[{"data":1,"prerenderedAt":2260},["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":2169,"rows":2178,"entryCount":174,"source":2236,"notes":2238,"relatedTopics":2246,"relatedElements":2250,"seoKeywords":2251},21,"titration-curves","Titration Curves: pH vs Volume for the Four Classic Titrations","Titration Curves","Acids & Bases","Interactive titration curves for the four classic cases — strong acid + strong base, weak acid + strong base, weak base + strong acid, and strong base + strong acid (25.00 mL of 0.100 M analyte, 0.100 M titrant). Click or tap any curve to read the pH at any volume; toggle the indicator bands to see why phenolphthalein fits a weak-acid titration and methyl orange does not.","Interactive titration curve chart: pH vs volume for strong acid-strong base and weak acid-strong base titrations with equivalence points, buffer regions, half-equivalence pH = pKa, and indicator ranges.",{"type":6,"xLabel":13,"yLabel":14,"veq":15,"bands":16,"series":25},"Volume of titrant added (mL)","pH",25,[17,21],{"name":18,"low":19,"high":20},"Methyl orange",3.1,4.4,{"name":22,"low":23,"high":24},"Phenolphthalein",8.3,10,[26,821,1231,1764],{"key":27,"name":28,"detail":29,"points":30},"sa_sb","Strong acid + strong base","25.00 mL of 0.100 M HCl titrated with 0.100 M NaOH",[31,34,37,40,43,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,132,135,138,141,144,147,150,152,155,158,161,164,167,170,173,176,179,182,185,188,191,194,197,200,203,206,209,212,215,218,221,224,227,230,233,236,239,242,245,248,251,254,257,260,263,266,269,272,275,278,281,283,286,289,292,295,298,301,304,307,310,313,316,319,322,325,328,331,334,337,340,343,346,349,352,355,358,361,364,367,370,373,376,379,382,385,388,391,394,397,400,403,406,409,412,415,418,421,424,425,428,431,434,437,440,443,446,449,452,455,458,461,464,467,470,473,476,479,482,485,488,491,494,497,500,503,506,509,512,515,518,521,524,527,530,533,536,539,542,545,548,551,554,557,560,563,566,569,572,575,578,581,584,587,590,593,596,599,602,605,608,611,614,617,620,623,626,629,632,635,638,641,644,647,650,653,656,659,662,665,668,671,674,677,680,683,686,689,692,695,698,701,704,707,710,713,716,719,722,725,728,731,734,737,740,743,746,749,752,755,758,761,764,767,770,773,776,779,782,785,788,791,794,797,800,803,806,809,812,815,818],[32,33],0,1,[35,36],0.25,1.0087,[38,39],0.5,1.0174,[41,42],0.75,1.0261,[33,44],1.0348,[46,47],1.25,1.0435,[49,50],1.5,1.0522,[52,53],1.75,1.0609,[55,56],2,1.0696,[58,59],2.25,1.0784,[61,62],2.5,1.0872,[64,65],2.75,1.0959,[67,68],3,1.1047,[70,71],3.25,1.1136,[73,74],3.5,1.1224,[76,77],3.75,1.1313,[79,80],4,1.1402,[82,83],4.25,1.1491,[85,86],4.5,1.1581,[88,89],4.75,1.1671,[91,92],5,1.1761,[94,95],5.25,1.1852,[97,98],5.5,1.1943,[100,101],5.75,1.2034,[103,104],6,1.2126,[106,107],6.25,1.2218,[109,110],6.5,1.2311,[112,113],6.75,1.2405,[115,116],7,1.2499,[118,119],7.25,1.2593,[121,122],7.5,1.2688,[124,125],7.75,1.2784,[127,128],8,1.2881,[130,131],8.25,1.2978,[133,134],8.5,1.3076,[136,137],8.75,1.3174,[139,140],9,1.3274,[142,143],9.25,1.3374,[145,146],9.5,1.3475,[148,149],9.75,1.3577,[24,151],1.368,[153,154],10.25,1.3784,[156,157],10.5,1.3889,[159,160],10.75,1.3995,[162,163],11,1.4102,[165,166],11.25,1.421,[168,169],11.5,1.432,[171,172],11.75,1.443,[174,175],12,1.4543,[177,178],12.25,1.4656,[180,181],12.5,1.4771,[183,184],12.75,1.4888,[186,187],13,1.5