[{"data":1,"prerenderedAt":2291},["ShallowReactive",2],{"reference-titration-curves":3},{"table":4},{"id":5,"slug":6,"title":7,"shortTitle":8,"category":9,"description":10,"metaDescription":11,"chart":12,"columns":2192,"rows":2201,"entryCount":51,"source":2259,"notes":2261,"relatedTopics":2270,"relatedElements":2274,"seoKeywords":2275,"relatedReferences":2284,"tableTitle":2288,"tableDescription":2289,"seoTitle":2290},21,"titration-curves","Titration Curves: pH vs Volume for the Four Classic Titrations","Titration Curves","acids-bases","Explore four classic titration curves: strong acid + strong base, weak acid + strong base, weak base + strong acid, and strong base + strong acid. Each uses 25.00 mL of 0.100 M analyte and 0.100 M titrant. Read the pH at any volume and compare eight indicator transition ranges.","pH-versus-volume curves for the four classic acid-base titrations, with equivalence and half-equivalence points and indicator transition ranges.",{"type":6,"xLabel":13,"yLabel":14,"veq":15,"bands":16,"series":52},"Volume of titrant added (mL)","pH",25,[17,23,28,31,35,39,43,48],{"name":18,"low":19,"high":20,"acidColor":21,"baseColor":22},"Methyl orange",3.1,4.4,"Red","Yellow",{"name":24,"low":25,"high":26,"acidColor":22,"baseColor":27},"Bromocresol green",3.8,5.4,"Blue",{"name":29,"low":20,"high":30,"acidColor":21,"baseColor":22},"Methyl red",6.2,{"name":32,"low":33,"high":34,"acidColor":21,"baseColor":27},"Litmus",4.5,8.3,{"name":36,"low":37,"high":38,"acidColor":22,"baseColor":27},"Bromothymol blue",6,7.6,{"name":40,"low":41,"high":42,"acidColor":22,"baseColor":21},"Phenol red",6.4,8,{"name":44,"low":34,"high":45,"acidColor":46,"baseColor":47},"Phenolphthalein",10,"Colorless","Purple-pink",{"name":49,"low":50,"high":51,"acidColor":22,"baseColor":21},"Alizarin yellow R",10.2,12,[53,844,1254,1787],{"key":54,"name":55,"detail":56,"points":57},"sa_sb","Strong acid + strong base","25.00 mL of 0.100 M HCl titrated with 0.100 M NaOH",[58,61,64,67,70,72,75,78,81,84,87,90,93,96,99,102,105,108,111,113,116,119,122,125,128,130,133,136,139,142,145,148,151,153,156,159,162,165,168,171,174,176,179,182,185,188,191,194,197,199,202,205,208,211,214,217,220,223,226,229,232,235,238,241,244,247,250,253,256,259,262,265,268,271,274,277,280,283,286,289,292,295,298,301,304,306,309,312,315,318,321,324,327,330,333,336,339,342,345,348,351,354,357,360,363,366,369,372,375,378,381,384,387,390,393,396,399,402,405,408,411,414,417,420,423,426,429,432,435,438,441,444,447,448,451,454,457,460,463,466,469,472,475,478,481,484,487,490,493,496,499,502,505,508,511,514,517,520,523,526,529,532,535,538,541,544,547,550,553,556,559,562,565,568,571,574,577,580,583,586,589,592,595,598,601,604,607,610,613,616,619,622,625,628,631,634,637,640,643,646,649,652,655,658,661,664,667,670,673,676,679,682,685,688,691,694,697,700,703,706,709,712,715,718,721,724,727,730,733,736,739,742,745,748,751,754,757,760,763,766,769,772,775,778,781,784,787,790,793,796,799,802,805,808,811,814,817,820,823,826,829,832,835,838,841],[59,60],0,1,[62,63],0.25,1.0087,[65,66],0.5,1.0174,[68,69],0.75,1.0261,[60,71],1.0348,[73,74],1.25,1.0435,[76,77],1.5,1.0522,[79,80],1.75,1.0609,[82,83],2,1.0696,[85,86],2.25,1.0784,[88,89],2.5,1.0872,[91,92],2.75,1.0959,[94,95],3,1.1047,[97,98],3.25,1.1136,[100,101],3.5,1.1224,[103,104],3.75,1.1313,[106,107],4,1.1402,[109,110],4.25,1.1491,[33,112],1.1581,[114,115],4.75,1.1671,[117,118],5,1.1761,[120,121],5.25,1.1852,[123,124],5.5,1.1943,[126,127],5.75,1.2034,[37,129],1.2126,[131,132],6.25,1