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‰½ôÇ…ø½(‰½üÇ…½0‰½Ç…½8‰½Ç…Ç…€Ç…ÄÿÿÇ…ÈÇ…ÌPTAB‹…h‰…À…¸‰…hQRÿuèûŸGþd$ZY¸ë(U‹l$SQRVW¸€}'uQRUèAÇþd$ZYé!þÿÿ_^ZY[]ÃU‹l$SQRVW‹t$$‹|$(é¦ÈSQRVWP‹E‰EüXP‹E‰EøXQRhhÿuøhP‹Eü‹‰D$Xhè¥¥!þd$ZY=tëM¸Eü¸EøQRhhÿuøhP‹Eü‹‰D$Xhè]¥!þd$ZY=të¸_^ZY[ÉÃÿuP‡$P‡$èFÿÿÿd$_^ZY[]ÃU‹l$SQRVW‹u¸E´)‰F¸2¶)‰F¸³¡)‰F@¸?·)‰FDQRhUè÷¸þd$ZY_^ZY[]ÃTüBl—l9Û99+9ù$s$í$ÃŽ&9_9:nðþ<Á"ëÈWŸ¡`¡)ÿÿÿÿ.Ã&4ún>`xV²Êì¨âíõý%J ÷ #«ÂÙð $ > X r Œ ¦ À Ú ô (BLiŠÃCODEtD(€6.0rc5Oldest compatible LabVIEW., ZZpTPP@P,@ 'Concentration of Acid to Be Titrated, M @ Initial Volume of Acid, mL@ Concentration of Base, M*@ %Volume of Base Added at Each Step, mL*@ $Total Volume of Base to be Added, mL@ Kw@ K1J@P@ÿÿÿÿ @ Vtot@ÿÿÿÿ@ pHDiprotic Titration Simulation@0ÿÿÿÿformula @ start@ endÿÿõñThis vi simulates a titration curve. The theory of a titration curve starts with the four equations that govern the concentration of the various species involved. When these are solved for the proton concentration, the result is a cubic polynomial. One of the roots of this poynomial represents the pH as function of the added base concentration. The physically correct root is real and posative. The root is found by the Newton-Raphson procedure. The vi begins by allowing the operator to select the parameters that govern the titration. These include specifying the concentration and volume of the acid, the concentration and volume increments of the base and the values of the relevant equilibrium constants. With these values the values of the constants of the polynomial expression are calculated using a formula node. The calculation is done for each addition of the base. Once the vaues of the constants of the polynomial are calculated, the real positive root ot the cubic polynomial are found. The root finding vi requires that the polynomial be entered into formula control as a string with string representation of the numerical constants. To make the root finding vi work for a sequence of values of the constant, we use the substitute variables vi which lets us continuously update the formula control of the Newton-Raphson vi. The substitute