2384:
29:
336:
878:
1857:
1779:
1805:
1702:
372:. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added. Similarly, if strong alkali is added to the mixture, the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added. In Figure 1, the effect is illustrated by the simulated titration of a weak acid with
1831:
1728:
1648:
1622:
1753:
1882:
1676:
3009:
2502:
values is less than about 3, there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. In the case of citric acid, the overlap is extensive and solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5.
1032:. Buffer capacity is negligible when the concentration of buffering agent is very small and increases with increasing concentration of the buffering agent. Some authors show only this region in graphs of buffer capacity. Buffer capacity falls to 33% of the maximum value at pH = p
2515:
818:
1019:
1174:
389: ± 1, centered at pH = 4.7, where = . The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction
421:
Buffer capacity is a quantitative measure of the resistance to change of pH of a solution containing a buffering agent with respect to a change of acid or alkali concentration. It can be defined as follows:
28:
2333:
581:
484:
1185:
The pH of a solution containing a buffering agent can only vary within a narrow range, regardless of what else may be present in the solution. In biological systems this is an essential condition for
3481:
2247:
634:
2520:
1112:
3004:{\displaystyle {\begin{aligned}C_{{\ce {A}}}&=+\beta _{1}+\beta _{2}^{2}+\beta _{3}^{3},\\C_{{\ce {H}}}&=+\beta _{1}+2\beta _{2}^{2}+3\beta _{3}^{3}-K_{\text{w}}^{-1}.\end{aligned}}}
382: = 4.7. The relative concentration of undissociated acid is shown in blue, and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = p
368:
When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, hydrogen ions (H) are added, and the equilibrium is shifted to the left, in accordance with
1117:
With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH:
2170:
1375:
may be added. Alternatively, a buffer mixture can be made from a mixture of an acid and its conjugate base. For example, an acetate buffer can be made from a mixture of acetic acid and
1070:
With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH:
1937:
This shows that when the acid dissociates, equal amounts of hydrogen ion and anion are produced. The equilibrium concentrations of these three components can be calculated in an
299:
is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. Its pH changes very little when a small amount of
1176:
This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent.
845:
3055:
in two unknown quantities and . Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS.
1114:
This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent.
611:
514:
903:
307:
is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. In nature, there are many
1120:
3477:
1232:
fraction; this constitutes the major mechanism for maintaining the pH of blood between 7.35 and 7.45. Outside this narrow range (7.40 ± 0.05 pH unit),
2507:
2387:
3504:"Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species"
2254:
3193:
519:
425:
1258:
processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis and calibration of
3568:
2177:
3143:
Cumulative association constants are used in general-purpose computer programs such as the one used to obtain the speciation diagram above.
1073:
3034:
221:
162:
282:
3064:
Relationship between cumulative association constant (β) values and stepwise dissociation constant (K) values for a tribasic acid.
2394:
Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as
1247:, which is usually irreversible. The majority of biological samples that are used in research are kept in a buffer solution, often
1338:
3671:
2087:
1405:
values, separated by less than two. The buffer range can be extended by adding other buffering agents. The following mixtures (
1240:
metabolic conditions rapidly develop, ultimately leading to death if the correct buffering capacity is not rapidly restored.
3426:
3358:
3333:
3305:
3240:
3203:
3058:
N.B. The numbering of cumulative, overall constants is the reverse of the numbering of the stepwise, dissociation constants.
3400:
2065:
for "change", specifies the changes that occur when the acid dissociates. The acid concentration decreases by an amount −
3152:
1243:
If the pH value of a solution rises or falls too much, the effectiveness of an enzyme decreases in a process, known as
399:
and only a little is consumed in the neutralization reaction (which is the reaction that results in an increase in pH)
1551:
for the historic design principles and favourable properties of these buffer substances in biochemical applications.
3853:
3561:
874:
of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration.
3848:
3762:
3523:
3858:
813:{\displaystyle \beta =2.303\left(+{\frac {T_{{\ce {HA}}}K_{a}}{(K_{a}+)^{2}}}+{\frac {K_{\text{w}}}{}}\right),}
2510:
to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance:
1318:
275:
3820:
3724:
3554:
2061:
will have a negative sign because alkali removes hydrogen ions from the solution. The second row, labelled
312:
3633:
3261:
Urbansky, Edward T.; Schock, Michael R. (2000). "Understanding, Deriving and
Computing Buffer Capacity".
1532:
1255:
1244:
369:
3740:
1563:
1367:
For buffers in acid regions, the pH may be adjusted to a desired value by adding a strong acid such as
373:
3863:
3648:
3616:
1248:
53:
1394:
values differing by only two or less and adjusting the pH, a wide range of buffers can be obtained.
413:, the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.
3789:
3784:
3745:
3045:
2057:
strong acid, such as hydrochloric acid. If strong alkali, such as sodium hydroxide, is added, then
855:
823:
268:
118:
103:
98:
900:
In the central region of the curve (coloured green on the plot), the second term is dominant, and
2077:
for "equilibrium", adds together the first two rows and shows the concentrations at equilibrium.
1517:
123:
304:
241:
3808:
3698:
1379:. Similarly, an alkaline buffer can be made from a mixture of the base and its conjugate acid.
48:
3801:
3796:
3774:
3719:
3626:
3606:
3540:
3052:
1406:
251:
226:
167:
133:
93:
83:
586:
489:
3683:
3666:
3577:
3451:
3270:
3172:
896:
This equation shows that there are three regions of raised buffer capacity (see figure 2).
359:
128:
8:
3779:
3757:
3643:
3601:
624:
With either definition the buffer capacity for a weak acid HA with dissociation constant
324:
3455:
3274:
3767:
3658:
3591:
3192:
J. Gordon Betts (25 April 2013). "Inorganic compounds essential to human functioning".
1418:
3519:
3395:
2174:
Substitute the concentrations with the values found in the last row of the ICE table:
3813:
3693:
3621:
3611:
3422:
3354:
3329:
3301:
3236:
3199:
3162:
3157:
1548:
1368:
138:
3351:
Fundamentals of Acids, Bases, Buffers & Their
Application to Biochemical Systems
3752:
3638:
3515:
3459:
3390:
3278:
3167:
1603:
1372:
1060: ± 1. When choosing a buffer for use at a specific pH, it should have a p
211:
73:
63:
3231:
Skoog, Douglas A.; West, Donald M.; Holler, F. James; Crouch, Stanley R. (2014).