006,[189,190],13.25,1.5126,[192,193],13.5,1.5248,[195,196],13.75,1.5371,[198,199],14,1.5497,[201,202],14.25,1.5624,[204,205],14.5,1.5754,[207,208],14.75,1.5886,[210,211],15,1.6021,[213,214],15.25,1.6158,[216,217],15.5,1.6297,[219,220],15.75,1.644,[222,223],16,1.6585,[225,226],16.25,1.6734,[228,229],16.5,1.6886,[231,232],16.75,1.7042,[234,235],17,1.7202,[237,238],17.25,1.7365,[240,241],17.5,1.7533,[243,244],17.75,1.7706,[246,247],18,1.7884,[249,250],18.25,1.8067,[252,253],18.5,1.8256,[255,256],18.75,1.8451,[258,259],19,1.8653,[261,262],19.25,1.8862,[264,265],19.5,1.908,[267,268],19.75,1.9306,[270,271],20,1.9542,[273,274],20.25,1.9789,[276,277],20.5,2.0048,[279,280],20.75,2.032,[5,282],2.0607,[284,285],21.25,2.0911,[287,288],21.5,2.1234,[290,291],21.75,2.1579,[293,294],22,2.195,[296,297],22.25,2.2351,[299,300],22.5,2.2788,[302,303],22.75,2.3268,[305,306],23,2.3802,[308,309],23.05,2.3917,[311,312],23.1,2.4034,[314,315],23.15,2.4154,[317,318],23.2,2.4278,[320,321],23.25,2.4405,[323,324],23.3,2.4535,[326,327],23.35,2.4669,[329,330],23.4,2.4807,[332,333],23.45,2.495,[335,336],23.5,2.5097,[338,339],23.55,2.5248,[341,342],23.6,2.5405,[344,345],23.65,2.5567,[347,348],23.7,2.5736,[350,351],23.75,2.5911,[353,354],23.8,2.6092,[356,357],23.85,2.6282,[359,360],23.9,2.6479,[362,363],23.95,2.6686,[365,366],24,2.6902,[368,369],24.05,2.7129,[371,372],24.1,2.7368,[374,375],24.15,2.7621,[377,378],24.2,2.7889,[380,381],24.25,2.8173,[383,384],24.3,2.8477,[386,387],24.35,2.8804,[389,390],24.4,2.9156,[392,393],24.45,2.9538,[395,396],24.5,2.9956,[398,399],24.55,3.0418,[401,402],24.6,3.0934,[404,405],24.65,3.1519,[407,408],24.7,3.2192,[410,411],24.75,3.2989,[413,414],24.8,3.3962,[416,417],24.85,3.5216,[419,420],24.9,3.6981,[422,423],24.95,3.9996,[15,115],[426,427],25.05,9.9996,[429,430],25.1,10.3002,[432,433],25.15,10.4758,[435,436],25.2,10.6003,[438,439],25.25,10.6968,[441,442],25.3,10.7756,[444,445],25.35,10.8421,[447,448],25.4,10.8996,[450,451],25.45,10.9504,[453,454],25.5,10.9957,[456,457],25.55,11.0366,[459,460],25.6,11.074,[462,463],25.65,11.1083,[465,466],25.7,11.1401,[468,469],25.75,11.1696,[471,472],25.8,11.1972,[474,475],25.85,11.2231,[477,478],25.9,11.2475,[480,481],25.95,11.2706,[483,484],26,11.2924,[486,487],26.05,11.3132,[489,490],26.1,11.333,[492,493],26.15,11.3519,[495,496],26.2,11.3699,[498,499],26.25,11.3872,[501,502],26.3,11.4038,[504,505],26.35,11.4198,[507,508],26.4,11.4352,[510,511],26.45,11.45,[513,514],26.5,11.4643,[516,517],26.55,11.4781,[519,520],26.6,11.4915,[522,523],26.65,11.5044,[525,526],26.7,11.517,[528,529],26.75,11.5291,[531,532],26.8,11.5409,[534,535],26.85,11.5524,[537,538],26.9,11.5636,[540,541],26.95,11.5744,[543,544],27,11.585,[546,547],27.25,11.6341,[549,550],27.5,11.6778,[552,553],27.75,11.7171,[555,556],28,11.7528,[558,559],28.25,11.7856,[561,562],28.5,11.8157,[564,565],28.75,11.8437,[567,568],29,11.8697,[570,571],29.25,11.894,[573,574],29.5,11.9168,[576,577],29.75,11.9383,[579,580],30,11.9586,[582,583],30.25,11.9778,[585,586],30.5,11.9961,[588,589],30.75,12.0134,[591,592],31,12.03,[594,595],31.25,12.0458,[597,598],31.5,12.0609,[600,601],31.75,12.0753,[603,604],32,12.0892,[606,607],32.25,12.1026,[609,610],32.5,12.1154,[612,613],32.75,12.1277,[615,616],33,12.1397,[618,619],33.25,12.1512,[621,622],33.5,12.1623,[624,625],33.75,12.173,[627,628],34,12.1834,[630,631],34.25,12.1935