.2218,[134,135],6.5,1.2311,[137,138],6.75,1.2405,[140,141],7,1.2499,[143,144],7.25,1.2593,[146,147],7.5,1.2688,[149,150],7.75,1.2784,[42,152],1.2881,[154,155],8.25,1.2978,[157,158],8.5,1.3076,[160,161],8.75,1.3174,[163,164],9,1.3274,[166,167],9.25,1.3374,[169,170],9.5,1.3475,[172,173],9.75,1.3577,[45,175],1.368,[177,178],10.25,1.3784,[180,181],10.5,1.3889,[183,184],10.75,1.3995,[186,187],11,1.4102,[189,190],11.25,1.421,[192,193],11.5,1.432,[195,196],11.75,1.443,[51,198],1.4543,[200,201],12.25,1.4656,[203,204],12.5,1.4771,[206,207],12.75,1.4888,[209,210],13,1.5006,[212,213],13.25,1.5126,[215,216],13.5,1.5248,[218,219],13.75,1.5371,[221,222],14,1.5497,[224,225],14.25,1.5624,[227,228],14.5,1.5754,[230,231],14.75,1.5886,[233,234],15,1.6021,[236,237],15.25,1.6158,[239,240],15.5,1.6297,[242,243],15.75,1.644,[245,246],16,1.6585,[248,249],16.25,1.6734,[251,252],16.5,1.6886,[254,255],16.75,1.7042,[257,258],17,1.7202,[260,261],17.25,1.7365,[263,264],17.5,1.7533,[266,267],17.75,1.7706,[269,270],18,1.7884,[272,273],18.25,1.8067,[275,276],18.5,1.8256,[278,279],18.75,1.8451,[281,282],19,1.8653,[284,285],19.25,1.8862,[287,288],19.5,1.908,[290,291],19.75,1.9306,[293,294],20,1.9542,[296,297],20.25,1.9789,[299,300],20.5,2.0048,[302,303],20.75,2.032,[5,305],2.0607,[307,308],21.25,2.0911,[310,311],21.5,2.1234,[313,314],21.75,2.1579,[316,317],22,2.195,[319,320],22.25,2.2351,[322,323],22.5,2.2788,[325,326],22.75,2.3268,[328,329],23,2.3802,[331,332],23.05,2.3917,[334,335],23.1,2.4034,[337,338],23.15,2.4154,[340,341],23.2,2.4278,[343,344],23.25,2.4405,[346,347],23.3,2.4535,[349,350],23.35,2.4669,[352,353],23.4,2.4807,[355,356],23.45,2.495,[358,359],23.5,2.5097,[361,362],23.55,2.5248,[364,365],23.6,2.5405,[367,368],23.65,2.5567,[370,371],23.7,2.5736,[373,374],23.75,2.5911,[376,377],23.8,2.6092,[379,380],23.85,2.6282,[382,383],23.9,2.6479,[385,386],23.95,2.6686,[388,389],24,2.6902,[391,392],24.05,2.7129,[394,395],24.1,2.7368,[397,398],24.15,2.7621,[400,401],24.2,2.7889,[403,404],24.25,2.8173,[406,407],24.3,2.8477,[409,410],24.35,2.8804,[412,413],24.4,2.9156,[415,416],24.45,2.9538,[418,419],24.5,2.9956,[421,422],24.55,3.0418,[424,425],24.6,3.0934,[427,428],24.65,3.1519,[430,431],24.7,3.2192,[433,434],24.75,3.2989,[436,437],24.8,3.3962,[439,440],24.85,3.5216,[442,443],24.9,3.6981,[445,446],24.95,3.9996,[15,140],[449,450],25.05,9.9996,[452,453],25.1,10.3002,[455,456],25.15,10.4758,[458,459],25.2,10.6003,[461,462],25.25,10.6968,[464,465],25.3,10.7756,[467,468],25.35,10.8421,[470,471],25.4,10.8996,[473,474],25.45,10.9504,[476,477],25.5,10.9957,[479,480],25.55,11.0366,[482,483],25.6,11.074,[485,486],25.65,11.1083,[488,489],25.7,11.1401,[491,492],25.75,11.1696,[494,495],25.8,11.1972,[497,498],25.85,11.2231,[500,501],25.9,11.2475,[503,504],25.95,11.2706,[506,507],26,11.2924,[509,510],26.05,11.3132,[512,513],26.1,11.333,[515,516],26.15,11.3519,[518,519],26.2,11.3699,[521,522],26.25,11.3872,[524,525],26.3,11.4038,[527,528],26.35,11.4198,[530,531],26.4,11.4352,[533,534],26.45,11.45,[536,537],26.5,11.4643,[539,540],26.55,11.4781,[542,543],26.6,11.4915,[545,546],26.65,11.5044,[548,549],26.7,11.517,[551,552],26.75,11.5291,[554,555],26.8,11.5409,[557,558],26.85,11.5524,[560,561],26.9,11.5636,[563,564],26.95,11.5744,[566,567],27,11.585,[569,570],27.25,11.6341,[572,573],27.5,11.6778,[575,576],27.75,11.7171,[578,579],28,11.7528,[581,582],28.25,11.7856,[584,585],28.5,11.8157,[587,588],28.75,11.8437,[590,591],29,11.8697,[593,594],29.25,11.894,[596,597],29.5,11.9168,[599,600],29.75,11.9383,[602