Results and Discussion
Many Many titrat titratio ions ns are are now now done done auto automa matic tical ally ly by instr instrume ument nts s wh whic ich h are are calib calibrat rated ed to deliv deliver er smal smalll incre increme ment nts s of titra titrant nt betw betwee een n pH meas measur urem emen ents ts.. Titration is one of the techniques by which the characteristics of any substance can be analyz analyzed. ed. Poten Potentio tiomet metric ric titrat titration ion is one of them. them. During During titrat titration ion,, pH were were determined and plotted against the buret readings to obtain characteristic curves that were used to determine the equivalence points of the solution !"#. $n this e%periment a wea& acid as sample 'co&e( and a strong base ')a*H(, sodium hydro%ide is commonly &nown as lye or caustic soda and dissolving )a*H in water water genera generates tes cons consider iderabl able e heat, heat, was used used where where three three trials trials made. made. +ee +ee tratment tratment of data 'tables( 'tables( in ppendi% . Data from trial " were used thoughout the discussion. The amount of )a*H used to prepare -M )a*H was ./-0- grams 'see calculation in ppendi% 1(. 1y reading the pH meter, the pH acquired by the sample is /.-. $n second year college, students were familiarized with the appearance of a plot plot of pH vs. m2 of base added added in typical typical titraio titraion. n. 3sing these these &nowledg &nowledge, e, the behavior of the pH at the beginning, at the neuralization and towards the end of titration were compared with the titration graphs attained from the e%periment using potentiometric titration. 4igure -a and -b 'see reference /( were used to compare the graph obtained from the e%periment.
Figure 1a. Titration curve for weak acid (ethanoic acid) vs. strong base (sodium hydroxide). Running acid into alkali.
4or 4or the 5rst part of the graph '4igur '4igure e -a(, there there is an e%cess e%cess of sodium sodium hydro%ide. The curve will be e%actly the the same when an addition of hydrochloric acid
to sodium hydro%ide was made. *nce the acid is in e%cess, there will be a di6erence. Past the equivalence point, a bu6er solution containing sodium ethanoate and ethanoic acid was gotten. This resists any large fall in pH.
Figure 1b. Titration curve for weak acid (ethanoic acid) vs. strong base (sodium hydroxide). Running alkali into acid
The start of the graph shows a relatively rapid rise in pH but this slows down as a bu6er solution containing ethanoic acid and sodium ethanoate is produced. 1eyond the equivalence point 'when the sodium hydro%ide is in e%cess( the curve is 7ust the same as that end of the titration graph of strong acid vs. strong base.
olume vs. !" -/ -0 - : !" 9 / 0
#$ui !t
.8
-
-.8
0
0.8
olume
"
".8
/
/.8
8
Figure %. Titration curve from ex!erimental !otentiometric titration. (!" data versus the volume readings of the base.
*n the graph shown above the wea& acid only partially dissociates from its salt. The pH raised normally at 5rst, but as it reaches a zone where the solution seems to be bu6ered, the slope levels out. fter this zone, the pH rises sharply through its equivalence point and levels out again li&e the strong acidstrong base reaction. There are two main points to notice about this curve. The 5rst is the half; equivalence point. This point occurs halfway through a bu6ered region where the pH barely changes for a lot of base added. The half;equivalence point is w hen 7ust enough base is added for half of the acid to be converted to the con7ugate base. a value of the acid. Ta&e this one step further, pH ? p>a. The second point is the higher equivalence point. *nce the acid has been neutralized, notice the point is above pH?@.
Bm 2 -. 0 -." -./ 8 -.9 -.@ -.: 0.0 0.9 " ".0 ".8 ".9 /.-
pH /. /./ 9 /. 8./ 9.9.@ @ @." 8 @.: " :." " :.: / ." : . 0 -. /8 -. 9 --. /9 --.
Bmi d
CphCvol
.8
./8
-.-.0 8 -." @8 -.8 08 -.9 8 -.@ 8
0.0 8 /.999999 99@ /./99999 99@ 8.: /.:
0
-.08
0./
-.0@8
0.:
-."8
"."." 8 ".8 8 ".: 8
0.@ -.@99999 99@ 8.-
mid vs. &!"'&ol @ 9 8 / &!"'&ol "
0 .8 - -.8 0 0.8 " ".8 / /.8 mid
This is perhaps the simplest method for interpreting pH titration data. 1ecause e%periments do not always proceed so neatly, various other methods are often used to determine equivalence points. 4or e%ample, since the region of ma%imum slope contains this point, a graph of the slope '&nown as a EderivativeE in calculus terminology( versus the average volume for the slope interval provides a way to zero in on the desired volume. The slope could be represented as FpHFB 'i.e., FyF%( and Bmid. plot of the same data as shown earlier was treated in this way is shown belowG
Figure . First derivative. The e$uivalence !oint corres!onds to the volume at the !eak of the curve
*ccasionally it is still dicult to 7udge the equivalence point even by this method. +ometimes the Epea&E is rounded or has a plateau. second derivative plot 'the change in the slope( may be used in such cases. The values for the plot are obtained by operating on the 5rst derivative data in the same way as the orig ginal data was processed. plot of FratioFB0 vs. B0mid for the same titration data is shown belowG
Cratio
CB0
B0mid
CratioCB0
%
&ratio'&%
"./9 .0 ;-.:
.88 ..-8
.@@8 -.-.008
8
.-8
/.9
.@8
;@.8 ; 0.8999 @ ;-.-
.@8
-."@8 -./:@ 8 -.890 8
.-08 ."@8
-.990 8 -.-0 8
9.0 0 ;-0 "".""""""" " 9-.""""""" " ;- ; 0.8"""""" " ; 0."""""""
