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{"sheet":"Eingabe","index":0,"n_rows":23,"n_cols":15,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["Titrationskurven",null,null,null,null,null,null,"Berücksichtigung der Verdünnung",null,null,"x-Achse",null,null,"y-Achse"]
[null,null,null,null,null,null,null,null,null,null,"Minimum",0,null,"Minimum",0]
["Probenvolumen",null,null,null,null,null,null,null,null,null,"Maximum",25,null,"Maximum",14]
["Vp [mL]",100]
[]
["Säure 1"]
["c0 [mol/L]",0.1]
["pKS1",-8]
["pKS2"]
["pKS3"]
[]
["Säure 2"]
["c0 [mol/L]",0.1]
["pKS1",-8]
["pKS2"]
["pKS3"]
[]
["Titrans"]
["cT [mol/L]",2]
["pKS1",20]
["pKS2"]
["pKS3"]
["=pKS-Werte der konjugierten Säuren"]

{"sheet":"Speziierung","index":1,"n_rows":149,"n_cols":16,"rows_kept":149,"cut":false,"hidden":false,"merged":[]}
["Speziierung von Säure 1 oder Base 1"]
["zudem [H+] und [OH-]",null,null,"c",{"$f":"Berechnung!F2","v":0.1}]
["sowie Titrationskurve",null,null,"pK1",{"$f":"Berechnung!F3","v":-8}]
["letztere sind nur korrekt, wenn ",null,null,"pK2",{"$f":"Berechnung!F4","v":30}]
["unter \"Eingabe\" die konzentration von Säure 2 ",null,null,"pK3",{"$f":"Berechnung!F5","v":30}]
["Null gesetzt wird",null,null,null,"Relative Anteile",null,null,null,"ohne Verdünnung",null,null,null,"Mit Verdünnung"]
[null,null,null,null,"H3A","H2A","HA","A","H3A","H2A","HA","A","H3A","H2A","HA","A"]
["pH","vt","H+","OH-",3,2,1,0,3,2,1,0,3,2,1,0]
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{"sheet":"Herleitung","index":3,"n_rows":46,"n_cols":3,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
["Herleitung Formel"]
["Definitionen"]
["Anfangskonzentrationen"]
["ct",null,"Titrans, also OH-"]
["c0","=HA+A","Säure Startkonzentration"]
["V0, Vt","Probenvolumen, Titransvolumen bis zum betrachteten Punkt"]
["Algw-Konzentrationen",null,"molare Mengen (n) im Gleichgewicht"]
["[H]",null,"H"]
["[OH]",null,"OH"]
["[HA]",null,"HA"]
["[A] ",null,"A"]
[]
["ct·Vt-OH","Menge an zugegebenen OH-, die insgesamt mit Säuremolekülen wegreagiert sind = (zugegeben) - (noch vorhanden)"]
[]
[]
["[A] und [HA] im Gleichgewicht: Kolonne cBase"]
["pH = pKs + log(A/HA) = pKs + log (A/(c0-A))"]
["10^(pH-pKs)=(A/c0-A)"]
["cBase = [A]unverdünnt =[ c0·10^(pH-pKs)]  /  [(1+10^(pH-pKs))] =c0· 1/(1+(1/10^(pH-pKs)))"]
["Bei Verdünnung wird c0 und damit auch HA und A (bei konstantem pH) verdünnt um den Faktor V0/(Vt+V0)"]
["[A] verdünnt = [A] = [A]unverdünnt ·V0/(Vt+V0) = cBase·V0/(Vt+V0)"]
[]
["Protonenbilanz:"]
["(Gesamte Menge aller als Säure zugegebener H+)  = (H+, die im Glgw noch an undeprotonierter Säure sind) + (H+ im Gleichgeweicht) + (Menge, die mit OH- wegreagiert ist) "]
["c0 = HA + H  + (ct·Vt-OH)"]
["c0 ersetzen und Gleichung umstellen"]
["HA + A = HA + H + (ct·Vt-OH)"]
["A = H + (ct·Vt-OH)"]