,603],30,11.9586,[605,606],30.25,11.9778,[608,609],30.5,11.9961,[611,612],30.75,12.0134,[614,615],31,12.03,[617,618],31.25,12.0458,[620,621],31.5,12.0609,[623,624],31.75,12.0753,[626,627],32,12.0892,[629,630],32.25,12.1026,[632,633],32.5,12.1154,[635,636],32.75,12.1277,[638,639],33,12.1397,[641,642],33.25,12.1512,[644,645],33.5,12.1623,[647,648],33.75,12.173,[650,651],34,12.1834,[653,654],34.25,12.1935,[656,657],34.5,12.2032,[659,660],34.75,12.2127,[662,663],35,12.2218,[665,666],35.25,12.2308,[668,669],35.5,12.2394,[671,672],35.75,12.2479,[674,675],36,12.2561,[677,678],36.25,12.264,[680,681],36.5,12.2718,[683,684],36.75,12.2794,[686,687],37,12.2868,[689,690],37.25,12.294,[692,693],37.5,12.301,[695,696],37.75,12.3079,[698,699],38,12.3146,[701,702],38.25,12.3212,[704,705],38.5,12.3276,[707,708],38.75,12.3338,[710,711],39,12.3399,[713,714],39.25,12.3459,[716,717],39.5,12.3518,[719,720],39.75,12.3576,[722,723],40,12.3632,[725,726],40.25,12.3687,[728,729],40.5,12.3741,[731,732],40.75,12.3794,[734,735],41,12.3846,[737,738],41.25,12.3897,[740,741],41.5,12.3947,[743,744],41.75,12.3996,[746,747],42,12.4044,[749,750],42.25,12.4091,[752,753],42.5,12.4137,[755,756],42.75,12.4183,[758,759],43,12.4228,[761,762],43.25,12.4272,[764,765],43.5,12.4315,[767,768],43.75,12.4357,[770,771],44,12.4399,[773,774],44.25,12.444,[776,777],44.5,12.448,[779,780],44.75,12.452,[782,783],45,12.4559,[785,786],45.25,12.4598,[788,789],45.5,12.4636,[791,792],45.75,12.4673,[794,795],46,12.471,[797,798],46.25,12.4746,[800,801],46.5,12.4781,[803,804],46.75,12.4816,[806,807],47,12.4851,[809,810],47.25,12.4885,[812,813],47.5,12.4918,[815,816],47.75,12.4951,[818,819],48,12.4984,[821,822],48.25,12.5016,[824,825],48.5,12.5048,[827,828],48.75,12.5079,[830,831],49,12.511,[833,834],49.25,12.514,[836,837],49.5,12.517,[839,840],49.75,12.52,[842,843],50,12.5229,{"key":845,"name":846,"detail":847,"points":848},"wa_sb","Weak acid + strong base","25.00 mL of 0.100 M CH₃COOH (Ka = 1.8 × 10⁻⁵) titrated with 0.100 M NaOH",[849,851,853,855,857,859,861,863,865,867,869,871,873,875,877,879,881,883,885,887,889,891,893,895,897,899,901,903,905,907,909,911,913,915,917,919,921,923,925,927,929,931,933,935,937,939,941,943,945,947,949,951,953,955,957,959,961,963,965,967,969,971,973,975,977,979,981,983,985,987,989,991,993,995,997,999,1001,1003,1005,1007,1009,1011,1013,1015,1017,1019,1021,1023,1025,1027,1029,1031,1033,1035,1037,1039,1041,1043,1045,1047,1049,1051,1053,1055,1057,1059,1061,1063,1065,1067,1069,1071,1073,1075,1077,1079,1081,1083,1085,1087,1089,1091,1093,1095,1097,1099,1101,1103,1105,1107,1109,1111,1113,1115,1117,1119,1121,1123,1125,1126,1127,1128,1129,1130,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253],[59,850],2.87,[62,852],3.0378,[65,854],3.1829,[68,856],3.3055,[60,858],3.4084,[73,860],3.4957,[76,862],3.5712,[79,864],3.6375,[82,866],3.6967,[85,868],3.7501,[88,870],3.7989,[91,872],3.8437,[94,874],3.8854,[97,876],3.9243,[100,878],3.9608,[103,880],3.9953,[106,882],4.0281,[109,884],4.0592,[33,886],4.089,[114,888],4.1176,[117,890],4.145,[120,892],4.1715,[123,894],4.197,[126,896],4.2218,[37,898],4.2458,[131,900],4.2692,[134,902],4.2919,[137,904],4.3141,[140,906],4.3358,[143,908],4.3571,[146,910],4.3779,[149,912],4.3983,[42,914],4.4184,[154,916],4.4381,[157,918],4.4576,[160,920],4.4767,[163,922],4.4957,[166,924],4.5144,[169,926],4.5329,[172,928],4.5512,[45,930],4.5693,[177,932],4.5873,[180,934],4.6052,[183,936],4.6229,[186,938],4.6406,[189,940],4.6581,[192,942],4.6756,[195,944],4.6931,[51,946],4.7105