113:
38:
3502:
Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. (1999).
3825:
3375:
1718:
1376:
1371:
to the particular buffering agent. For alkaline buffers, a strong base such as
1014:{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}}{(K_{a}+)^{2}}}.}
308:
3842:
3678:
1612:
1194:
410:
58:
3417:
Mendham, J.; Denny, R. C.; Barnes, J. D.; Thomas, M. (2000). "Appendix 5".
2084:, use the formula for the equilibrium constant in terms of concentrations:
2049:, initially undissociated, so the concentrations of A and H would be zero;
1872:
1769:
1229:
231:
182:
177:
172:
88:
1169:{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}
2409:
2383:
1513:
1432:
1395:
1305:
1292:
1216:
335:
300:
236:
187:
68:
2073:. This follows from the equilibrium expression. The third row, labelled
3688:
3442:
Carmody, Walter R. (1961). "Easily prepared wide range buffer series".
3282:
3049:
1847:
1521:
202:
3546:
3503:
3463:
3596:
1938:
1237:
863:
340:
256:
246:
197:
192:
143:
877:
1525:
1259:
1233:
871:
1856:
1692:
2069:, and the concentrations of A and H both increase by an amount +
1778:
1398:
is a useful component of a buffer mixture because it has three p
1638:
1351:
1186:
613:
is an infinitesimal amount of added acid. pH is defined as −log
2401:, and the constants for dissociation of successive protons as
2042:, lists the initial conditions: the concentration of acid is
1821:
1743:
1190:
1053:± 2. For this reason the most useful range is approximately p
320:
2328:{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}
1795:
1664:
1021:
Buffer capacity rises to a local maximum at pH =
576:{\displaystyle \beta =-{\frac {dC_{a}}{d(\mathrm {pH} )}},}
152:
43:
1804:
1701:
1538:
479:{\displaystyle \beta ={\frac {dC_{b}}{d(\mathrm {pH} )}},}
1647:
3501:
3416:
3026:
is the analytical concentration of added hydrogen ions,
2506:
Calculation of the pH with a polyprotic acid requires a
1830:
1752:
1727:
1382:
2242:{\displaystyle K_{\text{a}}={\frac {x(x+y)}{C_{0}-x}}.}
1675:
1621:
1531:
Other universal buffers are the
Carmody buffer and the
316:
311:
that use buffering for pH regulation. For example, the
108:
2390:
calculated for a 10-millimolar solution of citric acid
1881:
16:
Aqueous solution of a weak acid and its conjugate base
3230:
2518:
2257:
2180:
2090:
1748:(4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid)
1123:
1076:
906:
826:
637:
589:
522:
492:
428:
3326:
Reactions of acids and bases in analytical chemistry
1028:. The height of this peak depends on the value of pK
1941:(ICE standing for "initial, change, equilibrium").
362:between the weak acid HA and its conjugate base A:
3419:Vogel's textbook of quantitative chemical analysis
3003:
2327:
2241:
2164:
1409:solutions) have a buffer range of pH 3 to 8.
1168:
1107:{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}
1106:
1013:
839:
820:where is the concentration of hydrogen ions, and
812:
605:
575:
508:
478:
3298:Ionic Equilibrium: Solubility and pH calculations
2363:, the pH can be calculated as pH = −log
885:for a 0.1 M solution of a weak acid with a p
3840:
3376:"A buffer solution for colorimetric comparaison"
358:Buffer solutions resist pH change because of a
3191:
3260:
3562:
3019:is the analytical concentration of the acid,
1826:(piperazine-N,N′-bis(2-ethanesulfonic acid))
1528:can be made to cover the pH range 2.6 to 12.
516:is an infinitesimal amount of added base, or
276:
1931:First write down the equilibrium expression
3421:(5th ed.). Harlow: Pearson Education.
3342:
3319:
3317:
1671:2-amino-2-(hydroxymethyl)propane-1,3-diol)
3569:
3555:
3256:
3254:
3252:
3235:(9th ed.). Brooks/Cole. p. 226.
2165:{\displaystyle K_{\text{a}}={\frac {}{}}.}
1643:(2-(bis(2-hydroxyethyl)amino)acetic acid)
1265:
1254:In industry, buffering agents are used in
1180:
862:10. Note that in solution H exists as the
847:is the total concentration of added acid.
330:
283:
269:
3394:
3373:
3328:. Translated by Masson, Mary R. Horwood.
3323:
343:of an acidified solution of a weak acid (
3314:
2495:When the difference between successive p
2382:
1921:
876:
621:(pH) is an infinitesimal change in pH.
334:
3576:
3441:
3348:
3249:
3226:
3224:
3222:
3185:
1800:(3-(N-morpholino)propanesulfonic acid)
1539:Common buffer compounds used in biology
1189:to function correctly. For example, in
3841:
3435:
3295:
1877:(2-(N-morpholino)ethanesulfonic acid)
1067:value as close as possible to that pH.
3550:
1669:(tris(hydroxymethyl)aminomethane, or
3233:Fundamentals of Analytical Chemistry
3219:
2412:is an example of a polyprotic acid H
1914:= 8.07 refers to its conjugate acid.
1544:
3353:. Kendall/Hunt Publishing Company.
2378:
2359:. Assuming that pH = −log
1926:
1723:(3--2-hydroxypropanesulfonic acid)
1577:
13:
2355:, this equation can be solved for
1147:
1139:
1136:
1095:
1092:
560:
557:
463:
460:
416:
14:
3875:
3534:
2416:A, as it can lose three protons.
323:, and bicarbonate also acts as a
3526:from the original on 2007-07-04.
3406:from the original on 2015-02-26.