,[633,634],34.5,12.2032,[636,637],34.75,12.2127,[639,640],35,12.2218,[642,643],35.25,12.2308,[645,646],35.5,12.2394,[648,649],35.75,12.2479,[651,652],36,12.2561,[654,655],36.25,12.264,[657,658],36.5,12.2718,[660,661],36.75,12.2794,[663,664],37,12.2868,[666,667],37.25,12.294,[669,670],37.5,12.301,[672,673],37.75,12.3079,[675,676],38,12.3146,[678,679],38.25,12.3212,[681,682],38.5,12.3276,[684,685],38.75,12.3338,[687,688],39,12.3399,[690,691],39.25,12.3459,[693,694],39.5,12.3518,[696,697],39.75,12.3576,[699,700],40,12.3632,[702,703],40.25,12.3687,[705,706],40.5,12.3741,[708,709],40.75,12.3794,[711,712],41,12.3846,[714,715],41.25,12.3897,[717,718],41.5,12.3947,[720,721],41.75,12.3996,[723,724],42,12.4044,[726,727],42.25,12.4091,[729,730],42.5,12.4137,[732,733],42.75,12.4183,[735,736],43,12.4228,[738,739],43.25,12.4272,[741,742],43.5,12.4315,[744,745],43.75,12.4357,[747,748],44,12.4399,[750,751],44.25,12.444,[753,754],44.5,12.448,[756,757],44.75,12.452,[759,760],45,12.4559,[762,763],45.25,12.4598,[765,766],45.5,12.4636,[768,769],45.75,12.4673,[771,772],46,12.471,[774,775],46.25,12.4746,[777,778],46.5,12.4781,[780,781],46.75,12.4816,[783,784],47,12.4851,[786,787],47.25,12.4885,[789,790],47.5,12.4918,[792,793],47.75,12.4951,[795,796],48,12.4984,[798,799],48.25,12.5016,[801,802],48.5,12.5048,[804,805],48.75,12.5079,[807,808],49,12.511,[810,811],49.25,12.514,[813,814],49.5,12.517,[816,817],49.75,12.52,[819,820],50,12.5229,{"key":822,"name":823,"detail":824,"points":825},"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",[826,828,830,832,834,836,838,840,842,844,846,848,850,852,854,856,858,860,862,864,866,868,870,872,874,876,878,880,882,884,886,888,890,892,894,896,898,900,902,904,906,908,910,912,914,916,918,920,922,924,926,928,930,932,934,936,938,940,942,944,946,948,950,952,954,956,958,960,962,964,966,968,970,972,974,976,978,980,982,984,986,988,990,992,994,996,998,1000,1002,1004,1006,1008,1010,1012,1014,1016,1018,1020,1022,1024,1026,1028,1030,1032,1034,1036,1038,1040,1042,1044,1046,1048,1050,1052,1054,1056,1058,1060,1062,1064,1066,1068,1070,1072,1074,1076,1078,1080,1082,1084,1086,1088,1090,1092,1094,1096,1098,1100,1102,1103,1104,1105,1106,1107,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230],[32,827],2.87,[35,829],3.0378,[38,831],3.1829,[41,833],3.3055,[33,835],3.4084,[46,837],3.4957,[49,839],3.5712,[52,841],3.6375,[55,843],3.6967,[58,845],3.7501,[61,847],3.7989,[64,849],3.8437,[67,851],3.8854,[70,853],3.9243,[73,855],3.9608,[76,857],3.9953,[79,859],4.0281,[82,861],4.0592,[85,863],4.089,[88,865],4.1176,[91,867],4.145,[94,869],4.1715,[97,871],4.197,[100,873],4.2218,[103,875],4.2458,[106,877],4.2692,[109,879],4.2919,[112,881],4.3141,[115,883],4.3358,[118,885],4.3571,[121,887],4.3779,[124,889],4.3983,[127,891],4.4184,[130,893],4.4381,[133,895],4.4576,[136,897],4.4767,[139,899],4.4957,[142,901],4.5144,[145,903],4.5329,[148,905],4.5512,[24,907],4.5693,[153,909],4.5873,[156,911],4.6052,[159,913],4.6229,[162,915],4.6406,[165,917],4.6581,[168,919],4.6756,[171,921],4.6931,[174,923],4.7105,[177,925],4.7278,[180,927],4.74,[183,929],4.7626,[186,931],4.7799,[189,933],4.7973,[192,935],4.8148,[195,937],4.8323,[198,939],4.8499,[201,941],4.8675,[204,943],4.8853,[207,945],4.9032,[210,947],4.9212,[213,949],4.9393,[216,951],4.9577,[219,953],4.9762,[222,955],4.9949,[225,957],5.0139,[228,959],5.0331,[231,961],