,[200,948],4.7278,[203,950],4.74,[206,952],4.7626,[209,954],4.7799,[212,956],4.7973,[215,958],4.8148,[218,960],4.8323,[221,962],4.8499,[224,964],4.8675,[227,966],4.8853,[230,968],4.9032,[233,970],4.9212,[236,972],4.9393,[239,974],4.9577,[242,976],4.9762,[245,978],4.9949,[248,980],5.0139,[251,982],5.0331,[254,984],5.0526,[257,986],5.0724,[260,988],5.0925,[263,990],5.113,[266,992],5.1339,[269,994],5.1552,[272,996],5.1769,[275,998],5.1992,[278,1000],5.2221,[281,1002],5.2456,[284,1004],5.2697,[287,1006],5.2946,[290,1008],5.3204,[293,1010],5.347,[296,1012],5.3747,[299,1014],5.4035,[302,1016],5.4336,[5,1018],5.4651,[307,1020],5.4983,[310,1022],5.5333,[313,1024],5.5705,[316,1026],5.6102,[319,1028],5.6529,[322,1030],5.6992,[325,1032],5.7497,[328,1034],5.8056,[331,1036],5.8175,[334,1038],5.8298,[337,1040],5.8423,[340,1042],5.8551,[343,1044],5.8683,[346,1046],5.8818,[349,1048],5.8957,[352,1050],5.91,[355,1052],5.9247,[358,1054],5.9399,[361,1056],5.9555,[364,1058],5.9717,[367,1060],5.9884,[370,1062],6.0057,[373,1064],6.0236,[376,1066],6.0423,[379,1068],6.0617,[382,1070],6.0819,[385,1072],6.103,[388,1074],6.1251,[391,1076],6.1483,[394,1078],6.1727,[397,1080],6.1984,[400,1082],6.2256,[403,1084],6.2545,[406,1086],6.2854,[409,1088],6.3185,[412,1090],6.3541,[415,1092],6.3928,[418,1094],6.4351,[421,1096],6.4817,[424,1098],6.5337,[427,1100],6.5926,[430,1102],6.6604,[433,1104],6.7405,[436,1106],6.8382,[439,1108],6.964,[442,1110],7.1408,[445,1112],7.4418,[15,1114],8.72,[449,1116],10.0008,[452,1118],10.3005,[455,1120],10.476,[458,1122],10.6004,[461,1124],10.6969,[464,465],[467,468],[470,471],[473,474],[476,477],[479,1131],11.0367,[482,483],[485,486],[488,489],[491,492],[494,495],[497,498],[500,501],[503,504],[506,507],[509,510],[512,513],[515,516],[518,519],[521,522],[524,525],[527,528],[530,531],[533,534],[536,537],[539,540],[542,543],[545,546],[548,549],[551,552],[554,555],[557,558],[560,561],[563,564],[566,567],[569,570],[572,573],[575,576],[578,579],[581,582],[584,585],[587,588],[590,591],[593,594],[596,597],[599,600],[602,603],[605,606],[608,609],[611,612],[614,615],[617,618],[620,621],[623,624],[626,627],[629,630],[632,633],[635,636],[638,639],[641,642],[644,645],[647,648],[650,651],[653,654],[656,657],[659,660],[662,663],[665,666],[668,669],[671,672],[674,675],[677,678],[680,681],[683,684],[686,687],[689,690],[692,1203],12.3,[695,696],[698,699],[701,702],[704,705],[707,708],[710,711],[713,714],[716,717],[719,720],[722,723],[725,726],[728,729],[731,732],[734,735],[737,738],[740,741],[743,744],[746,747],[749,750],[752,753],[755,756],[758,759],[761,762],[764,765],[767,768],[770,771],[773,774],[776,777],[779,780],[782,783],[785,786],[788,789],[791,792],[794,795],[797,798],[800,801],[803,804],[806,807],[809,810],[812,813],[815,816],[818,819],[821,822],[824,825],[827,828],[830,831],[833,834],[836,837],[839,840],[842,843],{"key":1255,"name":1256,"detail":1257,"points":1258},"wb_sa","Weak base + strong acid","25.00 mL of 0.100 M NH₃ (Kb = 1.8 × 10⁻⁵) titrated with 0.100 M