["Berechnung der molaren Mengen aus Konzentrationen"]
["Mit Verdünnung: Bei der Titration wird c0 verdünnt um den Faktor V0/(Vt+V0)"]
["[A] (V0+Vt)= [H] (V0+Vt) + (ct·Vt-[OH] (V0+Vt))"]
[" cBase·V0/(Vt+V0) (V0+Vt)=cBase· V0 =  [H]· (V0+Vt) + (ct·Vt-[OH] (V0+Vt))"]
["(cBase + [OH] - [H]) · V0= (ct  -  [OH] +  [H])·Vt "]
["Vt=(cBase + [OH] - [H]) · V0 / (ct  - [OH] +  [H]) "]
["Näherung unverdünnt: hier setzt man statt [H] (V0+Vt) bzw. [OH] (V0+Vt) nur [H]·V0 bzw. [OH]·V0: "]
["Vt=(cBase + [OH] - [H]) · V0 / (ct ) "]
[]
["Mehrpotonige Säure"]
["Fürs Gleichgewicht Anteile ausrechnen: "]
["setzen: Anteil von H3A=1"]
["aus A = HA*10^(pH-pKs)"]
["ergibt sich H2A = H3A*10^(pH-pKS)"]
["-> Anteil von H2A, diesen verwendet man wiederum für Berechnung des Anteils von HA etc"]
["c0/(Summe aller Anteile) * betreffender Anteil = Konzentration der Spezies, ohne Verdünnung"]
["Verdünnung: alle Konzentrationen mal den Verdünnungsfaktor (bei konstantem pH!) V0/(Vt+V0)"]
["Also am Schluss auch wieder Anwendung des Verdünnungsfaktors"]

{"sheet":"Pufferkurven","index":4,"n_rows":147,"n_cols":13,"rows_kept":147,"cut":false,"hidden":false,"merged":[]}
["Beim Einfüllen der pKS- oder pH-Werte (graue Flächen) werden die Kurven automatisch erzeugt, beim Löschen verschwinden sie wieder. (im Gelben Bereich nichts ändern!!)"]
[]
[null,"Pufferkurven",null,null,null,"Linie 1",null,"Linie 2",null,"1%-Linie"]
[null,"pKs","pKs","pKs","pKs","pH",null,"pH"]
[null,null,null,4,null,7]
["pH","Schwarz","rot","blau","braun","schwarz",null,"grün"]
[0,{"$f":"IF(B$5<>\"\",ALPHA(0,$A7,B$5),\"\")","v":""},{"$f":"IF(C$5<>\"\",ALPHA(0,$A7,C$5),\"\")","v":""},{"$f":"IF(D$5<>\"\",ALPHA(0,$A7,D$5),\"\")","v":9.9990000999900015E-5},""]
[{"$f":"A7+0.1","v":0.1},{"$f":"IF(B$5<>\"\",ALPHA(0,$A8,B$5),\"\")","v":""},{"$f":"IF(C$5<>\"\",ALPHA(0,$A8,C$5),\"\")","v":""},1.258766942425033E-4,"",{"$f":"IF(F5<>\"\",0,\"\")","v":0},{"$f":"IF(F5<>\"\",F5,\"\")","v":7},{"$f":"IF(H5<>\"\",0,\"\")","v":""},{"$f":"IF(H5<>\"\",H5,\"\")","v":""},0.01,0,0.99,0]
[{"$f":"A8+0.1","v":0.2},"","",1.5846420436223715E-4,"",{"$f":"IF(F5<>\"\",1,\"\")","v":1},{"$f":"IF(F5<>\"\",F5,\"\")","v":7},{"$f":"IF(H5<>\"\",1,\"\")","v":""},{"$f":"IF(H5<>\"\",H5,\"\")","v":""},0.01,14,0.99,14]
[0.30000000000000004,"","",1.994864287215303E-4,""]
[0.4,"","",2.5112556326146182E-4,""]
[0.5,"","",3.1612779762961766E-4,""]
[0.6,"","",3.9794874430487676E-4,""]
[0.7,"","",5.0093617081359862E-4,""]
[0.79999999999999993,"","",6.3055948833989331E-4,""]
[0.89999999999999991,"","",7.9369777816924356E-4,""]
[0.99999999999999989,"","",9.99000999000999E-4,""]
[1.0999999999999999,"","",1.2573425113552919E-3,""]
[1.2,"","",1.5823852808017208E-3,""]
[1.3,"","",1.9912891707283189E-3,""]
[1.4000000000000001,"","",2.5055926672857371E-3,""]
[1.5000000000000002,"","",3.1523091832602115E-3,""]