variables requires the variable names and numerical values to be entered in a specific format. In addition the numerical values must be converted to strings. pPTH0h DCallis FilesCallisClassesChem 464 C464_Sp-03C464_Lec_Sp-03C464_Lec10_Sp-03Weak_Acid_Sim.doc€ÿÿÿÿ€¿ÿÿ ¶9¶9 ¯ÿ½¯ÿ¥Ý½ªªµ«w¯ÿµ¯ÿ½ ¯® ¿ÿpÁ€1€ € 1€`pÁ€ € € € € €€ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÜDTHPDh88 Ô Û˜~ô8ƒ,@ 'Concentration of Acid to Be Titrated, M,ƒ @ Initial Volume of Acid, mL.ƒ@ Concentration of Base, M:ƒ*@ %Volume of Base Added at Each Step, mL:ƒ*@ $Total Volume of Base to be Added, mLƒ@ Kwƒ@ K1ƒ @ startƒ@ endZƒJ@P@ÿÿÿÿ @ Vtot@ÿÿÿÿ@ pHDiprotic Titration Simulationƒƒ &ƒP0ÿÿÿÿ0ÿÿÿÿƒ @ Vtotƒ@0ÿÿÿÿformulaƒ@ accuracy ƒ@ÿÿÿÿ @ Vtotƒ@ÿÿÿÿ 4ƒ(P@ÿÿÿÿ @ Vtot@ÿÿÿÿ ƒ@ bƒ@ aƒ @ zeroƒ@ f(zero)ƒ @ticksƒ @errorƒ@ dƒ@ cƒ@ hŠƒzð h @error @ticks@ f(zero) @ zero@ accuracy@0ÿÿÿÿformula@ end @ start@ hFƒ6@P@!status @code@0ÿÿÿÿsource error out0ƒ$@0ÿÿÿÿformula after substitutionLƒ@@P@!status @code@0ÿÿÿÿsourceerror in (no error)fƒV@@ÿÿÿÿ8P@0ÿÿÿÿparameter name@0ÿÿÿÿparameter contentSubstitution Rules*ƒ@0ÿÿÿÿoriginal formula(ƒð8 6@P@!status @code@0ÿÿÿÿsource error out$@0ÿÿÿÿformula after substitution@@P@!status @code@0ÿÿÿÿsourceerror in (no error)V@@ÿÿÿÿ8P@0ÿÿÿÿparameter name@0ÿÿÿÿparameter contentSubstitution Rules@0ÿÿÿÿoriginal formulaƒ@ aoƒ@ boƒ0ÿÿÿÿƒ2ƒ"@!use system decimal point (T),ƒ @ÿÿÿÿP0ÿÿÿÿ0ÿÿÿÿìtÜÜ@@ll¤¤ÜÜðð00ˆˆ˜l¤¨ÌÜ@lÜðˆÜÜ@@llÜÜððä<X<ŒÌ˜ ´Ìäü(<PääØL˜ü$L`ttttˆ˜¨˜˜˜ˆttttt¨ttttˆ¨¨¨È˜t˜˜˜t˜ˆˆ˜ˆ §DZs„Zs„%%ÿÿBÿCSimulation of a Titration of a Mono Protic Acid with a Strong Base HØGŒ9™eŒ:™eúúúdD5®6®ÿConcentration of Base, MsD5œî6œî$$ÿ'Concentration of Acid to Be Titrated, MHhG¢9¯e¢:¯eúúúŠD=5Pû=6Pû&&ÿÿÿ& Volume of Base Added at Each Step, mLNDá5îCá6îCÿK1HGô9{ô:{úúúHäF9#e:#eúúúND°5½E°6½EÿKwHœFÃ9Ð{Ã:Ð{úúúfDÇ5Ô¬Ç6Ô¬ÿInitial Volume of Acid, mLHXFÚ9çeÚ:çeúúúpDy5†ìy6†ì ÿ$Total Volume of Base to be Added, mLH$FV9ceV:ceúúúiD—Qª—RªÿDiprotic Titration SimulationQDË®ØÃË¯ØÃstartlD$Å¹Ò_ÅºÒ_ Current Amount of added Base, mLHD$øD¶]Ãs¶^ÃsHDÐDÇqÔ‡ÇrÔ‡N D$+`:m,`9npHN4öA04÷A00.SD’‘Ÿ´’’Ÿ´formulaHpD¦•º4¦–³4³³³ODÌ÷Ù ÌøÙ endHDÞ°ëÜÞ±ëÜ³³³HðCßùì%ßúì%³³³H€D€GH#UÜH$UÜÿÿÿH€DôEâïâïÿÿÿH€D G«%¸ž«&¸žÿÿÿH€DHF*á+áÿÿÿH€D„Fz%‡œz&‡œÿÿÿH€DPGâ)ïîâ*ïîÿÿÿH€DÈFG/T?G0T?