5.0526,[234,963],5.0724,[237,965],5.0925,[240,967],5.113,[243,969],5.1339,[246,971],5.1552,[249,973],5.1769,[252,975],5.1992,[255,977],5.2221,[258,979],5.2456,[261,981],5.2697,[264,983],5.2946,[267,985],5.3204,[270,987],5.347,[273,989],5.3747,[276,991],5.4035,[279,993],5.4336,[5,995],5.4651,[284,997],5.4983,[287,999],5.5333,[290,1001],5.5705,[293,1003],5.6102,[296,1005],5.6529,[299,1007],5.6992,[302,1009],5.7497,[305,1011],5.8056,[308,1013],5.8175,[311,1015],5.8298,[314,1017],5.8423,[317,1019],5.8551,[320,1021],5.8683,[323,1023],5.8818,[326,1025],5.8957,[329,1027],5.91,[332,1029],5.9247,[335,1031],5.9399,[338,1033],5.9555,[341,1035],5.9717,[344,1037],5.9884,[347,1039],6.0057,[350,1041],6.0236,[353,1043],6.0423,[356,1045],6.0617,[359,1047],6.0819,[362,1049],6.103,[365,1051],6.1251,[368,1053],6.1483,[371,1055],6.1727,[374,1057],6.1984,[377,1059],6.2256,[380,1061],6.2545,[383,1063],6.2854,[386,1065],6.3185,[389,1067],6.3541,[392,1069],6.3928,[395,1071],6.4351,[398,1073],6.4817,[401,1075],6.5337,[404,1077],6.5926,[407,1079],6.6604,[410,1081],6.7405,[413,1083],6.8382,[416,1085],6.964,[419,1087],7.1408,[422,1089],7.4418,[15,1091],8.72,[426,1093],10.0008,[429,1095],10.3005,[432,1097],10.476,[435,1099],10.6004,[438,1101],10.6969,[441,442],[444,445],[447,448],[450,451],[453,454],[456,1108],11.0367,[459,460],[462,463],[465,466],[468,469],[471,472],[474,475],[477,478],[480,481],[483,484],[486,487],[489,490],[492,493],[495,496],[498,499],[501,502],[504,505],[507,508],[510,511],[513,514],[516,517],[519,520],[522,523],[525,526],[528,529],[531,532],[534,535],[537,538],[540,541],[543,544],[546,547],[549,550],[552,553],[555,556],[558,559],[561,562],[564,565],[567,568],[570,571],[573,574],[576,577],[579,580],[582,583],[585,586],[588,589],[591,592],[594,595],[597,598],[600,601],[603,604],[606,607],[609,610],[612,613],[615,616],[618,619],[621,622],[624,625],[627,628],[630,631],[633,634],[636,637],[639,640],[642,643],[645,646],[648,649],[651,652],[654,655],[657,658],[660,661],[663,664],[666,667],[669,1180],12.3,[672,673],[675,676],[678,679],[681,682],[684,685],[687,688],[690,691],[693,694],[696,697],[699,700],[702,703],[705,706],[708,709],[711,712],[714,715],[717,718],[720,721],[723,724],[726,727],[729,730],[732,733],[735,736],[738,739],[741,742],[744,745],[747,748],[750,751],[753,754],[756,757],[759,760],[762,763],[765,766],[768,769],[771,772],[774,775],[777,778],[780,781],[783,784],[786,787],[789,790],[792,793],[795,796],[798,799],[801,802],[804,805],[807,808],[810,811],[813,814],[816,817],[819,820],{"key":1232,"name":1233,"detail":1234,"points":1235},"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",[1236,1238,1240,1242,1244,1246,1248,1250,1252,1254,1256,1258,1260,1262,1264,1266,1268,1270,1272,1274,1276,1278,1280,1282,1284,1286,1288,1290,1292,1294,1296,1298,1300,1302,1304,1306,1308,1310,1312,1314,1316,1318,1320,1322,1324,1326,1328,1330,1332,1334,1336,1338,1340,1342,1344,1346,1348,1350,1352,1354,1356,1358,1360,1362,1364,1366,1368,1370,1372,1374,1376,1378,1380,1382,1384,1386,1388,1390,1392,1394,1396,1398,1400,1402,1404,1406,1408,1410,1412,1414,1416,1418,1420,1422,1424,1426,1428,1430,1432,1434,1436,1438,1440,1442,1444,1446,1448,1450,1452,1454,1456,1458,1460,1462,1464,1466,1468,1470,1472,1474,1476,1478,1480,1482,1484,1486,1488,1490,1492,1494,1496,1498,1500,1502,1504,1506,1508,1510,1512,1514,1516,1518,1520,