[1.6000000000000003,"","",3.9652856191522059E-3,""]
[1.7000000000000004,"","",4.9868787366879721E-3,""]
[1.8000000000000005,"","",6.2700123414338518E-3,""]
[1.9000000000000006,"","",7.8806838503302917E-3,""]
[2.0000000000000004,"","",9.9009900990099115E-3,""]
[2.1000000000000005,"","",1.2432735254442419E-2,""]
[2.2000000000000006,"","",1.5601662241829621E-2,""]
[2.3000000000000007,"","",1.956230387257955E-2,""]
[2.4000000000000008,"","",2.4503367550336035E-2,""]
[2.5000000000000009,"","",3.0653430031715573E-2,""]
[2.600000000000001,"","",3.8286503882254817E-2,""]
[2.7000000000000011,"","",4.7726721034204021E-2,""]
[2.8000000000000012,"","",5.9350943102767742E-2,""]
[2.9000000000000012,"","",7.3587556117573727E-2,""]
[3.0000000000000013,"","",9.0909090909091161E-2,""]
[3.1000000000000014,"","",0.11181576977811727,""]
[3.2000000000000015,"","",0.13680688860321041,""]
[3.3000000000000016,"","",0.16633753081656241,""]
[3.4000000000000017,"","",0.20076000891310239,""]
[3.5000000000000018,"","",0.24025307335204293,""]
[3.6000000000000019,"","",0.28474724895080228,""]
[3.700000000000002,"","",0.33386057541687891,""]
[3.800000000000002,"","",0.38686317984685809,""]
[3.9000000000000021,"","",0.44268836623770846,""]
[4.0000000000000018,"","",0.500000000000001,""]
[4.1000000000000014,"","",0.55731163376229353,""]
[4.2000000000000011,"","",0.61313682015314364,""]
[4.3000000000000007,"","",0.66613942458312236,""]
[4.4000000000000004,"","",0.71525275104919883,""]
[4.5,"","",0.75974692664795784,""]
[4.5999999999999996,"","",0.79923999108689814,""]
[4.6999999999999993,"","",0.83366246918343789,""]
[4.7999999999999989,"","",0.86319311139678978,""]
[4.8999999999999986,"","",0.88818423022188264,""]
[4.9999999999999982,"","",0.90909090909090884,""]
[5.0999999999999979,"","",0.92641244388242605,""]
[5.1999999999999975,"","",0.94064905689723211,""]
[5.2999999999999972,"","",0.95227327896579572,""]
[5.3999999999999968,"","",0.96171349611774493,""]
[5.4999999999999964,"","",0.96934656996828417,""]
[5.5999999999999961,"","",0.97549663244966367,""]
[5.6999999999999957,"","",0.98043769612742038,""]
[5.7999999999999954,"","",0.98439833775817021,""]
[5.899999999999995,"","",0.98756726474555756,""]
[5.9999999999999947,"","",0.99009900990098987,""]
[6.0999999999999943,"","",0.99211931614966953,""]
[6.199999999999994,"","",0.99372998765856613,""]
[6.2999999999999936,"","",0.99501312126331187,""]
[6.3999999999999932,"","",0.99603471438084767,""]
[6.4999999999999929,{"$f":"IF(B$5<>\"\",ALPHA(0,$A72,B$5),\"\")","v":""},{"$f":"IF(C$5<>\"\",ALPHA(0,$A72,C$5),\"\")","v":""},0.99684769081673963,""]
[{"$f":"A72+0.1","v":6.5999999999999925},"","",0.99749440733271422,""]
[6.6999999999999922,"","",0.99800871082927178,""]
[6.7999999999999918,"","",0.99841761471919821,""]