".:999 9@
."8
0.0@8
;0.0 ;0.:
.-8 .08 .0
0.808 0.@08 0.8
;-.:8 ; .-99 @ ; .""" "
.-8
".-08
.08
"."08
.88
".@08
" --./@9- 8 ; -/.9999999 @ ;/ -/ ; -0.""""""" " ; ".99999999 @ ; -.9999 @
Figure . *econd Derivative+ The euivalence !oint corres!onds to the volume where the curve crosses the ,-axis.
The equivalence point is found at the average volume where the function crosses y ? . The downside to the derivative methods is that each involves a compromise in the accuracy of the volume since the interval chosen for the derivative requires an average volume. Ma&ing the intervals small improves the accuracy and is a good reason for adding titrant in very small increments in the vicinity of the equivalence point. 4or the reaction of a wea& acid, such as the acid used in this e%periment, with a strong base ')a*H(, the equivalence point pH is no longer @ unli&e with the reaction between strong acid and strong base. The equivalence point region on the titration curve is not centered at pH @. There is also a more pronounced ElevelE region at the beginning of the titration and approaching the equivalence point as bu6ering occurs due to the partial neutralization of the acid as base is added, and the simultaneous formation of substantial amounts of con7ugate base.
onclusion
Potentiometric titration involves the measurement of the potential of a suitable indicator electrode with respect to a reference electrode as a function of titrant volume. !8#Potentiometric titrations provide more reliable data than data
from titrations that use chemical indicators and are particularly useful with colored or turbid solutions and for detecting the presence of unsuspected species.
Recommendation
$n this e%periment our group recommend that students must have a well; trained hand because it is an important tool. +tudents should strive to develop good control of the buret stopcoc&, delivering single drops with -I reliability and no false squirts. ccurately reading the volume on the buret is another important s&ill. 1e sure the meniscus is at eye;level when recording a volume. Many people 5nd it helpful to place a card behind the buret with a whiteblac& boundary to help determine the e%act position of the meniscus.
References
!-# )eumann, JrzsKbet. '0-(. dvanced PotentiometryG Potentiometric Titrations and Their +ystematic Jrrors. !0# +&oog, D. ,
httpGchemistry.about.comodacidsbase-sstitrationcurvesO0.htm
!8#
httpGmemo.cgu.edu.twhsiu;ponalyticalI0hem2ectureI0@.pdf
/!!endix /
Table 1. Treatment of data for 0rst trial in !otentiometric titration
Bm 2 -.-
pH /./.8@ /.:
-."8
8.@8
-./
9./:
CB
Cp H
.0 8 . 8
.@ @ .@ "
-.00 8 -."@ 8
-.9
@.8
.-
.8 / ./ :
0.0
@.@
.9
0./
:.//
.0
./ @ ./ @
."
.8 "
".@
./9 -. 0 -.8 / --. -
/."
--.8 -
"." ".8
/.9 /.98
--.9 --.@ 8
.89
-.8
.-
"
.8
.-
-
@.0
:.@
CphCvol
.8 9 ./ -
-.8
0.@
Bmid
." ." .0 .0
./ .8 9 .8 0 ./ @
/.-
Cratio
".8/
CB0
B0mid
.88
.@@8
".:
;-.0
.-@8
-.-"@ 8
-/.9
--.80
.-8
-."
-./8
8./
;.0
.@8
-./-0 8
-.88
/.:
.-
-.8
-.
.@:""""" ""
."8
-.@08
0."
0."8
./
0.-
0.88
-.@999999 9@
;.9 ; /.-99 @ -.8999 9@ ; .8:"" " ; .-""" " .0""" "" .@""" ""
.08
0./08
."
0.@
."
"
.08
".0@8
.0
".8
".-8
-.9"""""" "" -.:999999 9@
"./
0.9
".9
0."8 .:"""""" ""
0.:8
.9
.8
/
." . 8
.: . 9
/./8 /.90 8
./
".:
.9
;.08 ; -.8-99 @ ; .0""" "
./8
-.0
.9
.-@8
/.008 /.8"@ 8
CratioCB0
9./"9"9"9" 9 ; 8.:0:8@-/0 @9.: ; -00.999999 @ ;9 ; --./@9-/ : ".-999999 @ ; 0."""""""" " ; .//////// / .@@@@@@@@ : 0.""""""" " ;-.08 ; ".@-99999 @ ; .8-:8-:8 "./0:8@-/0
ra!hs 2btained From Table 1
olume vs. !" -8 - !"