1522,1524,1526,1528,1530,1532,1534,1536,1538,1540,1542,1544,1546,1548,1550,1552,1554,1556,1558,1560,1562,1564,1566,1568,1570,1572,1574,1576,1578,1580,1582,1584,1586,1588,1590,1592,1594,1596,1598,1600,1602,1604,1606,1608,1610,1612,1614,1615,1617,1619,1621,1623,1625,1627,1629,1631,1633,1635,1637,1639,1641,1643,1645,1647,1649,1651,1653,1655,1657,1659,1661,1663,1665,1667,1669,1671,1673,1675,1677,1679,1681,1683,1685,1687,1689,1691,1693,1695,1697,1699,1701,1703,1705,1707,1709,1711,1713,1715,1717,1719,1721,1723,1725,1727,1729,1731,1733,1735,1737,1739,1741,1743,1745,1747,1749,1751,1753,1755,1757,1759,1761,1763],[32,1237],11.1247,[35,1239],10.9622,[38,1241],10.8171,[41,1243],10.6945,[33,1245],10.5916,[46,1247],10.5043,[49,1249],10.4288,[52,1251],10.3625,[55,1253],10.3033,[58,1255],10.2499,[61,1257],10.2011,[64,1259],10.1563,[67,1261],10.1146,[70,1263],10.0757,[73,1265],10.0392,[76,1267],10.0047,[79,1269],9.9719,[82,1271],9.9408,[85,1273],9.911,[88,1275],9.8824,[91,1277],9.855,[94,1279],9.8285,[97,1281],9.803,[100,1283],9.7782,[103,1285],9.7542,[106,1287],9.7308,[109,1289],9.7081,[112,1291],9.6859,[115,1293],9.6642,[118,1295],9.6429,[121,1297],9.6221,[124,1299],9.6017,[127,1301],9.5816,[130,1303],9.5619,[133,1305],9.5424,[136,1307],9.5233,[139,1309],9.5043,[142,1311],9.4856,[145,1313],9.4671,[148,1315],9.4488,[24,1317],9.4307,[153,1319],9.4127,[156,1321],9.3948,[159,1323],9.3771,[162,1325],9.3594,[165,1327],9.3419,[168,1329],9.3244,[171,1331],9.3069,[174,1333],9.2895,[177,1335],9.2722,[180,1337],9.26,[183,1339],9.2374,[186,1341],9.2201,[189,1343],9.2027,[192,1345],9.1852,[195,1347],9.1677,[198,1349],9.1501,[201,1351],9.1325,[204,1353],9.1147,[207,1355],9.0968,[210,1357],9.0788,[213,1359],9.0607,[216,1361],9.0423,[219,1363],9.0238,[222,1365],9.0051,[225,1367],8.9861,[228,1369],8.9669,[231,1371],8.9474,[234,1373],8.9276,[237,1375],8.9075,[240,1377],8.887,[243,1379],8.8661,[246,1381],8.8448,[249,1383],8.8231,[252,1385],8.8008,[255,1387],8.7779,[258,1389],8.7544,[261,1391],8.7303,[264,1393],8.7054,[267,1395],8.6796,[270,1397],8.653,[273,1399],8.6253,[276,1401],8.5965,[279,1403],8.5664,[5,1405],8.5349,[284,1407],8.5017,[287,1409],8.4667,[290,1411],8.4295,[293,1413],8.3898,[296,1415],8.3471,[299,1417],8.3008,[302,1419],8.2503,[305,1421],8.1944,[308,1423],8.1825,[311,1425],8.1702,[314,1427],8.1577,[317,1429],8.1449,[320,1431],8.1317,[323,1433],8.1182,[326,1435],8.1043,[329,1437],8.09,[332,1439],8.0753,[335,1441],8.0601,[338,1443],8.0445,[341,1445],8.0283,[344,1447],8.0116,[347,1449],7.9943,[350,1451],7.9764,[353,1453],7.9577,[356,1455],7.9383,[359,1457],7.9181,[362,1459],7.897,[365,1461],7.8749,[368,1463],7.8517,[371,1465],7.8273,[374,1467],7.8016,[377,1469],7.7744,[380,1471],7.7455,[383,1473],7.7146,[386,1475],7.6815,[389,1477],7.6459,[392,1479],7.6072,[395,1481],7.5649,[398,1483],7.5183,[401,1485],7.4663,[404,1487],7.4074,[407,1489],7.3396,[410,1491],7.2595,[413,1493],7.1618,[416,1495],7.036,[419,1497],6.8592,[422,1499],6.5582,[15,1501],5.28,[426,1503],3.9992,[429,1505],3.6995,[432,1507],3.524,[435,1509],3.3996,[438,1511],3.3031,[441,1513],3.2244,[444,1515],3.1579,[447,1517],3.1004,[450,1519],3.0496,[453,1521],3.0043,[456,1523],2.9633,[459,1525],2.926,[462,1527],2.8917,[465,1529],2.8599,[468,1531],2.8304,[471,1533],2.8028,[474,1535],2.7769,[477,1537],2.7525,[480,1539],2.7294,[483,1541],2.7076,[486,1543],2