[6.8999999999999915,"","",0.99874265748864455,""]
[6.9999999999999911,"","",0.99900099900099892,""]
[7.0999999999999908,"","",0.99920630222183082,""]
[7.1999999999999904,"","",0.99936944051165999,""]
[7.2999999999999901,"","",0.9994990638291863,""]
[7.3999999999999897,"","",0.99960205125569523,""]
[7.4999999999999893,"","",0.99968387220237032,""]
[7.599999999999989,"","",0.99974887443673865,""]
[7.6999999999999886,"","",0.99980051357127853,""]
[7.7999999999999883,"","",0.99984153579563773,""]
[7.8999999999999879,"","",0.99987412330575753,""]
[7.9999999999999876,"","",0.99990000999900008,""]
[8.0999999999999872,"","",0.99992057348559993,""]
[8.1999999999999869,"","",0.99993690824637249,""]
[8.2999999999999865,"","",0.99994988378839778,""]
[8.3999999999999861,"","",0.99996019086777466,""]
[8.4999999999999858,"","",0.99996837822336659,""]
[8.5999999999999854,"","",0.99997488176662652,""]
[8.6999999999999851,"","",0.99998004777494953,""]
[8.7999999999999847,"","",0.99998415131926,""]
[8.8999999999999844,"","",0.99998741090436949,""]
[8.999999999999984,"","",0.99999000009999894,""]
[9.0999999999999837,"","",0.99999205678074798,""]
[9.1999999999999833,"","",0.99999369046636566,""]
[9.2999999999999829,"","",0.99999498815278243,""]
[9.3999999999999826,"","",0.99999601894414325,""]
[9.4999999999999822,"","",0.99999683773233983,""]
[9.5999999999999819,"","",0.99999748811987799,""]
[9.6999999999999815,"","",0.99999800474166611,""]
[9.7999999999999812,"","",0.99999841510931942,""]
[9.8999999999999808,"","",0.99999874107617315,""]
[9.9999999999999805,"","",0.99999900000100006,""]
[10.09999999999998,"","",0.9999992056723962,""]
[10.19999999999998,"","",0.99999936904305375,""]
[10.299999999999979,"","",0.99999949881301753,""]
[10.399999999999979,"","",0.99999960189298798,""]
[10.499999999999979,"","",0.99999968377233406,""]
[10.599999999999978,"","",0.99999974881141984,""]
[10.699999999999978,"","",0.99999980047380832,""]
[10.799999999999978,"","",0.99999984151070587,""]
[10.899999999999977,"","",0.9999998741074746,""]
[10.999999999999977,"","",0.99999990000000993,""]
[11.099999999999977,"","",0.9999999205671829,""]
[11.199999999999976,"","",0.99999993690426958,""]
[11.299999999999976,"","",0.99999994988127916,""]
[11.399999999999975,"","",0.99999996018928461,""]
[11.499999999999975,"","",0.99999996837722438,""]
[11.599999999999975,"","",0.99999997488113634,""]
[11.699999999999974,"","",0.99999998004737733,""]
[11.799999999999974,"","",0.99999998415106828,""]
[11.899999999999974,"","",0.99999998741074603,""]
[11.999999999999973,"","",0.99999999000000017,""]
[12.099999999999973,"","",0.99999999205671786,""]
[12.199999999999973,"","",0.99999999369042647,""]
[12.299999999999972,"","",0.99999999498812775,""]
[12.399999999999972,"","",0.99999999601892831,""]
[12.499999999999972,"","",0.99999999683772245,""]
