
929:), presented here above in the former Frost diagram for nitrogen.
898:: This Frost diagram for nitrogen is also incomplete as it lacks
240:
719:â under acidic conditions, hydrazoic acid disproportionates as:
196:
of the species multiplied by the sign minus and divided by the
57:
to illustrate the relative stability of a number of different
338:
Species thermodynamical stability indicated by peaks and dips
1140:
991:
935:
890:
351:
70:
1372:
Diagrams providing useful oxidation-reduction information
1013:°, implicitly refers to acid conditions ( = 1 M, pH = 0).
231:
exchanged in the reduction reaction multiplied by the
61:
of a particular substance. The graph illustrates the
794:
is when two equivalents of an element, differing in
450:here below, the slope of the straight line between
69:of a chemical species. This effect is dependent on
1332:
748:â under neutral, or basic, conditions, the azide
617:transferred in the half-reaction (10 versus 6).
53:is a type of graph used by inorganic chemists in
609:releasing energy) because of the larger number (
1291:
1289:
1192:
1190:
1188:
1186:
1184:
1182:
1180:
251:The standard free-energy scale is measured in
30:, invented by and named after the same person.
8:
1232:
1230:
1228:
1226:
1224:
1222:
1220:
125:is the number of transferred electrons, and
1353:: CS1 maint: location missing publisher (
477:) being slightly more pronounced than for
1277:
786:Disproportionation and comproportionation
443:°, for the corresponding half-reaction.
1199:Journal of the American Chemical Society
1122:
1118:
1076:
1061:
1049:
1046:is exacerbated under acidic conditions (
938:dependence is given by the factor â0.059
924:
777:
773:
769:
731:
727:
707:
679:
666:
646:
569:
565:
529:
525:
517:
507:
464:
453:
429:
425:
398:
389:
376:
354:= 0 illustrating the instability of the
341:
177:of the species in question, and on its
1176:
1058:is exacerbated under basic conditions (
481:, indicates that nitrite is a stronger
1346:
1254:"Where Is Ozone in the Frost Diagram?"
299:of the line therefore represents the
95:° shown in the graph by the formula:
7:
1006:, classically constructed with the
639:On the Frost diagram for nitrogen,
575:
535:
500:This is confirmed by the values of
147:. The Frost diagram is named after
14:
403:) and their spontaneous trend to
311:has an oxidation state of +6 and
37:Example of Frost diagram for the
593:is located above nitrate in the
457:(at the origin of the plot) and
166:The Frost diagram shows on its
1339:. Oxford University. pp.
1054:) while the reducing power of
322:the oxidation state is +4 and
1:
1298:Journal of Chemical Education
1258:Journal of Chemical Education
988:Journal of Chemical Education
417:, this diagram does not show
162:X,Y axes of the Frost diagram
986:In a paper published in the
90:standard electrode potential
1331:Phillips, C. S. G. (1965).
1403:
18:
1241:. W. H. Freeman & Co.
1042:, the oxidizing power of
950:relates to the number of
446:On the Frost diagram for
1040:Le Chatelier's principle
19:Not to be confused with
806:Disproportionation: 2 M
326:° = 0, then the slope Î
263:° = 0 and is scaled in
194:half-reduction reaction
1252:Villafañe, F. (2009).
1026:ions participate into
931:
605:° < 0 indicates an
436:
138:â 96,485 coulomb/(mol
51:FrostâEbsworth diagram
42:
1030:reactions to balance
954:in the equation, and
884:
829:Comproportionation: M
752:disproportionates as:
597:and so is a stronger
372:, here protonated as
345:
36:
630:intrinsically stable
149:Arthur Atwater Frost
88:° is related to the
1335:Inorganic Chemistry
1310:1994JChEd..71..480M
1270:2009JChEd..86..432V
1239:Inorganic Chemistry
1211:10.1021/ja01150a074
1032:acidâbase reactions
946:per pH unit, where
893:values (0 and 14).
871:Jensen's inequality
607:exothermic reaction
564:+ 12 H + 10 e â N
75:oxidationâreduction
1008:standard potential
932:
885:Frost diagram for
800:Disproportionation
792:Comproportionation
702:molecular nitrogen
634:comproportionation
622:disproportionation
437:
405:disproportionation
346:Frost diagram for
301:standard potential
233:standard potential
184:the difference in
43:
1318:10.1021/ed071p480
1279:10.1021/ed086p432
1165:Ellingham diagram
930:
864:in both examples.
632:, giving rise to
585:° = â1 206 J/mol)
435:
292:may not be zero.
186:Gibbs free energy
1394:
1387:Electrochemistry
1359:
1358:
1352:
1344:
1338:
1328:
1322:
1321:
1293:
1284:
1283:
1281:
1249:
1243:
1242:
1237:Shriver (2010).
1234:
1215:
1214:
1205:(6): 2680â2682.