3035:cumulative association constants
2422:Stepwise dissociation constants
2053:is the initial concentration of
1947:ICE table for a monoprotic acid
1880:
1855:
1829:
1803:
1777:
1751:
1726:
1700:
1674:
1646:
1620:
854:is the equilibrium constant for
27:
3495:
3484:from the original on 2009-04-17
3470:
1901:
409:Once the acid is more than 95%
3508:Coordination Chemistry Reviews
3410:
3367:
3289:
3153:Henderson–Hasselbalch equation
2982:
2966:
2944:
2928:
2925:
2907:
2882:
2866:
2863:
2845:
2826:
2811:
2808:
2790:
2774:
2759:
2724:
2708:
2705:
2687:
2665:
2649:
2646:
2628:
2612:
2597:
2594:
2576:
2560:
2542:
2290:
2271:
2212:
2200:
2153:
2145:
2140:
2125:
2122:
2107:
1774:(2-amino]ethanesulfonic acid)
1387:By combining substances with p
996:
992:
977:
961:
956:
941:
796:
781:
753:
749:
734:
718:
713:
698:
667:
652:
564:
553:
467:
456:
1:
3520:10.1016/S0010-8545(98)00260-4
3396:10.1016/S0021-9258(18)86000-8
3263:Journal of Chemical Education
3178:
840:{\displaystyle T_{\text{HA}}}
1557:Common name (chemical name)
313:bicarbonate buffering system
7:
3300:. Wiley. pp. 133–136.
3146:
1383:"Universal" buffer mixtures
10:
3880:
881:Figure 2. Buffer capacity
3733:
3707:
3657:
3649:Thermodynamic equilibrium
3584:
3478:"Buffer Reference Center"
3374:McIlvaine, T. C. (1921).
2337:With specific values for
1249:phosphate buffered saline
1046:± 1.5 and to 1% at pH = p
3802:Distribution coefficient
3746:Hammett acidity function
3725:Liquid–liquid extraction
3634:Le Chatelier's principle
3046:self-ionization of water
2038:The first row, labelled
1543:For effective range see
856:self-ionization of water
370:Le Chatelier's principle
315:is used to regulate the
119:Self-ionization of water
104:Hammett acidity function
1852:(dimethylarsenic acid)
1617:(propanesulfonic acid)
1533:Britton–Robinson buffer
1526:diethyl barbituric acid
1518:monopotassium phosphate
1266:Simple buffering agents
1181:Applications of buffers
331:Principles of buffering
3763:Coordination complexes
3699:Thermodynamic activity
3324:Hulanicki, A. (1987).
3296:Butler, J. N. (1998).
3195:Anatomy and Physiology
3053:simultaneous equations
3005:
2508:speciation calculation
2391:
2329:
2243:
2166:
1251:(PBS) at pH 7.4.
1170:
1108:
1015:
893:
841:
814:
607:
606:{\displaystyle dC_{a}}
577:
510:
509:{\displaystyle dC_{b}}
480:
355:
3859:Equilibrium chemistry
3775:Dissociation constant
3720:Equilibrium unfolding
3607:Equilibrium chemistry
3006:
2386:
2330:
2244:
2167:
1922:Calculating buffer pH
1907:Tris is a base, the p
1535:, developed in 1931.
1512:A mixture containing
1171:
1109:
1039:± 1, to 10% at pH = p
1016:
880:
842:
815:
608:
578:
511:
481:
338:
134:Frustrated Lewis pair
94:Equilibrium chemistry
84:Dissociation constant
54:Acid–base homeostasis
3854:Acid–base physiology
3684:Predominance diagram
3667:Equilibrium constant
3541:"Biological buffers"
3349:Scorpio, R. (2000).
3173:Mineral redox buffer
3044:is the constant for
2516:
2255:
2178:
2088:
1228:) is present in the
1121:
1074:
904:
824:
635:
631:can be expressed as
587:
520:
490:
426:
360:chemical equilibrium
339:Figure 1. Simulated
129:Lewis acid catalysis
3849:Acid–base chemistry
3758:Binding selectivity
3734:Specific equilibria
3644:Reversible reaction
3602:Dynamic equilibrium
3578:Chemical equilibria
3456:1961JChEd..38..559C
3275:2000JChEd..77.1640U
3065:
2423:
2388:% species formation
1948:
325:buffer in the ocean
3768:Macrocyclic effect
3592:Chemical stability
3283:10.1021/ed077p1640
3063:
3001:
2999:
2421:
2392:
2325:
2239:
2162:
1946:
1547:, above. Also see
1407:McIlvaine's buffer
1166:
1104:
1011:
894:
837:
810:
603:
573:
506:
476:
356:
49:Acid–base reaction
3836:
3835:
3814:Common-ion effect
3741:Acid dissociation
3694:Reaction quotient
3612:Equilibrium stage
3480:. Sigma-Aldrich.
3464:10.1021/ed038p559
3428:978-0-582-22628-9
3360:978-0-7872-7374-3
3335:978-0-85312-330-9
3307:978-0-471-58526-8
3269:(12): 1640–1644.
3242:978-0-495-55828-6
3205:978-1-947172-04-3
3163:Common-ion effect
3139:
3138:
2973:
2963:
2935:
2914:
2873:
2852:
2818:
2797:
2766:
2748:
2715:
2694:
2656:
2635:
2604:
2583:
2549:
2531:
2491:
2490:
2306:
2281:
2234:
2188:
2157:
2151:
2132:
2114:
2098:
2034:
2033:
1897:
1896:
1508:
1507:
1369:hydrochloric acid
1363:
1362:
1158:
1006:
984:
948:
927:
834:
800:
788:
777:
763:
741:
705:
684:
659:
568:
471:
293:
292:
139:Chiral Lewis acid
3871:
3864:Buffer solutions
3753:Binding constant
3639:Phase separation
3571:
3564:
3557:
3548:
3547:
3544:
3543:. REACH Devices.