[12.599999999999971,"","",0.99999999748811352,""]
[12.699999999999971,"","",0.9999999980047376,""]
[12.799999999999971,"","",0.99999999841510689,""]
[12.89999999999997,{"$f":"IF(B$5<>\"\",ALPHA(0,$A136,B$5),\"\")","v":""},{"$f":"IF(C$5<>\"\",ALPHA(0,$A136,C$5),\"\")","v":""},0.99999999874107459,""]
[{"$f":"A136+0.1","v":12.99999999999997},"","",0.99999999899999992,""]
[13.099999999999969,"","",0.99999999920567184,""]
[13.199999999999969,"","",0.99999999936904271,""]
[13.299999999999969,"","",0.99999999949881269,""]
[13.399999999999968,"","",0.9999999996018929,""]
[13.499999999999968,"","",0.99999999968377229,""]
[13.599999999999968,"","",0.99999999974881137,""]
[13.699999999999967,"","",0.99999999980047383,""]
[13.799999999999967,"","",0.99999999984151078,""]
[13.899999999999967,"","",0.99999999987410737,""]
[13.999999999999966,"","",0.99999999989999999,""]

{"sheet":"Berechnung alt","index":5,"n_rows":158,"n_cols":23,"rows_kept":158,"cut":false,"hidden":false,"merged":[]}
["Titrationskurven Säuren",null,null,null,"Berechnung mit H+ als unabhängiger, Vt als abhängiger Variabel"]
["Probenvolumen mL",null,100]
["Titranskonzentration mol/L",null,1]
[null,null,20]
[]
[null,null,null,"Einprotonige Säuren",null,null,"Mehrprotonige Säuren"]
[null,null,null,"müssen nicht nach aufsteigendem pKS geordnet sein",null,null,"Nach aufsteigenden pKS"]
[null,null,null,"Zusätzliche Säuren",null,null,"Für zweiprotonige Säure: letzten pKs über 14 wählen"]
[null,null,null," zwischen Säure 1 und Säure 3 einfügen"]
[null,null,null,"Säure 1","Säure 3"]
[null,"pKS",null,10,4,null,-3,5,20]
[null,"c0","mol/L",0.05,0.1,null,0,"=[H3A]0"]
[]
["delta pH",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Folgeberechnungen"]
[0.1,null,null,null,null,null,null,null,null,null,null,null,null,null,"V","V ","pH"]
[null,null,null,null,null,null,"Für H3A=1",null,null,null,null,null,null,null,"ohne Verdünnung","mit Verdünnung",null,null,null,null,"Säure 1","Säure 1"]
["pH","H3O+","OH-","cBase","cBase",null,"H2A","HA","A","Anteile total","cBAseTotal",null,"Summe(Basen)",null,null,null,null,null,"H","OH","HA","A"]
[0,{"$f":"10^-A18","v":1},{"$f":"10^-(14-A18)","v":1E-14},{"$f":"1/(1+(10^-($A18-D$11)))*D$12","v":4.9999999995000005E-12},9.9990000999900019E-6,null,{"$f":"10^($A18-G$11)","v":1000},{"$f":"10^($A18-H$11)*G18","v":0.01},9.9999999999999993E-23,{"$f":"1+G18+H18+I18","v":1001.01},{"$f":"$G$12/J18*(G18+2*H18+3*I18)","v":0},null,{"$f":"SUM(D18:F18)+K18","v":9.9990050999900005E-6},null,{"$f":"(M18+C18-B18)*$C$2/$C$3","v":-99.999000099488995},{"$f":"(M18+C18-B18)*$C$2/($C$3-C18+B18)","v":-49.999500049744746},{"$f":"A18","v":0},null,{"$f":"B18","v":1},{"$f":"C18","v":1E-14},{"$f":"($D$12-D18)*$C$2/($C$2+P18)","v":9.9999000099487506E-2},{"$f":"D18*$C$2/($C$2+P18)","v":9.9999000099487515E-12},{"$f":"SUM(U18:V18)","v":9.999900010948741E-2}]