.6868,[489,1545],2.667,[492,1547],2.6481,[495,1549],2.6301,[498,1551],2.6128,[501,1553],2.5962,[504,1555],2.5802,[507,1557],2.5648,[510,1559],2.55,[513,1561],2.5357,[516,1563],2.5219,[519,1565],2.5085,[522,1567],2.4956,[525,1569],2.483,[528,1571],2.4709,[531,1573],2.4591,[534,1575],2.4476,[537,1577],2.4364,[540,1579],2.4256,[543,1581],2.415,[546,1583],2.3659,[549,1585],2.3222,[552,1587],2.2829,[555,1589],2.2472,[558,1591],2.2144,[561,1593],2.1843,[564,1595],2.1563,[567,1597],2.1303,[570,1599],2.106,[573,1601],2.0832,[576,1603],2.0617,[579,1605],2.0414,[582,1607],2.0222,[585,1609],2.0039,[588,1611],1.9866,[591,1613],1.97,[594,271],[597,1616],1.9391,[600,1618],1.9247,[603,1620],1.9108,[606,1622],1.8974,[609,1624],1.8846,[612,1626],1.8723,[615,1628],1.8603,[618,1630],1.8488,[621,1632],1.8377,[624,1634],1.827,[627,1636],1.8166,[630,1638],1.8065,[633,1640],1.7968,[636,1642],1.7873,[639,1644],1.7782,[642,1646],1.7692,[645,1648],1.7606,[648,1650],1.7521,[651,1652],1.7439,[654,1654],1.736,[657,1656],1.7282,[660,1658],1.7206,[663,1660],1.7132,[666,1662],1.706,[669,1664],1.699,[672,1666],1.6921,[675,1668],1.6854,[678,1670],1.6788,[681,1672],1.6724,[684,1674],1.6662,[687,1676],1.6601,[690,1678],1.6541,[693,1680],1.6482,[696,1682],1.6424,[699,1684],1.6368,[702,1686],1.6313,[705,1688],1.6259,[708,1690],1.6206,[711,1692],1.6154,[714,1694],1.6103,[717,1696],1.6053,[720,1698],1.6004,[723,1700],1.5956,[726,1702],1.5909,[729,1704],1.5863,[732,1706],1.5817,[735,1708],1.5772,[738,1710],1.5728,[741,1712],1.5685,[744,1714],1.5643,[747,1716],1.5601,[750,1718],1.556,[753,1720],1.552,[756,1722],1.548,[759,1724],1.5441,[762,1726],1.5402,[765,1728],1.5364,[768,1730],1.5327,[771,1732],1.529,[774,1734],1.5254,[777,1736],1.5219,[780,1738],1.5184,[783,1740],1.5149,[786,1742],1.5115,[789,1744],1.5082,[792,1746],1.5049,[795,1748],1.5016,[798,1750],1.4984,[801,1752],1.4952,[804,1754],1.4921,[807,1756],1.489,[810,1758],1.486,[813,1760],1.483,[816,1762],1.48,[819,181],{"key":1765,"name":1766,"detail":1767,"points":1768},"sb_sa","Strong base + strong acid","25.00 mL of 0.100 M NaOH titrated with 0.100 M HCl",[1769,1770,1772,1774,1776,1778,1780,1782,1784,1786,1788,1790,1792,1794,1796,1798,1800,1802,1804,1806,1808,1810,1812,1814,1816,1818,1820,1822,1824,1826,1828,1830,1832,1834,1836,1838,1840,1842,1844,1846,1848,1850,1852,1854,1856,1858,1860,1862,1864,1866,1868,1869,1871,1873,1875,1877,1879,1881,1883,1885,1887,1889,1891,1893,1895,1897,1899,1901,1903,1905,1907,1909,1911,1913,1915,1917,1919,1921,1923,1925,1927,1928,1930,1932,1934,1936,1938,1940,1942,1944,1946,1948,1950,1952,1954,1956,1958,1960,1962,1964,1966,1968,1970,1972,1974,1976,1978,1980,1982,1984,1986,1988,1990,1992,1994,1996,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2026,2028,2030,2031,2033,2035,2037,2039,2041,2042,2043,2044,2045,2046,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168],[32,186],[35,1771],12.9913,[38,1773],12.9826,[41,1775],12.9739,[33,1777],12.9652,[46,1779],12.9565,[49,1781],12.9478,[52,1783],12.9391,[55,1785],12.9304,[58,1787],12.9216,[61,1789],12.9128,[64,1791],12.9041,[67,1793],12.8953,[70,1795],12.8864,[73,1797],12.8776,[76,1799],12.8687,[79,1801],12.8598,[82,1803],12.8509,[85,1805],12.8419,[88,1807],12.8329,[91,1809],12.8239,[94,1811],12.8148,[97,1813],12.8057,[100,1815],12.7966,[103,1817],12.7874,[106,1819],12.7782,[109,1821],12.7689,