8 .8 - -.8 0 0.8 " ".8 / /.8 8 olume
mid vs. &!"'&vol 0 -8 &!"'&vol -
8 .8 - -.8 0 0.8 " ".8 / /.8 8 mid
%mid vs. &ratio'&% - 8 &ratio'&%
.8 - -.8 0 0.8 " ".8 / /.8 8 ;8
trial -
;- ;-8 %mid
Table %. Treatment of data for second trial in !otentiometric titration
Bm2 -
pH /./.88
CB
CpH
-
.8/
CphCv Bmid ol .8
Cratio
CB0
CratioCB B0mid 0
.8/
-.-.0 -./
/.8 8."@ 8.:8
...0
./ ./0 ./:
-.8 -.-8 -."
/ /.0 0./
"./9 .0 ;-.:
.88 ..-8
.@@8 -.-.008
-.8
9.8
.-
.@/
-./8
@./
8
.-8
-.88
@.-
.8
.9
-.808
-0
/.9
.@8
-."@8 -./:@ 8
9.0 0 ;-0 "".""""" """ 9-.""""" """
-.98 -.:
@.9/ @."
..-8
./8 .0
-.9
/.8
-.@08
-.""" ""
;@.8 ; 0.8999 @
.@8
-.890 8
.-08
-.990 8
."@8
-.-0 8
."8
0.0@8
0./
:./"
.9
.8
0.-
.:""" ""
0.8
:.
.-
./@
0./8
/.@
;-.".:999 9@
0.@ " ".-
./ .:8 -.0:
.0 ." .-
.8 ./8 ./"
0.9 0.:8 ".8
0.8 -.8 /."
;0.0 ;0.:
.-8 .08 .0
0.808 0.@08 0.8
"."
-.@@
.0
./
".0
0./8
;-.:8 ; .-99 @ ; .""" "
.-8
".-08
.08
"."08
.88
".@08
".9
--.0"
."
./9
"./8
-.8""" ""
/./
--.@-
.:
./:
/
.9
ra!hs 2btained From Table %
;- ; 0.8"""" "" ; 0.""""" "" --./@98 ; -/.99999 99 ;/ -/ ; -0.""""" "" ; ".999999 99 ; -.999 9
volume vs. !" -8 - !"
8
.8
-
-.8
0
0.8
"
".8
/
/.8
8
volume
mid vs. &!"'&vol -8 - &!"'&vol
8
.8
-
-.8
0
0.8
"
".8
/
/.8
mid
%mid vs. &ratio'&% - 8 &ratio'&%
.8 ;8
-
-.8
0
0.8
;- ;-8 %mid
"
".8
/
Table . Treatment of data for third trial in !otentiometric titration
Bm2 -.0
pH /././9 /.
CB
CpH
Bmid
CphCvol
Cratio
CB0
B0mid
CratioCB0
.0
./8 .//
.8 -.-
./8 0.0
-.@8
.9
.:
-."
8./
.-
.8
-.08
8
0.:
.-8
-.-@8
-./8
9.-
.-8
.@
-."@8
9.@@
.-8
.9@
-.808
; ."""" ;.0
.-08
-.9
-."-0 8 -./8
-.@
@."8
.-
.8:
-.98
/.9999999 9@ /./999999 9 8.:
.-08
-.: 0.0 0.9 " ".0 ".8
@.:" :."" :.:/ .": .0 -./8
../ ./ ./ .0 ."
./: .8 .8.8/ .8/ .8"
-.@8 0 0./ 0.: "."."8
".9
-.9
.-
.8-
".88
/.: -.08 -.0@8 -."8 0.@ -.@999999 9 8.-
-."""" "" ;;".88 .08 .@8 -."8 ; .""" ".""""
/.-
--./9
.8
.8
".:8
-
/."
--.@/
.0
.0:
/.0
-./
0.-999999 @ -:.9999999 @ ; 0.99999999 ; -."""""""" -.9999999 @ ;- ;-/.0 .908 .-:@8 /.8 ".@""""""" " -9.9999999 @ ; -".9999999 -.-/0:8@-/ "
.-8
..08 ./ ./ ." .08
-.8:@ 8 -.@ -.:@8 0.0 0.9 0.8 ".008
.0
"./8
;/.-
."
".@
./
."8
/.08
ra!hs 2btained From Table
olume vs. !" -8 - !"
8
.8
-
-.8
0
0.8
"
".8
/
/.8
8
olume
mid vs. &!"'&ol : 9 &!"'&ol /
0
.8
-
-.8
0
0.8
mid
"
".8
/
/.8
%mid vs. &ratio'&% " 0 - &ratio'&%
.8 ;-
-
-.8
0
0.8
"
".8
/
/.8
;0 %mid
/!!endix 3 alculation for the !re!aration of 4.15 6a2"
gNaOH =( 100 mL H 2 O)( 0.1 mol / L NaOH )( 1 L /( 1000 mL))( 2539.9969 g /( 1 mol ) NaOH ) gNaOH =¿ 0.399969 grams