[{"$f":"A18+A$15","v":0.1},{"$f":"10^-A19","v":0.79432823472428149},{"$f":"10^-(14-A19)","v":1.2589254117941644E-14},6.2946270581783821E-12,1.2587669424250328E-5,null,{"$f":"10^($A19-G$11)","v":1258.925411794168},1.5848931924611127E-2,1.9952623149688753E-22,{"$f":"1+G19+H19+I19","v":1259.9412607260927},{"$f":"$G$12/J19*(G19+2*H19+3*I19)","v":0},null,{"$f":"SUM(D19:F19)+K19","v":1.2587675718877386E-5},null,{"$f":"(M19+C19-B19)*$C$2/$C$3","v":-79.431564704855006},{"$f":"(M19+C19-B19)*$C$2/($C$3-C19+B19)","v":-44.268135097958321},{"$f":"A19","v":0.1},null,{"$f":"B19","v":0.79432823472428149},{"$f":"C19","v":1.2589254117941644E-14},8.9715282418036738E-2,{"$f":"D19*$C$2/($C$2+P19)","v":1.1294484886235674E-11},{"$f":"SUM(U19:V19)","v":8.9715282429331217E-2}]
[{"$f":"A19+A$15","v":0.2},0.63095734448019325,1.5848931924611084E-14,7.924465961049606E-12,1.5846420436223698E-5,null,1584.8931924611156,2.5118864315095829E-2,3.9810717055349663E-22,1585.9183113254308,0,null,1.5846428360689659E-5,null,-63.094149805181679,-38.685346381815521,0.2,null,0.63095734448019325,1.5848931924611084E-14,8.1546574989125792E-2,1.2924261156878487E-11,8.1546575002050051E-2]
[0.30000000000000004,0.50118723362727224,1.9952623149688784E-14,9.9763115728538654E-12,1.9948642872153003E-5,null,1995.2623149688804,3.9810717055349686E-2,7.943282347242778E-22,1996.3021256859358,0,null,1.9948652848464575E-5,null,-50.116728497440391,-33.384728683273941,0.30000000000000004,null,0.50118723362727224,1.9952623149688784E-14,7.5057864363106602E-2,1.4976012820575228E-11,7.5057864378082609E-2]
[0.4,0.3981071705534972,2.511886431509576E-14,1.2559432154393106E-11,2.5112556326146157E-5,null,2511.8864315095811,6.3095734448019331E-2,1.5848931924611065E-21,2512.949527244029,0,null,2.5112568885578313E-5,null,-39.808205798458651,-28.472928711680719,0.4,null,0.3981071705534972,2.511886431509576E-14,6.9903603051067215E-2,1.7558991201760726E-11,6.9903603068626211E-2]
[0.5,0.31622776601683794,3.1622776601683714E-14,1.5811388295841871E-11,3.1612779762961762E-5,null,3162.2776601683804,9.9999999999999895E-2,3.1622776601683585E-21,3163.3776601683803,0,null,3.1612795574350059E-5,null,-31.619615322123195,-24.022905562774355,0.5,null,0.31622776601683794,3.1622776601683714E-14,6.5809307863832545E-2,2.0810730408894058E-11,6.5809307884643273E-2]
[0.6,0.25118864315095801,3.9810717055349592E-14,1.9905358519750344E-11,3.9794874430487659E-5,null,3981.0717055349769,0.15848931924611115,6.3095734448019278E-21,3982.2301948542231,0,null,3.9794894335846176E-5,null,-25.114884825658233,-20.072820324208202,0.6,null,0.25118864315095801,3.9810717055349592E-14,6.2556942685716418E-2,2.4904367451087786E-11,6.2556942710620789E-2]
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