[112,1823],12.7595,[115,1825],12.7501,[118,1827],12.7407,[121,1829],12.7312,[124,1831],12.7216,[127,1833],12.7119,[130,1835],12.7022,[133,1837],12.6924,[136,1839],12.6826,[139,1841],12.6726,[142,1843],12.6626,[145,1845],12.6525,[148,1847],12.6423,[24,1849],12.632,[153,1851],12.6216,[156,1853],12.6111,[159,1855],12.6005,[162,1857],12.5898,[165,1859],12.579,[168,1861],12.568,[171,1863],12.557,[174,1865],12.5457,[177,1867],12.5344,[180,820],[183,1870],12.5112,[186,1872],12.4994,[189,1874],12.4874,[192,1876],12.4752,[195,1878],12.4629,[198,1880],12.4503,[201,1882],12.4376,[204,1884],12.4246,[207,1886],12.4114,[210,1888],12.3979,[213,1890],12.3842,[216,1892],12.3703,[219,1894],12.356,[222,1896],12.3415,[225,1898],12.3266,[228,1900],12.3114,[231,1902],12.2958,[234,1904],12.2798,[237,1906],12.2635,[240,1908],12.2467,[243,1910],12.2294,[246,1912],12.2116,[249,1914],12.1933,[252,1916],12.1744,[255,1918],12.1549,[258,1920],12.1347,[261,1922],12.1138,[264,1924],12.092,[267,1926],12.0694,[270,595],[273,1929],12.0211,[276,1931],11.9952,[279,1933],11.968,[5,1935],11.9393,[284,1937],11.9089,[287,1939],11.8766,[290,1941],11.8421,[293,1943],11.805,[296,1945],11.7649,[299,1947],11.7212,[302,1949],11.6732,[305,1951],11.6198,[308,1953],11.6083,[311,1955],11.5966,[314,1957],11.5846,[317,1959],11.5722,[320,1961],11.5595,[323,1963],11.5465,[326,1965],11.5331,[329,1967],11.5193,[332,1969],11.505,[335,1971],11.4903,[338,1973],11.4752,[341,1975],11.4595,[344,1977],11.4433,[347,1979],11.4264,[350,1981],11.4089,[353,1983],11.3908,[356,1985],11.3718,[359,1987],11.3521,[362,1989],11.3314,[365,1991],11.3098,[368,1993],11.2871,[371,1995],11.2632,[374,1997],11.2379,[377,1999],11.2111,[380,2001],11.1827,[383,2003],11.1523,[386,2005],11.1196,[389,2007],11.0844,[392,2009],11.0462,[395,2011],11.0044,[398,2013],10.9582,[401,2015],10.9066,[404,2017],10.8481,[407,2019],10.7808,[410,2021],10.7011,[413,2023],10.6038,[416,2025],10.4784,[419,2027],10.3019,[422,2029],10.0004,[15,115],[426,2032],4.0004,[429,2034],3.6998,[432,2036],3.5242,[435,2038],3.3997,[438,2040],3.3032,[441,1513],[444,1515],[447,1517],[450,1519],[453,1521],[456,2047],2.9634,[459,1525],[462,1527],[465,1529],[468,1531],[471,1533],[474,1535],[477,1537],[480,1539],[483,1541],[486,1543],[489,1545],[492,1547],[495,1549],[498,1551],[501,1553],[504,1555],[507,1557],[510,1559],[513,1561],[516,1563],[519,1565],[522,1567],[525,1569],[528,1571],[531,1573],[534,1575],[537,1577],[540,1579],[543,1581],[546,1583],[549,1585],[552,1587],[555,1589],[558,1591],[561,1593],[564,1595],[567,1597],[570,1599],[573,1601],[576,1603],[579,1605],[582,1607],[585,1609],[588,1611],[591,1613],[594,271],[597,1616],[600,1618],[603,1620],[606,1622],[609,1624],[612,1626],[615,1628],[618,1630],[621,1632],[624,1634],[627,1636],[630,1638],[633,1640],[636,1642],[639,1644],[642,1646],[645,1648],[648,1650],[651,1652],[654,1654],[657,1656],[660,1658],[663,1660],[666,1662],[669,1664],[672,1666],[675,1668],[678,1670],[681,1672],[684,1674],[687,1676],[690,1678],[693,1680],[696,1682],[699,1684],[702,1686],[705,1688],[708,1690],[711,1692],[714,1694],[717,1696],[720,1698],[723,1700],[726,1702],[729,1704],[732,1706],[735,1708],[738,1710],[741,1712],[744,1714],[747,1716],[750,1718],[753,1720],[756,1722],[759,1724],[762,1726],[765,1728],[768,1730],[771,1732],[774,1734],[777,1736],[780,1738],[783,1740],[786,1742],[789,1744],[792,1746],[795,1748],[798,1750],[801,1752],[804,1754],[807,1756],[810,1758],[813,1760],[816,1762],[819,181],[2170,2174,2175,2176,2177],{"key":2171,"label":2172,"type":2173},"v","Volume