3528:
3527:
3499:
3493:
3492:
3490:
3489:
3474:
3468:
3467:
3439:
3433:
3432:
3414:
3408:
3407:
3405:
3398:
3380:
3371:
3365:
3364:
3346:
3340:
3339:
3321:
3312:
3311:
3293:
3287:
3286:
3258:
3247:
3246:
3228:
3217:
3216:
3214:
3212:
3189:
3168:Metal ion buffer
3066:
3062:
3048:. There are two
3010:
3008:
3007:
3002:
3000:
2993:
2992:
2980:
2979:
2978:
2971:
2965:
2964:
2961:
2952:
2951:
2942:
2941:
2940:
2933:
2924:
2923:
2922:
2912:
2906:
2905:
2890:
2889:
2880:
2879:
2878:
2871:
2862:
2861:
2860:
2850:
2844:
2843:
2825:
2824:
2823:
2816:
2807:
2806:
2805:
2795:
2789:
2788:
2773:
2772:
2771:
2764:
2751:
2750:
2749:
2746:
2732:
2731:
2722:
2721:
2720:
2713:
2704:
2703:
2702:
2692:
2686:
2685:
2673:
2672:
2663:
2662:
2661:
2654:
2645:
2644:
2643:
2633:
2627:
2626:
2611:
2610:
2609:
2602:
2593:
2592:
2591:
2581:
2575:
2574:
2559:
2558:
2557:
2547:
2534:
2533:
2532:
2529:
2424:
2420:
2379:Polyprotic acids
2334:
2332:
2331:
2326:
2318:
2317:
2308:
2307:
2304:
2283:
2282:
2279:
2267:
2266:
2248:
2246:
2245:
2240:
2235:
2233:
2226:
2225:
2215:
2195:
2190:
2189:
2186:
2171:
2169:
2168:
2163:
2158:
2156:
2152:
2149:
2143:
2139:
2138:
2137:
2130:
2121:
2120:
2119:
2112:
2105:
2100:
2099:
2096:
1949:
1945:
1927:Monoprotic acids
1915:
1905:
1884:
1859:
1833:
1807:
1781:
1755:
1730:
1704:
1678:
1650:
1624:
1599:
1597:
1596:
1590:
1587:
1579:
1554:
1553:
1414:
1413:
1373:sodium hydroxide
1297:3.13, 4.76, 6.40
1287:Useful pH range
1272:
1271:
1227:
1226:
1214:
1213:
1205:
1204:
1175:
1173:
1172:
1167:
1162:
1161:
1160:
1159:
1156:
1150:
1142:
1113:
1111:
1110:
1105:
1100:
1099:
1098:
1020:
1018:
1017:
1012:
1007:
1005:
1004:
1003:
991:
990:
989:
982:
973:
972:
959:
955:
954:
953:
946:
940:
939:
930:
929:
928:
925:
917:
861:
846:
844:
843:
838:
836:
835:
832:
819:
817:
816:
811:
806:
802:
801:
799:
795:
794:
793:
786:
779:
778:
775:
769:
764:
762:
761:
760:
748:
747:
746:
739:
730:
729:
716:
712:
711:
710:
703:
697:
696:
687:
686:
685:
682:
674:
666:
665:
664:
657:
612:
610:
609:
604:
602:
601:
582:
580:
579:
574:
569:
567:
563:
548:
547:
546:
533:
515:
513:
512:
507:
505:
504:
485:
483:
482:
477:
472:
470:
466:
451:
450:
449:
436:
353:
285:
278:
271:
252:Non-nucleophilic
79:Buffer solutions
64:Acidity function
31:
19:
18:
3879:
3878:
3874:
3873:
3872:
3870:
3869:
3868:
3839:
3838:
3837:
3832:
3785:Self-ionization
3729:
3715:Buffer solution
3703:
3653:
3580:
3575:
3539:
3537:
3532:
3531:
3500:
3496:
3487:
3485:
3476:
3475:
3471:
3450:(11): 559–560.
3440:
3436:
3429:
3415:
3411:
3403:
3378:
3372:
3368:
3361:
3347:
3343:
3336:
3322:
3315:
3308:
3294:
3290:
3259:
3250:
3243:
3229:
3220:
3210:
3208:
3206:
3190:
3186:
3181:
3149:
3135:
3131:
3127:
3123:
3117:
3109:
3105:
3101:
3095:
3087:
3083:
3043:
3031:
3025:
3018:
2998:
2997:
2985:
2981:
2974:
2970:
2969:
2960:
2956:
2947:
2943:
2936:
2932:
2931:
2915:
2911:
2910:
2901:
2897:
2885:
2881:
2874:
2870:
2869:
2853:
2849:
2848:
2839:
2835:
2819:
2815:
2814:
2798:
2794:
2793:
2784:
2780:
2767:
2763:
2762:
2752:
2745:
2744:
2740:
2737:
2736:
2727:
2723:
2716:
2712:
2711:
2695:
2691:
2690:
2681:
2677:
2668:
2664:
2657:
2653:
2652:
2636:
2632:
2631:
2622:
2618:
2605:
2601:
2600:
2584:
2580:
2579:
2570:
2566:
2550:
2546:
2545:
2535:
2528:
2527:
2523:
2519:
2517:
2514:
2513:
2501:
2486:
2471:
2461:
2452:
2442:
2438:
2415:
2407:
2400:
2381:
2366:
2362:
2350:
2343:
2313:
2309:
2303:
2299:
2278:
2274:
2262:
2258:
2256:
2253:
2252:
2221:
2217:
2216:
2196:
2194:
2185:
2181:
2179:
2176:
2175:
2148:
2144:
2133:
2129:
2128:
2115:
2111:
2110:
2106:
2104:
2095:
2091:
2089:
2086:
2085:
2048:
2012:
1970:
1935:
1929:
1924:
1919:
1918:
1913:
1906:
1902:
1876:
1851:
1825:
1799:
1773:
1747:
1722:
1696:
1670:
1668:
1642:
1616:
1605:
1591:
1588:
1585:
1584:
1582:
1581:
1573:
1570:
1545:Buffer capacity
1541:
1426:
1422:
1404:
1393:
1385:
1326:
1322:
1284:
1275:Buffering agent
1268:
1225:
1222:
1221:
1220:
1212:
1209:
1208:
1207:
1203:
1200:
1199:
1198:
1183:
1155:
1151:
1146:
1135:
1134:
1130:
1122:
1119:
1118:
1091:
1087:
1083:
1075:
1072:
1071:
1066:
1059:
1052:
1045:
1038:
1031:
1027:
999:
995:
985:
981:
980:
968:
964:
960:
949:
945:
944:
935:
931:
924:
923:
919:
918:
916:
905:
902:
901:
891:
870:O, and further
869:
859:
853:
831:
827:
825:
822:
821:
789:
785:
784:
780:
774:
770:
768:
756:
752:
742:
738:
737:
725:
721:
717:
706:
702:
701:
692:
688:
681:
680:
676:
675:
673:
660:
656:
655:
651:
647:
636:
633:
632:
630:
616:
597:
593:
588:
585:
584:
556:
549:
542:
538:
534:
532:
521:
518:
517:
500:
496:
491:
488:
487:
459:
452:
445:
441:
437:
435:
427:
424:
423:
419:
417:Buffer capacity
407:
405:
397:
395:
388:
380:
366:
351:
344:
333:
297:buffer solution
289:
114:Proton affinity
39:Acceptor number
22:Acids and bases
17:
12:
11:
5:
3877:
3867:
3866:
3861:
3856:
3851:
3834:
3833:
3831:
3830:
3829:
3828:
3818:
3817:
3816:
3806:
3805:
3804:
3794:
3793:
3792:
3782:
3777:
3772:
3771:
3770:
3760:
3755:
3750:
3749:
3748:
3737:
3735:
3731:
3730:
3728:
3727:
3722:
3717:
3711:
3709:
3705:
3704:
3702:
3701:
3696:
3691:
3686:
3681:
3676:
3675:
3674:
3663:
3661:
3655:
3654:
3652:
3651:
3646:
3641:
3636:
3631:
3630:
3629:
3624:
3614:
3609:
3604:
3599:
3594:
3588:
3586:
3582:
3581:
3574:
3573:
3566:
3559:
3551:
3536:
3535:External links
3533:
3530:
3529:
3514:(1): 311–318.