1194:
1160:Pourbaix diagram
1126:
1079:
1065:
1053:
1044:oxidizing agents
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1022:
928:
915:
913:
912:
909:
894:
781:
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741:
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713:aqueous solution
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239:°, expressed in
198:Faraday constant
157:
146:
141:
131:Faraday constant
120:
106:
59:oxidation states
55:electrochemistry
29:
1402:
1401:
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1173:
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1120:
1116:
1110:
1102:
1094:
1078:
1075:2 H + 2 e â H
1074:
1063:
1059:
1056:reducing agents
1051:
1047:
1035:
1034:related to the
1020:
1014:
980:
926:
921:
910:
907:
906:
903:
889:at two extreme
879:
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796:oxidation state
788:
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320:
277:oxidation state
249:
175:oxidation state
164:
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139:
133:
108:
96:
82:Latimer diagram
67:oxidation state
31:
23:
17:
12:
11:
5:
1400:
1398:
1390:
1389:
1379:
1378:
1375:
1374:
1367:
1366:External links
1364:
1361:
1360:
1323:
1304:(6): 480â482.
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1169:
1168:
1167:
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1155:
1152:
1137:
1136:
1132:
1108:
1100:
1092:
1060:2 OH â O + H
979:
976:
964:pH-independent
958:the number of
918:hydrazoic acid
878:
875:
866:
865:
849:
848:
842:
836:
830:
826:
825:
819:
813:
807:
787:
784:
783:
782:
753:
745:
744:
730:+ 3 H â 12 N
720:
641:hydrazoic acid
587:
586:
581:° = 1.250 V, â
551:
550:
541:° = 1.455 V, â
485:than nitrate (
339:
336:
318:
315:° = 4, and in
253:electron-volts
248:
247:Unit and scale
245:
223:, the number,
163:
160:
78:half-reactions
15:
13:
10:
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1121:O + 2 e â H
1114:
1106:
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1067:
1057:
1048:2 H + O â H
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877:pH dependence
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661:hydroxylamine
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628:sink, and is
627:
626:thermodynamic
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47:Frost diagram
40:
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27:
22:
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591:nitrous acid
588:
582:
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117:
113:
109:
102:
98:
92:
85:
50:
46:
44:
21:Frost circle
1148:equilibrium
595:redox scale
549:â842 J/mol)
350:species at
207:The term -Î
152: [
63:free energy
24: [
1264:(4): 432.
1171:References
1135:+ 0.828 V.
772:O â 12 N
711:). So, in
290:allotropes
255:, and the
192:°, of the
1349:cite book
960:electrons
615:electrons
589:Although
524:6 e â N
419:hydrazine
358:species (
306:manganese
284:of zero (
229:electrons
39:manganese
1381:Category
1154:See also
1019:Because
968:elements
887:nitrogen
686:ammonium
520:+ 6 H +
448:nitrogen
348:nitrogen
265:integers
121:, where
1341:314â321
1306:Bibcode
1266:Bibcode
1101:(pH 14)
1021:
952:protons
599:oxidant
522:
483:oxidant
479:nitrate
459:nitrite
140:
129:is the
41:species
1125:+ 2 OH
998:° = âÎ
780:+ 9 OH
776:+ 3 NH
734:+ 3 NH
700:) and
659:) and
636:(ââ).
381:) and
267:. The
112:° = âÎ
1145:redox
1133:basic
1109:basic
1082:basic
1028:redox
916:, or
900:azide
841:â 2 M
768:+ 9 H
750:anion
613:) of
568:+ 6 H
528:+ 4 H
516:2 HNO
356:azide
297:slope
227:, of
221:i. e.
156:]
101:° = â
28:]
1355:link
1127:) =
1093:(OH)
1066:).
934:The
896:Note
726:9 HN
678:/ NH
555:2 NO
545:° =
467:/ NO
415:e.g.
411:Note
295:The
275:The
241:volt
182:axis
173:the
171:axis
1314:doi
1274:doi
1207:doi
1117:2 H
1115:° (
1073:° (
835:+ M
818:+ M
812:â M
759:9 N
715::
649:/ N
497:).
463:HNO
428:-NH
317:MnO
308:in
219:°,
204:.
188:, Î
107:or
103:nFE
65:vs
49:or
1383::
1351:}}
1347:{{
1312:.
1302:71
1300:.
1288:^
1272:.
1262:86
1260:.
1256:.
1219:^
1203:73
1201:.
1179:^
1150:.
1141:pH
1111:â
1103:=
1095:=
1002:°/
996:nE
992:pH
936:pH
923:HN
920:,
891:pH
860:+
856:=
852:2
690:NH
682:OH
669:OH
665:NH
645:HN
511::
487:NO
424:NH
401:OH
397:NH
395:/
392:OH
388:NH
375:HN
352:pH
330:/Î
324:nE
313:nE
286:nE
261:nE
257:nE
243:.
235:,
217:nE
215:=
211:°/
200:,
154:de
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