HCl",[1259,1261,1263,1265,1267,1269,1271,1273,1275,1277,1279,1281,1283,1285,1287,1289,1291,1293,1295,1297,1299,1301,1303,1305,1307,1309,1311,1313,1315,1317,1319,1321,1323,1325,1327,1329,1331,1333,1335,1337,1339,1341,1343,1345,1347,1349,1351,1353,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405,1407,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427,1429,1431,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497,1499,1501,1503,1505,1507,1509,1511,1513,1515,1517,1519,1521,1523,1525,1527,1529,1531,1533,1535,1537,1539,1541,1543,1545,1547,1549,1551,1553,1555,1557,1559,1561,1563,1565,1567,1569,1571,1573,1575,1577,1579,1581,1583,1585,1587,1589,1591,1593,1595,1597,1599,1601,1603,1605,1607,1609,1611,1613,1615,1617,1619,1621,1623,1625,1627,1629,1631,1633,1635,1637,1638,1640,1642,1644,1646,1648,1650,1652,1654,1656,1658,1660,1662,1664,1666,1668,1670,1672,1674,1676,1678,1680,1682,1684,1686,1688,1690,1692,1694,1696,1698,1700,1702,1704,1706,1708,1710,1712,1714,1716,1718,1720,1722,1724,1726,1728,1730,1732,1734,1736,1738,1740,1742,1744,1746,1748,1750,1752,1754,1756,1758,1760,1762,1764,1766,1768,1770,1772,1774,1776,1778,1780,1782,1784,1786],[59,1260],11.1247,[62,1262],10.9622,[65,1264],10.8171,[68,1266],10.6945,[60,1268],10.5916,[73,1270],10.5043,[76,1272],10.4288,[79,1274],10.3625,[82,1276],10.3033,[85,1278],10.2499,[88,1280],10.2011,[91,1282],10.1563,[94,1284],10.1146,[97,1286],10.0757,[100,1288],10.0392,[103,1290],10.0047,[106,1292],9.9719,[109,1294],9.9408,[33,1296],9.911,[114,1298],9.8824,[117,1300],9.855,[120,1302],9.8285,[123,1304],9.803,[126,1306],9.7782,[37,1308],9.7542,[131,1310],9.7308,[134,1312],9.7081,[137,1314],9.6859,[140,1316],9.6642,[143,1318],9.6429,[146,1320],9.6221,[149,1322],9.6017,[42,1324],9.5816,[154,1326],9.5619,[157,1328],9.5424,[160,1330],9.5233,[163,1332],9.5043,[166,1334],9.4856,[169,1336],9.4671,[172,1338],9.4488,[45,1340],9.4307,[177,1342],9.4127,[180,1344],9.3948,[183,1346],9.3771,[186,1348],9.3594,[189,1350],9.3419,[192,1352],9.3244,[195,1354],9.3069,[51,1356],9.2895,[200,1358],9.2722,[203,1360],9.26,[206,1362],9.2374,[209,1364],9.2201,[212,1366],9.2027,[215,1368],9.1852,[218,1370],9.1677,[221,1372],9.1501,[224,1374],9.1325,[227,1376],9.1147,[230,1378],9.0968,[233,1380],9.0788,[236,1382],9.0607,[239,1384],9.0423,[242,1386],9.0238,[245,1388],9.0051,[248,1390],8.9861,[251,1392],8.9669,[254,1394],8.9474,[257,1396],8.9276,[260,1398],8.9075,[263,1400],8.887,[266,1402],8.8661,[269,1404],8.8448,[272,1406],8.8231,[275,1408],8.8008,[278,1410],8.7779,[281,1412],8.7544,[284,1414],8.7303,[287,1416],8.7054,[290,1418],8.6796,[293,1420],8.653,[296,1422],8.6253,[299,1424],8.5965,[302,1426],8.5664,[5,1428],8.5349,[307,1430],8.5017,[310,1432],8.4667,[313,1434],8.4295,[316,1436],8.3898,[319,1438],8.3471,[322,1440],8.3008,[325,1442],8.2503,[328,1444],8.1944,[331,1446],8.1825,[334,1448],8.1702,[337,1450],8.1577,[340,1452],8.1449,[343,1454],8.1317,[346,1456],8.1182,[349,1458],8.1043,[352,1460],8.09,[355,1462],8.0753,[358,1464],8.0601,[361,1466],8.0445,[364,1468],8.0283,[367,1470],8.0116,[370,1472],7.9943,[373,1474],7.9764,[376,1476],7.9577,[379,1478],7.9383,[382,1480],7.9181,[385,1482],7.897,[388,1484],7.8749,[391,1486],7.8517,[394,1488],7.8273,[397,1490],7.8016,[400,1492],7.7744,[403,1494],7.7455,[406,1496],7.7146,[409,1498],7.6815,[412,1500],7.6459,[415,1502],7.6072,[418,1504],7.5649,[421,1506],7.5183,[424,1508],7.4663,[427,1510],7.4074,[430,1512],7.3396,[433,1514],7.2595,[436,1516],7.1618,[439,1518],7.036,[442,1520],6.8592,[445,1522],6.5582,[15,1524],5.28,[449,1526],3.9992,[452,1528],3.6995,[455,1530],3.524,[458,1532],3.3996,[461,1534],3.3031,[464,1536],3.2244,[467,1538],3.1579,[470,1540],3.1004,[473,1542],3.0496,[476,1544],3.0043,[479,1546],2.9633,[482,1548],2.926,[485,1550],2.8917,[488,1552],2.8599,[491,1554],2.8304,[494,1556],2.8028,[497,1558],2.7769,[500,1560],2.7525,[503,1562],2.7294,[506,1564],2.7076,[509,1566],2.6868,[512,1568],2.667,[515,1570],2.6481,[518,1572],2.6301,[521,1574],2.6128,[524,1576],2.5962,[527,1578],2.5802,[530