added (mL)","text",{"key":27,"label":28,"type":2173},{"key":822,"label":823,"type":2173},{"key":1232,"label":1233,"type":2173},{"key":1765,"label":1766,"type":2173},[2179,2185,2191,2197,2203,2209,2215,2220,2222,2226,2230,2234],{"v":2180,"sa_sb":2181,"wa_sb":2182,"wb_sa":2183,"sb_sa":2184},"0.00","1.00","2.87","11.12","13.00",{"v":2186,"sa_sb":2187,"wa_sb":2188,"wb_sa":2189,"sb_sa":2190},"5.00","1.18","4.14","9.86","12.82",{"v":2192,"sa_sb":2193,"wa_sb":2194,"wb_sa":2195,"sb_sa":2196},"12.50","1.48","4.74","9.26","12.52",{"v":2198,"sa_sb":2199,"wa_sb":2200,"wb_sa":2201,"sb_sa":2202},"20.00","1.95","5.35","8.65","12.05",{"v":2204,"sa_sb":2205,"wa_sb":2206,"wb_sa":2207,"sb_sa":2208},"24.00","2.69","6.13","7.87","11.31",{"v":2210,"sa_sb":2211,"wa_sb":2212,"wb_sa":2213,"sb_sa":2214},"24.90","3.70","7.14","6.86","10.30",{"v":2216,"sa_sb":2217,"wa_sb":2218,"wb_sa":2219,"sb_sa":2217},"25.00","7.00","8.72","5.28",{"v":2221,"sa_sb":2214,"wa_sb":2214,"wb_sa":2211,"sb_sa":2211},"25.10",{"v":2223,"sa_sb":2224,"wa_sb":2224,"wb_sa":2225,"sb_sa":2225},"26.00","11.29","2.71",{"v":2227,"sa_sb":2228,"wa_sb":2228,"wb_sa":2229,"sb_sa":2229},"30.00","11.96","2.04",{"v":2231,"sa_sb":2232,"wa_sb":2232,"wb_sa":2233,"sb_sa":2233},"37.50","12.30","1.70",{"v":2235,"sa_sb":2196,"wa_sb":2196,"wb_sa":2193,"sb_sa":2193},"50.00",{"label":2237},"Computed from the ChemWhiz course-canonical constants (Ka = Kb = 1.8 × 10⁻⁵, Kw = 1.0 × 10⁻¹⁴ at 25 °C) by exact charge-balance solution at every point — no approximations",[2239,2240,2241,2242,2243,2244,2245],"Every curve is the classic course 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.","The pH at every point solves the full charge-balance equation exactly, with the course's graded answers taking precedence at the classic anchor volumes (initial point, half-equivalence, equivalence, 50% excess). At half-equivalence (12.50 mL) pH = pKa = 4.74.","Exact charge-balance values and the standard approximation conventions (small-x, Henderson-Hasselbalch) can differ in the second decimal place — for example 2.88 vs 2.87 for the initial pH of 0.100 M acetic acid. Where a value is graded in the course, this chart shows the graded value; everywhere else it shows the exact solution. The difference never exceeds 0.01 pH units.","Equivalence-point pH depends on the titration type: 7.00 for strong + strong, 8.72 for the weak acid (the conjugate base hydrolyzes), 5.28 for the weak base (the conjugate acid hydrolyzes). Choose an indicator whose color change spans the equivalence pH.","The indicator bands show the classic pairing: phenolphthalein (8.3 to 10.0) brackets the weak-acid equivalence point; methyl orange (3.1 to 4.4) changes color far too early on that curve but works for a weak-base titration.","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 the general reference; ChemWhiz titration problems supply their own volumes and concentrations in the problem statement.",[2247,2248,2249],"solution-stoichiometry-and-titrations","acids-bases-and-ph","buffers-and-titration-curves",[],[2252,2253,2254,2255,2256,2257,2258,2259],"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",1785108608690]