3494:
3469:
3434:
3427:
3409:
3389:(1): 183–186.
3366:
3359:
3341:
3334:
3313:
3306:
3288:
3248:
3241:
3218:
3204:
3183:
3182:
3180:
3177:
3176:
3175:
3170:
3165:
3160:
3158:Good's buffers
3155:
3148:
3145:
3141:
3140:
3137:
3136:
3133:
3129:
3125:
3121:
3118:
3115:
3111:
3110:
3107:
3103:
3099:
3096:
3093:
3089:
3088:
3085:
3081:
3078:
3074:
3073:
3070:
3041:
3029:
3023:
3016:
2996:
2991:
2988:
2984:
2977:
2968:
2959:
2955:
2950:
2946:
2939:
2930:
2927:
2921:
2918:
2909:
2904:
2900:
2896:
2893:
2888:
2884:
2877:
2868:
2865:
2859:
2856:
2847:
2842:
2838:
2834:
2831:
2828:
2822:
2813:
2810:
2804:
2801:
2792:
2787:
2783:
2779:
2776:
2770:
2761:
2758:
2755:
2753:
2743:
2739:
2738:
2735:
2730:
2726:
2719:
2710:
2707:
2701:
2698:
2689:
2684:
2680:
2676:
2671:
2667:
2660:
2651:
2648:
2642:
2639:
2630:
2625:
2621:
2617:
2614:
2608:
2599:
2596:
2590:
2587:
2578:
2573:
2569:
2565:
2562:
2556:
2553:
2544:
2541:
2538:
2536:
2526:
2522:
2521:
2499:
2493:
2492:
2489:
2488:
2484:
2478:
2474:
2473:
2469:
2463:
2459:
2455:
2454:
2450:
2444:
2440:
2436:
2432:
2431:
2428:
2413:
2405:
2398:
2380:
2377:
2364:
2360:
2348:
2341:
2324:
2321:
2316:
2312:
2302:
2298:
2295:
2292:
2289:
2286:
2277:
2273:
2270:
2265:
2261:
2238:
2232:
2229:
2224:
2220:
2214:
2211:
2208:
2205:
2202:
2199:
2193:
2184:
2161:
2155:
2147:
2142:
2136:
2127:
2124:
2118:
2109:
2103:
2094:
2046:
2036:
2035:
2032:
2031:
2022:
2017:
2010:
2005:
2001:
2000:
1995:
1990:
1984:
1980:
1979:
1974:
1971:
1968:
1963:
1959:
1958:
1956:
1954:
1952:
1933:
1928:
1925:
1923:
1920:
1917:
1916:
1911:
1899:
1898:
1895:
1894:
1891:
1888:
1885:
1878:
1869:
1868:
1865:
1863:
1860:
1853:
1844:
1843:
1840:
1837:
1834:
1827:
1818:
1817:
1814:
1811:
1808:
1801:
1792:
1791:
1788:
1785:
1782:
1775:
1766:
1765:
1762:
1759:
1756:
1749:
1740:
1739:
1736:
1734:
1731:
1724:
1715:
1714:
1711:
1708:
1705:
1698:
1689:
1688:
1685:
1682:
1679:
1672:
1661:
1660:
1657:
1654:
1651:
1644:
1635:
1634:
1631:
1628:
1625:
1618:
1609:
1608:
1601:
1575:
1568:
1561:
1558:
1549:Good's buffers
1540:
1537:
1510:
1509:
1506:
1505:
1502:
1499:
1495:
1494:
1491:
1488:
1484:
1483:
1480:
1477:
1473:
1472:
1469:
1466:
1462:
1461:
1458:
1455:
1451:
1450:
1447:
1444:
1440:
1439:
1436:
1429:
1424:
1420:
1402:
1391:
1384:
1381:
1377:sodium acetate
1365:
1364:
1361:
1360:
1357:
1354:
1348:
1347:
1344:
1341:
1335:
1334:
1331:
1328:
1324:
1320:
1315:
1314:
1311:
1308:
1302:
1301:
1298:
1295:
1289:
1288:
1285:
1282:
1276:
1267:
1264:
1260:pH meters
1223:
1210:
1201:
1182:
1179:
1178:
1177:
1165:
1154:
1149:
1145:
1141:
1138:
1133:
1129:
1126:
1115:
1103:
1097:
1094:
1090:
1086:
1082:
1079:
1068:
1064:
1057:
1050:
1043:
1036:
1029:
1025:
1010:
1002:
998:
994:
988:
979:
976:
971:
967:
963:
958:
952:
943:
938:
934:
922:
915:
912:
909:
892: = 7
889:
867:
858:, equal to 1.0
851:
830:
809:
805:
798:
792:
783:
773:
767:
759:
755:
751:
745:
736:
733:
728:
724:
720:
715:
709:
700:
695:
691:
679:
672:
669:
663:
654:
650:
646:
643:
640:
628:
614:
600:
596:
592:
572:
566:
562:
559:
555:
552:
545:
541:
537:
531:
528:
525:
503:
499:
495:
475:
469:
465:
462:
458:
455:
448:
444:
440:
434:
431:
418:
415:
403:
401:
393:
391:
386:
378:
364:
349:
332:
329:
309:living systems
291:
290:
288:
287:
280:
273:
265:
262:
261:
260:
259:
254:
249:
244:
239:
234:
229:
224:
222:Brønsted–Lowry
216:
215:
208:
207:
206:
205:
200:
195:
190:
185:
180:
175:
170:
165:
163:Brønsted–Lowry
157:
156:
149:
148:
147:
146:
141:
136:
131:
126:
121:
116:
111:
106:
101:
96:
91:
86:
81:
76:
71:
66:
61:
56:
51:
46:
41:
33:
32:
24:
23:
15:
9:
6:
4:
3:
2:
3876:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3846:
3844:
3827:
3824:
3823:
3822:
3819:
3815:
3812:
3811:
3810:
3807:
3803:
3800:
3799:
3798:
3795:
3791:
3788:
3787:
3786:
3783:
3781:
3778:
3776:
3773:
3769:
3766:
3765:
3764:
3761:
3759:
3756:
3754:
3751:
3747:
3744:
3743:
3742:
3739:
3738:
3736:
3732:
3726:
3723:
3721:
3718:
3716:
3713:
3712:
3710:
3706:
3700:
3697:
3695:
3692:
3690:
3687:
3685:
3682:
3680:
3679:Phase diagram
3677:
3673:
3672:determination
3670:
3669:
3668:
3665:
3664:
3662:
3660:
3656:
3650:
3647:
3645:
3642:
3640:
3637:
3635:
3632:
3628:
3625:
3623:
3620:
3619:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3589:
3587:
3583:
3579:
3572:
3567:
3565:
3560:
3558:
3553:
3552:
3549:
3545:
3542:
3525:
3521:
3517:
3513:
3509:
3505:
3498:
3483:
3479:
3473:
3465:
3461:
3457:
3453:
3449:
3445:
3444:J. Chem. Educ
3438:
3430:
3424:
3420:
3413:
3402:
3397:
3392:
3388:
3384:
3383:J. Biol. Chem
3377:
3370:
3362:
3356:
3352:
3345:
3337:
3331:
3327:
3320:
3318:
3309:
3303:
3299:
3292:
3284:
3280:
3276:
3272:
3268:
3264:
3257:
3255:
3253:
3244:
3238:
3234:
3227:
3225:
3223:
3207:
3201:
3197:
3196:
3188:
3184:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3150:
3144:
3119:
3113:
3112:
3097:
3091:
3090:
3079:
3076:
3075:
3072:Relationship
3071:
3068:
3067:
3061:
3060:
3059:
3056:
3054:
3051:
3047:
3040:
3036:
3032:
3022:
3015:
3011:
2994:
2989:
2986:
2975:
2957:
2953:
2948:
2937:
2919:
2916:
2902:
2898:
2894:
2891:
2886:
2875:
2857:
2854:
2840:
2836:
2832:
2829:
2820:
2802:
2799:
2785:
2781:
2777:
2768:
2756:
2754:
2741:
2733:
2728:
2717:
2699:
2696:
2682:
2678:
2674:
2669:
2658:
2640:
2637:
2623:
2619:
2615:
2606:
2588:
2585:
2571:
2567:
2563:
2554:
2551:
2539:
2537:
2524:
2511:
2509:
2504:
2498:
2483:
2479:
2476:
2475:
2468:
2464:
2457:
2456:
2449:
2445:
2434:
2433:
2429:
2426:
2425:
2419:
2418:
2417:
2411:
2404:
2397:
2389:
2385:
2376:
2374:
2371: +
2370:
2358:
2354:
2347:
2340:
2335:
2322:
2319:
2314:
2310:
2300:
2296:
2293:
2287:
2284:
2275:
2268:
2263:
2259:
2249:
2236:
2230:
2227:
2222:
2218:
2209:
2206:
2203:
2197:
2191:
2182:
2172:
2159:
2134:
2116:
2101:
2092:
2083:
2078:
2076:
2072:
2068:
2064:
2060:
2056:
2052:
2045:
2041:
2030:
2026:
2023:
2021:
2018:
2016:
2009:
2006:
2003:
2002:
1999:
1996:
1994:
1991:
1989:
1985:
1982:
1981:
1978:
1975:
1972:
1967:
1964:
1961:
1960:
1957:
1955:
1953:
1951:
1950:
1944:
1943:
1942:
1940:
1932:
1910:
1904:
1900:
1892:
1889:
1886:
1883:
1879:
1874:
1871:
1870:
1866:
1864:
1861:
1858:
1854:
1849:
1846:
1845:
1841:
1838:
1835:
1832:
1828:
1823:
1820:
1819:
1815:
1812:
1809:
1806:
1802:
1797:
1794:
1793:
1789:
1786:
1783:
1780:
1776:
1771:
1768:
1767:
1763:
1760:
1757:
1754:
1750:
1745:
1742:
1741:
1737:
1735:
1732:
1729:
1725:
1720:
1717:
1716:
1712:
1709:
1706:
1703:
1699:
1694:
1691:
1690:
1686:
1683:
1680:
1677:
1673:
1666:
1663:
1662:
1658:
1655:
1652:
1649:
1645:
1640:
1637:
1636:
1632:
1629:
1626:
1623:
1619:
1614:
1611:
1610:
1607:
1602:
1595:
1576:
1571:
1567:
1562:
1559:
1556:
1555:
1552:
1550:
1546:
1536:
1534:
1529:
1527:
1523:
1519:
1515:
1503:
1500:
1497:
1496:
1492:
1489:
1486:
1485:
1481:
1478:
1475:
1474:
1470:
1467:
1464:
1463:
1459:
1456:
1453:
1452:
1448:
1445:
1442:
1441:
1437:
1434:
1430:
1427:
1416:
1415:
1412:
1411:
1410:
1408:
1401:
1397:
1390:
1380:
1378:
1374:
1370:
1358:
1355:
1353:
1350:
1349:
1345:
1342:
1340:
1337:
1336:
1332:
1329:
1327:
1317:
1316:
1312:
1309:
1307:
1304:
1303:
1299:
1296:
1294:
1291:
1290:
1286:
1281:
1277:
1274:
1273:
1270:
1269:
1263:
1261:
1257:
1252:
1250:
1246:
1241:
1239:
1235:
1231:
1218:
1196:
1195:carbonic acid
1193:a mixture of
1192:
1188:
1163:
1152:
1143:
1131:
1127:
1124:
1116:
1101:
1088:
1084:
1080:
1077:
1069:
1063:
1056:
1049:
1042:
1035:
1024:
1008:
1000:
986:
974:
969:
965:
950:
936:
932:
920:
913:
910:
907:
899:
898:
897:
888:
884:
879:
875:
873:
865:
857:
850:
828:
807:
803:
790:
771:
765:
757:
743:
731:
726:
722:
707:
693:
689:
677:
670:
661:
648:
644:
641:
638:
627:
622:
620:
598:
594:
590:
570:
550:
543:
539:
535:
529:
526:
523:
501:
497:
493:
473:
453:
446:
442:
438:
432:
429:
414:
412:
400:
390:
385:
381:
377:
371:
363:
361:
354:) with alkali
348:
342:
337:
328:
326:
322:
318:
314:
310:
306:
302:
298:
286:
281:
279:
274:
272:
267:
266:
264:
263:
258:
255:
253:
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
219:
218:
217:
213:
210:
209:
204:
201:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
164:
161:
160:
159:
158:
154:
151:
150:
145:
142:
140:
137:
135:
132:
130:
127:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
65:
62:
60:
59:Acid strength
57:
55:
52:
50:
47:
45:
42:
40:
37:
36:
35:
34:
30:
26:
25:
21:
20:
3821:Vapor–liquid
3714:
3708:Applications
3538:
3511:
3507:
3497:
3486:. Retrieved
3472:
3447:
3443:
3437:
3418:
3412:
3386:
3382:
3369:
3350:
3344:
3325:
3297:
3291:
3266:
3262:
3232:
3209:. Retrieved
3198:. OpenStax.
3194:
3187:
3142:
3057:
3038:
3027:
3020:
3013:
3012:
2512:
2505:
2496:
2494:
2481:
2466:
2447:
2430:Citric acid
2402:
2395:
2393:
2372:
2368:
2356:
2352:
2345:
2338:
2336:
2251:Simplify to
2250:
2173:
2081:
2079:
2074:
2070:
2066:
2062:
2058:
2054:
2050:
2043:
2039:
2037:
2028:
2024:
2019:
2014:
2007:
1997:
1992:
1987:
1976:
1965:
1936:
1930:
1908:
1903:
1697:(N-glycine)
1593:
1565:
1542:
1530:
1511:
1399:
1388:
1386:
1366:
1279:
1256:fermentation
1253:
1245:denaturation
1242:
1184:
1061:
1054:
1047:
1040:
1033:
1022:
895:
886:
882:
848:
625:
623:
618:
420:
411:deprotonated
408:
398:
383:
375:
367:
357:
346:
296:
294:
89:Donor number
78:
3826:Henry's law
3617:Free energy
3092:A + 2H ⇌ AH
3069:Equilibrium
2427:Equilibrium
2410:Citric acid
1574:25 °C
1514:citric acid
1433:citric acid
1431:0.1 M
1417:0.2 M
1396:Citric acid
1359:8.25–10.25
1306:Acetic acid
1293:Citric acid
1217:bicarbonate
1191:human blood
392:OH + HA → H
301:strong acid
69:Amphoterism
3843:Categories
3809:Solubility
3780:Hydrolysis
3689:Phase rule
3488:2009-04-17
3179:References
3114:A + 3H⇌ AH
3077:A + H ⇌ AH
3050:non-linear
2477:HA ⇌ A + H
2462:A ⇌ HA + H
1934:HA ⇌ A + H
1848:Cacodylate
1560:Structure
1522:boric acid
402:OH + H → H
365:HA ⇌ H + A
247:Superbases
193:Superacids
99:Extraction
3797:Partition
3627:Helmholtz
3597:Chelation
2987:−
2954:−
2920:−
2899:β
2858:−
2837:β
2803:−
2782:β
2700:−
2679:β
2641:−
2620:β
2589:−
2568:β
2555:−
2297:−
2228:−
2135:−
1939:ICE table
1346:8.3–10.3
1238:alkalosis
1144:−
1128:≈
1125:β
1089:−
1081:≈
1078:β
911:≈
908:β
864:hydronium
639:β
530:−
524:β
430:β
341:titration
144:ECW model
124:Titration
3790:of water
3585:Concepts
3524:Archived
3482:Archived
3401:Archived
3147:See also
3033:are the
2080:To find
1580:effect,
1333:6.2–8.2
1313:3.8–5.8
1300:2.1–7.4
1234:acidosis
872:aquation
3452:Bibcode
3271:Bibcode
2487:= 6.40
2472:= 4.76
2453:= 3.13
2408:, etc.
1790:229.20
1693:Tricine
1687:121.14
1598:
1583:
1187:enzymes
232:Organic
178:Organic
173:Mineral
3659:Models
3425:
3357:
3332:
3304:
3239:
3211:14 May
3202:
1893:195.2
1890:−0.011
1867:138.0
1842:302.4
1839:−0.008
1816:209.3
1813:−0.015
1787:−0.020
1764:238.3
1761:−0.014
1738:259.3
1713:179.2
1710:−0.021
1684:−0.028
1659:163.2
1656:−0.018
1639:Bicine
1633:243.3
1630:−0.018
1606:weight
1524:, and
1498:97.25
1490:17.65
1487:82.35
1479:36.85
1476:63.15
1468:48.50
1465:51.50
1457:61.45
1454:38.55
1446:79.45
1443:20.55
1352:Borate
1230:plasma
1215:) and
617:, and
583:where
486:where
242:Strong
188:Strong
3622:Gibbs
3404:(PDF)
3379:(PDF)
3120:Log β
3098:Log β
3080:Log β
2443:A + H
2439:A ⇌ H
2055:added
1822:PIPES
1744:HEPES
1733:7.635
1719:TAPSO
1604:Mol.
1578:Temp.