,1580],2.5648,[533,1582],2.55,[536,1584],2.5357,[539,1586],2.5219,[542,1588],2.5085,[545,1590],2.4956,[548,1592],2.483,[551,1594],2.4709,[554,1596],2.4591,[557,1598],2.4476,[560,1600],2.4364,[563,1602],2.4256,[566,1604],2.415,[569,1606],2.3659,[572,1608],2.3222,[575,1610],2.2829,[578,1612],2.2472,[581,1614],2.2144,[584,1616],2.1843,[587,1618],2.1563,[590,1620],2.1303,[593,1622],2.106,[596,1624],2.0832,[599,1626],2.0617,[602,1628],2.0414,[605,1630],2.0222,[608,1632],2.0039,[611,1634],1.9866,[614,1636],1.97,[617,294],[620,1639],1.9391,[623,1641],1.9247,[626,1643],1.9108,[629,1645],1.8974,[632,1647],1.8846,[635,1649],1.8723,[638,1651],1.8603,[641,1653],1.8488,[644,1655],1.8377,[647,1657],1.827,[650,1659],1.8166,[653,1661],1.8065,[656,1663],1.7968,[659,1665],1.7873,[662,1667],1.7782,[665,1669],1.7692,[668,1671],1.7606,[671,1673],1.7521,[674,1675],1.7439,[677,1677],1.736,[680,1679],1.7282,[683,1681],1.7206,[686,1683],1.7132,[689,1685],1.706,[692,1687],1.699,[695,1689],1.6921,[698,1691],1.6854,[701,1693],1.6788,[704,1695],1.6724,[707,1697],1.6662,[710,1699],1.6601,[713,1701],1.6541,[716,1703],1.6482,[719,1705],1.6424,[722,1707],1.6368,[725,1709],1.6313,[728,1711],1.6259,[731,1713],1.6206,[734,1715],1.6154,[737,1717],1.6103,[740,1719],1.6053,[743,1721],1.6004,[746,1723],1.5956,[749,1725],1.5909,[752,1727],1.5863,[755,1729],1.5817,[758,1731],1.5772,[761,1733],1.5728,[764,1735],1.5685,[767,1737],1.5643,[770,1739],1.5601,[773,1741],1.556,[776,1743],1.552,[779,1745],1.548,[782,1747],1.5441,[785,1749],1.5402,[788,1751],1.5364,[791,1753],1.5327,[794,1755],1.529,[797,1757],1.5254,[800,1759],1.5219,[803,1761],1.5184,[806,1763],1.5149,[809,1765],1.5115,[812,1767],1.5082,[815,1769],1.5049,[818,1771],1.5016,[821,1773],1.4984,[824,1775],1.4952,[827,1777],1.4921,[830,1779],1.489,[833,1781],1.486,[836,1783],1.483,[839,1785],1.48,[842,204],{"key":1788,"name":1789,"detail":1790,"points":1791},"sb_sa","Strong base + strong acid","25.00 mL of 0.100 M NaOH titrated with 0.100 M HCl",[1792,1793,1795,1797,1799,1801,1803,1805,1807,1809,1811,1813,1815,1817,1819,1821,1823,1825,1827,1829,1831,1833,1835,1837,1839,1841,1843,1845,1847,1849,1851,1853,1855,1857,1859,1861,1863,1865,1867,1869,1871,1873,1875,1877,1879,1881,1883,1885,1887,1889,1891,1892,1894,1896,1898,1900,1902,1904,1906,1908,1910,1912,1914,1916,1918,1920,1922,1924,1926,1928,1930,1932,1934,1936,1938,1940,1942,1944,1946,1948,1950,1951,1953,1955,1957,1959,1961,1963,1965,1967,1969,1971,1973,1975,1977,1979,1981,1983,1985,1987,1989,1991,1993,1995,1997,1999,2001,2003,2005,2007,2009,2011,2013,2015,2017,2019,2021,2023,2025,2027,2029,2031,2033,2035,2037,2039,2041,2043,2045,2047,2049,2051,2053,2054,2056,2058,2060,2062,2064,2065,2066,2067,2068,2069,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191],[59,209],[62,1794],12.9913,[65,1796],12.9826,[68,1798],12.9739,[60,1800],12.9652,[73,1802],12.9565,[76,1804],12.9478,[79,1806],12.9391,[82,1808],12.9304,[85,1810],12.9216,[88,1812],12.9128,[91,1814],12.9041,[94,1816],12.8953,[97,1818],12.8864,[100,1820],12.8776,[103,1822],12.8687,[106,1824],12.8598,[109,1826],12.8509,[33,1828],12.8419,[114,1830],12.8329,[117,1832],12.8239,[120,1834],12.8148,[123,1836],12.8057,[126,1838],12.7966,[37,1840],12.7874,[131,1842],12.7782,[134,1844],12.7689,[137,1846],12.7595,[140,1848],12.7501,[143,1850],12.7407,[146,1852],12.7312,[149,1854],12.7216,[42,1856],12.7119,[154,1858],12.7022,[157,1860],12.6924,[160,1862],12.6826,[163,1864],12.6726,[166,1866],12.6626,[169,1868],12.6525,[172,1870],12.6423,[45,1