ÿÿÿH„D,Gw2„@w3„@ÿÿÿPDÉ?ÖSÉ@ÖSÿÿÿÿVtotNDæIóWæJóWÿÿÿÿdBODIªYJªYÿÿÿÿCaiùD~\ÿ<~]4<ÿÿÿ¡¡ Vtot = i*dB; ao=Cai*Vai/(Vtot+Vai); bo=Cbi*Vtot/(Vtot+Vai); a = 1; b = bo + K1; c = K1*bo - K1*ao - Kw; d = -K1*Kw; OD¸IÅY¸JÅYÿÿÿÿVaiODÐIÝYÐJÝYÿÿÿÿCbiMDKIXLKJXLÿÿÿÿiNDÿIYÿJYÿÿÿÿKwNDI#WJ#WÿÿÿÿK1cDžÿÿÿSubstitute Variables.viMD¦L³S¦M³SÿÿÿÿbMDŽL›SŽM›SÿÿÿÿaH€D”Dâ}ï â~ï ÿÿÿMD»LÈS»MÈSÿÿÿÿcNDîFûSîGûSÿÿÿÿaoiDƒÌdƒÍdÿÿÿNewton Raphson Zero Finder.viMDÓLàSÓMàSÿÿÿÿdH€DD—ž¤±—Ÿ¤±ÿÿÿND FS GSÿÿÿÿboH€DÐEn¢{·n£{·ÿÿÿHDÄ(6cCp6dCpÿÿÿHD¬(…l’y…m’yÿÿÿHD”(fcspfdspÿÿÿTD]Àjí]ÁjíÿÿÿaccuracyHDd(mÀzìmÁzìÿÿÿ±Â³Â±hµhÍˆÍŒøŠøŒ&FPHPC464_Titr_Sim_Sp-03.vi#4FPHPD8#,#,#3˜~ÜtÄ•¤Ph2¬ ÿ{ÿXäcM“tXL¨ ¨H8v/ÿÿÿ\|`|ì7,À 4 ÜYt…ÿ÷Ø”|T|À4 2P ð‹8šfÿ¾úúúúúú˜||$@P tà)€ D ¤|„@P8)(¯ôÿþ¼, ”0`$( ähØà4 F” 4¯ÿ÷Øœp^q`–JØ à"ÌÔ>u< Äô,˜0 ” ð4(jþdk³³³@P¬Æ)ìèôÿþÌ@PÌx)ží \ ÿþ0Þ(˜äœ|¸0 P ð‡4žjþdk³³³( ¤<ÜL Ø@PèŽ)´ï¸8ÿþHð@PÈ<)hüìÿþ`(Ôü0 \(àDxˆ4 F Ž4ïÿ÷Ø 0 ð4´jþdk³³³4 2 ð¡8°fÿ¾úúúúúú¤p 6 0œ)¨5þcl¼¼¼¼¼¼œ)¨5¼¼¼¼¼¼þclœ)¨5––––––þcl0ÜÐ”ÿÿp 2 ¨)´5þbm¼¼¼¼¼¼¨)´5¼¼¼¼¼¼þbm¨)´5––––––þbmL: À¡8°>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ4 FP <4Qüÿ÷Ø¨|´(Ô $¼, X( l Ð ,ˆ 4 F@ à4ïDÿ÷Ø¬0 @ ðï4€þdk³³³4 2@ ðó8|ÿ¾úúúúúú°p 6@ 0î)ú5þcl¼¼¼¼¼¼î)ú5¼¼¼¼¼¼þclî)ú5––––––þcl0 Ü€@Ôœÿÿ@ PŒ¯)Õ€ ì4 2” ð8$fÿ¾úúúúúú´p 6” 0)5þcl¼¼¼¼¼¼)5¼¼¼¼¼¼þcl)5––––––þclL :@ Àó8>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ4 F ¤ ¯4¾Fÿ÷Ø¸0 ¤ ð¾4Õ€þdk³³³0Ü4”4ÿÿp 2” )(5þbm¼¼¼¼¼¼)(5¼¼¼¼¼¼þbm)(5––––––þbmL:” À8$>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ4 2 ¤ ðÂ8Ñ|ÿ¾úúúúúú¼L: ¤ ÀÂ8Ñ>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ4 F Æ4Õÿ÷ØÀ0 ðÕ4ìjþdk³³³4 2 ðÙ8èfÿ¾úúúúúúÄp 6 0Ô)à5þcl¼¼¼¼¼¼Ô)à5¼¼¼¼¼¼þclÔ)à5––––––þcl0ÜHtxÿÿp 2 à)ì5þbm¼¼¼¼¼¼à)ì5¼¼¼¼¼¼þbmà)ì5––––––þbmL: ÀÙ8è>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ4 FP x4‡íÿ÷ØÈ0Ü, P´êÿÿ4 2P ðU8dfÿ¾úúúúúúÌp 6P 0P)\5þcl¼¼¼¼¼¼P)\5¼¼¼¼¼¼þclP)\5––––––þclp 2P \)h5þbm¼¼¼¼¼¼\)h5¼¼¼¼¼¼þbm\)h5––––––þbmL:P ÀU8d>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ0 P ðQ4hjþdk³³³0Ü ¤ôfÿÿp 6 ¤ 0½)É5þcl¼¼¼¼¼¼½)É5¼¼¼¼¼¼þcl½)É5––––––þclp 2 ¤ É)Õ5þbm¼¼¼¼¼¼É)Õ5¼¼¼¼¼¼þbmÉ)Õ5––––––þbmp 6P 0†)’5þcl¼¼¼¼¼¼†)’5¼¼¼¼¼¼þcl†)’5––––––þclp 2P ’)ž5þbm¼¼¼¼¼¼’)ž5¼¼¼¼¼¼þbm’)ž5––––––þbmL:P À‹8š>ø0vÙÚÜu† ø0vø/wø.xø-y÷ÑÕ0Ü¼P4Àÿÿ4 FP –P«ÿ÷ØÐp 2@ ú)5þbm¼¼¼¼¼¼ú)5¼¼¼¼¼¼þbmú)5––––––þbm0 kP! À Øúþ>‘¼¼¼¼¼¼0 CP ˜7 þ>‘¼¼¼¼¼¼4 F` ÊÙÄÿ÷ØÔ@:PJ!