1501:2.75
1435:(mL)
1428:(mL)
914:2.303
866:ion H
645:2.303
396:O + A
352:= 4.7
321:blood
237:Oxide
227:Lewis
214:types
203:Solid
183:Oxide
168:Lewis
155:types
3423:ISBN
3355:ISBN
3330:ISBN
3302:ISBN
3237:ISBN
3213:2023
3200:ISBN
3132:+ pk
3128:+ pk
3124:= pk
3106:+ pk
3084:= pk
2351:and
1887:6.15
1862:6.27
1836:6.76
1810:7.20
1796:MOPS
1784:7.40
1758:7.48
1707:8.05
1681:8.07
1665:Tris
1653:8.35
1627:8.43
1613:TAPS
1600:(K)
1504:8.0
1493:7.0
1482:6.0
1471:5.0
1460:4.0
1449:3.0
1356:9.24
1339:CHES
1236:and
1219:(HCO
305:base
257:Weak
212:Base
198:Weak
153:Acid
74:Base
44:Acid
3516:doi
3512:184
3460:doi
3391:doi
3279:doi
3102:=pk
2375:).
1873:MES
1770:TES
1586:dpH
1438:pH
1423:HPO
1343:9.3
1330:7.2
1310:4.8
319:of
303:or
3845::
3522:.
3510:.
3506:.
3458:.
3448:38
3446:.
3399:.
3387:49
3385:.
3381:.
3316:^
3277:.
3267:77
3265:.
3251:^
3221:^
3134:a3
3130:a2
3126:a1
3108:a3
3104:a2
3086:a3
3037:.
2485:a3
2470:a2
2451:a1
2406:a2
2399:a1
2365:10
2361:10
2344:,
2323:0.
2150:HA
2027:+
2013:−
2004:E
1983:C
1962:I
1875:,
1850:,
1824:,
1798:,
1772:,
1746:,
1721:,
1695:,
1667:,
1641:,
1615:,
1572:,
1520:,
1516:,
1419:Na
1323:PO
1319:KH
1262:.
1206:CO
1197:(H
1132:10
1085:10
1023:pK
926:HA
833:HA
683:HA
615:10
406:O.
327:.
317:pH
295:A
109:pH
3570:e
3563:t
3556:v
3518::
3491:.
3466:.
3462::
3454::
3431:.
3393::
3363:.
3338:.
3310:.
3285:.
3281::
3273::
3245:.
3215:.
3122:3
3116:3
3100:2
3094:2
3082:1
3042:w
3039:K
3030:q
3028:β
3024:H
3021:C
3017:A
3014:C
2995:.
2990:1
2983:]
2976:+
2972:H
2967:[
2962:w
2958:K
2949:3
2945:]
2938:+
2934:H
2929:[
2926:]
2917:3
2913:A
2908:[
2903:3
2895:3
2892:+
2887:2
2883:]
2876:+
2872:H
2867:[
2864:]
2855:3
2851:A
2846:[
2841:2
2833:2
2830:+
2827:]
2821:+
2817:H
2812:[
2809:]
2800:3
2796:A
2791:[
2786:1
2778:+
2775:]
2769:+
2765:H
2760:[
2757:=
2747:H
2742:C
2734:,
2729:3
2725:]
2718:+
2714:H
2709:[
2706:]
2697:3
2693:A
2688:[
2683:3
2675:+
2670:2
2666:]
2659:+
2655:H
2650:[
2647:]
2638:3
2634:A
2629:[
2624:2
2616:+
2613:]
2607:+
2603:H
2598:[
2595:]
2586:3
2582:A
2577:[
2572:1
2564:+
2561:]
2552:3
2548:A
2543:[
2540:=
2530:A
2525:C
2500:a
2497:K
2482:K
2480:p
2467:K
2465:p
2460:2
2458:H
2448:K
2446:p
2441:2
2437:3
2435:H
2414:3
2403:K
2396:K
2373:y
2369:x
2367:(
2357:x
2353:y
2349:a
2346:K
2342:0
2339:C
2320:=
2315:0
2311:C
2305:a
2301:K
2294:x
2291:)
2288:y
2285:+
2280:a
2276:K
2272:(
2269:+
2264:2
2260:x
2237:.
2231:x
2223:0
2219:C
2213:)
2210:y
2207:+
2204:x
2201:(
2198:x
2192:=
2187:a
2183:K
2160:.
2154:]
2146:[
2141:]
2131:A
2126:[
2123:]
2117:+
2113:H
2108:[
2102:=
2097:a
2093:K
2082:x
2075:E
2071:x
2067:x
2063:C
2059:y
2051:y
2047:0
2044:C
2040:I
2029:y
2025:x
2020:x
2015:x
2011:0
2008:C
1998:x
1993:x
1988:x
1986:−
1977:y
1973:0
1969:0
1966:C
1912:a
1909:K
1594:T
1592:d
1589:/
1569:a
1566:K
1564:p
1425:4
1421:2
1403:a
1400:K
1392:a
1389:K
1325:4
1321:2
1283:a
1280:K
1278:p
1224:3
1211:3
1202:2
1164:.
1157:w
1153:K
1148:p
1140:H
1137:p
1102:.
1096:H
1093:p
1065:a
1062:K
1058:a
1055:K
1051:a
1048:K
1044:a
1041:K
1037:a
1034:K
1030:a
1026:a
1009:.
1001:2
997:)
993:]
987:+
983:H
978:[
975:+
970:a
966:K
962:(
957:]
951:+
947:H
942:[
937:a
933:K
921:T
890:a
887:K
883:β
868:3
860:×
852:w
849:K
829:T
808:,
804:)
797:]
791:+
787:H
782:[
776:w
772:K
766:+
758:2
754:)
750:]
744:+
740:H
735:[
732:+
727:a
723:K
719:(
714:]
708:+
704:H
699:[
694:a
690:K
678:T
671:+
668:]
662:+
658:H
653:[
649:(
642:=
629:a
626:K
619:d
599:a
595:C
591:d
571:,
565:)
561:H
558:p
554:(
551:d
544:a
540:C
536:d
527:=
502:b
498:C
494:d
474:,
468:)
464:H
461:p
457:(
454:d
447:b
443:C
439:d
433:=
404:2
394:2
387:a
384:K
379:a
376:K
374:p
350:a
347:K
345:p
284:e
277:t
270:v
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