872],12.632,[177,1874],12.6216,[180,1876],12.6111,[183,1878],12.6005,[186,1880],12.5898,[189,1882],12.579,[192,1884],12.568,[195,1886],12.557,[51,1888],12.5457,[200,1890],12.5344,[203,843],[206,1893],12.5112,[209,1895],12.4994,[212,1897],12.4874,[215,1899],12.4752,[218,1901],12.4629,[221,1903],12.4503,[224,1905],12.4376,[227,1907],12.4246,[230,1909],12.4114,[233,1911],12.3979,[236,1913],12.3842,[239,1915],12.3703,[242,1917],12.356,[245,1919],12.3415,[248,1921],12.3266,[251,1923],12.3114,[254,1925],12.2958,[257,1927],12.2798,[260,1929],12.2635,[263,1931],12.2467,[266,1933],12.2294,[269,1935],12.2116,[272,1937],12.1933,[275,1939],12.1744,[278,1941],12.1549,[281,1943],12.1347,[284,1945],12.1138,[287,1947],12.092,[290,1949],12.0694,[293,618],[296,1952],12.0211,[299,1954],11.9952,[302,1956],11.968,[5,1958],11.9393,[307,1960],11.9089,[310,1962],11.8766,[313,1964],11.8421,[316,1966],11.805,[319,1968],11.7649,[322,1970],11.7212,[325,1972],11.6732,[328,1974],11.6198,[331,1976],11.6083,[334,1978],11.5966,[337,1980],11.5846,[340,1982],11.5722,[343,1984],11.5595,[346,1986],11.5465,[349,1988],11.5331,[352,1990],11.5193,[355,1992],11.505,[358,1994],11.4903,[361,1996],11.4752,[364,1998],11.4595,[367,2000],11.4433,[370,2002],11.4264,[373,2004],11.4089,[376,2006],11.3908,[379,2008],11.3718,[382,2010],11.3521,[385,2012],11.3314,[388,2014],11.3098,[391,2016],11.2871,[394,2018],11.2632,[397,2020],11.2379,[400,2022],11.2111,[403,2024],11.1827,[406,2026],11.1523,[409,2028],11.1196,[412,2030],11.0844,[415,2032],11.0462,[418,2034],11.0044,[421,2036],10.9582,[424,2038],10.9066,[427,2040],10.8481,[430,2042],10.7808,[433,2044],10.7011,[436,2046],10.6038,[439,2048],10.4784,[442,2050],10.3019,[445,2052],10.0004,[15,140],[449,2055],4.0004,[452,2057],3.6998,[455,2059],3.5242,[458,2061],3.3997,[461,2063],3.3032,[464,1536],[467,1538],[470,1540],[473,1542],[476,1544],[479,2070],2.9634,[482,1548],[485,1550],[488,1552],[491,1554],[494,1556],[497,1558],[500,1560],[503,1562],[506,1564],[509,1566],[512,1568],[515,1570],[518,1572],[521,1574],[524,1576],[527,1578],[530,1580],[533,1582],[536,1584],[539,1586],[542,1588],[545,1590],[548,1592],[551,1594],[554,1596],[557,1598],[560,1600],[563,1602],[566,1604],[569,1606],[572,1608],[575,1610],[578,1612],[581,1614],[584,1616],[587,1618],[590,1620],[593,1622],[596,1624],[599,1626],[602,1628],[605,1630],[608,1632],[611,1634],[614,1636],[617,294],[620,1639],[623,1641],[626,1643],[629,1645],[632,1647],[635,1649],[638,1651],[641,1653],[644,1655],[647,1657],[650,1659],[653,1661],[656,1663],[659,1665],[662,1667],[665,1669],[668,1671],[671,1673],[674,1675],[677,1677],[680,1679],[683,1681],[686,1683],[689,1685],[692,1687],[695,1689],[698,1691],[701,1693],[704,1695],[707,1697],[710,1699],[713,1701],[716,1703],[719,1705],[722,1707],[725,1709],[728,1711],[731,1713],[734,1715],[737,1717],[740,1719],[743,1721],[746,1723],[749,1725],[752,1727],[755,1729],[758,1731],[761,1733],[764,1735],[767,1737],[770,1739],[773,1741],[776,1743],[779,1745],[782,1747],[785,1749],[788,1751],[791,1753],[794,1755],[797,1757],[800,1759],[803,1761],[806,1763],[809,1765],[812,1767],[815,1769],[818,1771],[821,1773],[824,1775],[827,1777],[830,1779],[833,1781],[836,1783],[839,1785],[842,204],[2193,2197,2198,2199,2200],{"key":2194,"label":2195,"type":2196},"v","Volume added (mL)","number",{"key":54,"label":55,"type":2196},{"key":845,"label":846,"type":2196},{"key":1255,"label":1256,"type":2196},{"key":1788,"label":1789,"type":2196},[2202,2208,2214,2220,2226,2232,2238,2243,2245,2249,2253,2257],{"v":2203,"sa_sb":2204,"wa_sb":2205,"wb_sa":2206,"sb_sa":2207},"0.00","1.00","2.87","11.12","13.00",{"v":2209,"sa_sb":2210,"wa_sb":2211,"wb_sa":2212,"sb_sa":2213},"5.00","1.18","4.14","9.86","12.82",{"v":2215,"sa_sb":2216,"wa_sb":2217,"wb_sa":2218,"sb_sa":2219},"12.50","1.48","4.74","9.26","12.52",{"v":2221,"sa_sb":2222,"wa_sb":2223,"wb_sa":2224,"sb_sa":2225},"20.00","1.95","5.35","8.65","12.05",{"v":2227,"sa_sb":2228,"wa_sb":2229,"wb_sa":2230,"sb_sa":2231},"24.00","2.69","6.13","7.87","11.31",{"v":2233,"sa_sb":2234,"wa_sb":2235,"wb_sa":2236,"sb_sa":2237},"24.90","3.70","7.14","6.86","10.30",{"v":2239,"sa_sb":2240,"wa_sb":2241,"wb_sa":2242,"sb_sa":2240},"25.00","7.00","8.72","5.28",{"v":2244,"sa_sb":2237,"wa_sb":2237,"wb_sa":2234,"sb_sa":2234},"25.10",{"v":2246,"sa_sb":2247,"wa_sb":2247,"wb_sa":2248,"sb_sa":2248},"26.00","11.29","2.71",{"v":2250,"sa_sb":2251,"wa_sb":2251,"wb_sa":2252,"sb_sa":2252},"30.00","11.96","2.04",{"v":2254,"sa_sb":2255,"wa_sb":2255,"wb_sa":2256,"sb_sa":2256},"37.50","12.30","1.70",{"v":2258,"sa_sb":2219,"wa_sb":2219,"wb_sa":2216,"sb_sa":2216},"50.00",{"label":2260},"Calculated from Ka = Kb = 1.8 × 10⁻⁵ and Kw = 1.0 × 10⁻¹⁴ at 25 °C using charge-balance equations",[2262,2263,2264,2265,2266,2267,2268,2269],"Every curve uses the same comparison setup: 25.00 mL of 0.100 M analyte titrated with 0.100 M titrant, so the equivalence point falls at 25.00 mL in all four cases.","For the weak-acid curve, the half-equivalence point occurs at 12.50 mL and pH = pKa = 4.74. For the weak-base curve, pH equals the pKa of NH₄⁺ at half-equivalence, giving pH 9.26.","Charge-balance calculations and standard shortcut methods can differ by 0.01 pH unit because of rounding. For example, the initial pH of 0.100 M acetic acid may appear as 2.87 or 2.88 depending on when values are rounded.","Equivalence-point pH depends on the titration type: 7.00 for strong + strong, 8.72 for the weak acid because the conjugate base hydrolyzes, and 5.28 for the weak base because the conjugate acid hydrolyzes.","Choose an indicator whose full color-change interval lies inside the steep region of the curve. The transition range does not need to contain the exact equivalence-point pH when the steep region is broad.","Phenolphthalein (pH 8.3 to 10.0) fits the weak-acid curve. Methyl orange (pH 3.1 to 4.4) changes too early on that curve. On the weak-base curve, methyl orange lies near the lower edge of the steep drop, while methyl red or bromocresol green is a closer match.","The steep central rise of the strong + strong curve spans roughly pH 3 to 11 within a fraction of a milliliter, which is why almost any indicator works there.","These curves are a general reference. Individual titration problems supply their own volumes and concentrations.",[2271,2272,2273],"solution-stoichiometry-and-titrations","acids-bases-and-ph","buffers-and-titration-curves",[],[2276,2277,2278,2279,2280,2281,2282,2283],"titration curve","pH vs volume graph","weak acid strong base titration curve","equivalence point pH","half equivalence point pKa","titration curve buffer region","choosing an indicator titration","interactive titration curve",[2285,2286,2287],"acid-base-indicators","strong-acids-bases","weak-acid-base-constants","Selected pH Values","Milestone values from each curve, including the initial solution, half-equivalence, equivalence, and excess-titrant regions. Use the interactive chart to inspect intermediate volumes.","Titration Curves and Indicator Choice",1787246032931]