ÄØÔìþfi¼¼¼¼¼¼þfiþ]r@O`4P0±†Ó“Ôh2±†Ä“ ÿÿÿÿ@:PL!Ä®ÔÂþvY¼¼¼¼¼¼þvYþo`@:PK!ÄÃÔ×þna¼¼¼¼¼¼þnaþgh0 2p-±Â´Ãþj4 3p^Ä¸Ó`Ø0 2p(±h¶iþk0 2X(ÍˆÎþ‘l0 2X-øŠùþ‘m4 6pµ\ÄtÜ@O@4PÀ°_¶ÀÈ”°p¶ ÿÿÿÿ4 6XÆpÕˆà0 P ð¶Ž°‰ÿöÙÿÿÿÿÿÿ0 P ðJØ þ>‘¼¼¼¼¼¼4 3X^*_;nä0Ü P4ÿÿ4 $P3õB1èTÌ < øÌ0°ðœpXÌü4Q˜‘Ž½7à ôA@PxËïï(¤"0Dÿþh | (0xø8¬|x 0dÈ0 ð£Ž½7ÿ÷Ø³³³³³³4 F ‘ µÿ÷Øì4 2 ð¥”»5ÿöÙ³³³³³³ð0ÜÌB„&ÿÿp 5+ À¥»’¥»’¥»’ÿÿÿÿÿÿÿòÝ(üd˜Ø H@PÊ¦îß8!x ¤ŽL:` Þ¯êµø0v³³³ø0vø/wø.xø-y÷ÑÕ|*ˆ0 P ðÜöï(ÿ÷Ø³³³³³³4 FP ËöÚÿ÷Øô4 2` ðÝ¯ìÝÿöÙ³³³³³³ø@ 2` @Û¦äÿp_³³³ÿp_ÿlc@ 2` €ä¦îÿo`³³³ÿo`ÿkd0ÜìC`Ôªÿÿ0 ` ðÛîßÿ÷Ø³³³³³³4 2P ðÞøí&ÿöÙ³³³³³³üL :P ßøëþø0v³³³ø0vø/wø.xø-y÷ÑÕ@ 2P @Üïåöÿp_³³³ÿp_ÿlc@ 2P €åïïöÿo`³³³ÿo`ÿkd0 ÜEPÿÿL è¬8ÈÌŒ t`˜xD Á0The initial volume ot acid to be titrated here. X ÁBThe original concentration of acid to be titrated is entered here.\ ÁEThe concentration of the base used in the titration is entered here. p ÁZThe incremental amount of base to be added at each step of the titration is entered here. L Á6The total volume of base to be added is entered here. L x˜` tŒÌÈ8¬èˆ„ ÁoThe polynomial equation representing the monoprotic titration is entered here. It is x^3 + bb*x^2 + cc*x + dd¸ Á£Start is the start point of the interval being searched to find a root. This value corresponds to the lowest concentration of the hydrogen ion expected (pH = 14).œ Á‡End is end point of the interval under investigation for a root. The default is 1.0 which is the highest concentration of acid used. . l ÁXThe titration curve is plotted here. It is a plot of pH vs amount of added strong base. ¬BDHPC464_Titr_Sim_Sp-03.viLVINSubstitute Variables.vipPTH0LVINNewton Raphson Zero Finder.vihPTH0hÀ BDHPDØ8h¸h¸h¿˜ ~ÜtL{&4CØ#ÿùÏÿ°ÿ-°“¯, €IÐp#,ÿÿÿ ¨0 ÜI” ´0 @À8`¹$ÉDÁ4H0 @¬ˆ$˜D4°0 @8èÀV"fB^2ð4 BÀG"VÝÿõÚÿÿÿ 0!@@Ì$ )0I(9|0!@üÈTð(Hø8ä0!@ t„…1•QA 0!@´`@ð;ø+ä4! 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