&(%)D!(+) ,-"('
D!&,.+&'-,
O@MHDI@LP<ODJIOJOC@QJGO<B@DN<GNJNCJRI2C@GDLPD?
EPI>ODJIKJO@IOD<GNDIOC@=PAA@MN<M@<NNPH@?OJ=@@LP<G
<
I?<M@@S<BB@M<O@?AJM>G<MDOT
'
AOC@GDLPD?EPI>ODJIKJO@IOD<GDIOC@N<HKG@?DAA@MNAMJHOC@
=PAA@MN < H@<NPM@H@IO @MMJM M@NPGON $DBPM@ DGGPN
OM<O@NCJROC@@MMJM>JH@N<=JPONNPH@OC@OMP@K&JA
OC@N<HKG@DNK&
N
<I?OC@>@GGQJGO<B@DN#
N
2C@KJDIOK&
N
#
N
DNNCJRIJIOC@BM<KC'AOC@GDLPD?EPI>ODJIKJO@IOD<GDI
OC@N<HKG@R@M@@LP<GOJOC@Q<GP@DIOC@=PAA@MNOC@KJDIO
RJPG?GD@JIOC@GDI@&JR@Q@MOC@GDLPD?EPI>ODJIKJO@IOD<G
DIOC@N<HKG@DNBM@<O@MNJOC@KJDIO#
N
GD@N<=JQ@OC@><G
D=M<ODJIGDI@2C@M@AJM@RC@IOC@>@GGQJGO<B@DN>JIQ@MO@?
OJK&OC@M@NPGODNBM@<O@MOC<IOC@OMP@K&=TOC@<HJPIO
NCJRI
OTKD><G HDNH<O>C =@OR@@I GDLPD? EPI>ODJI KJO@IOD<GN DI
=PAA@M<I?N<HKG@DNH4RCD>CDN@LPDQ<G@IOOJ<I@MMJM
JA<=JPO]K&PIDON2C@HDNH<O>CKMJ?P>@N<API?<
H@IO<G@MMJMDIK&?@O@MHDI<ODJINPNDIB<>@GGRDOCGDLPD?
EPI>ODJI
,',(+" '(,-",
1@INJM?D<BIJNOD>N<G@MOOC@PN@MOJKMJ=G@HNRDOCOC@N@I
NJMJMOJ<>OP<GN@INJMA<DGPM@N2C@ORJN@INJM?D<BIJNOD>N
<M@M@A@M@I>@DHK@?<I>@<I?BG<NNDHK@?<I>@
2C@H<EJM>JIOMD=POJMOJM@A@M@I>@DHK@?<I>@DNOC@M@NDNO
<I>@<>MJNNOC@GDLPD?EPI>ODJIKGPB'I<KMJK@MGTAPI>ODJI
DIB@G@>OMJ?@OC@M@NDNO<I>@JAOC@GDLPD?EPI>ODJINCJPG?=@
IJHJM@ OC<IN@Q@M<G CPI?M@?FDGJCHN 'AOC@EPI>ODJI DN
KGPBB@?JMDAOC@ADGGDIBNJGPODJIJMB@GDN?@KG@O@?OC@M@NDNO
<I>@ DI>M@<N@N CDBC M@A@M@I>@ DHK@?<I>@ H<T <GNJ
H@<IOC@N@INJMDNIJODHH@MN@?DIOC@KMJ>@NNNOM@<H
%G<NNDHK@?<I>@M@A@MNOJOC@DHK@?<I>@JAOC@K&N@IND
ODQ@BG<NNH@H=M<I@2C@DHK@?<I>@JAOC@BG<NNH@H
=M<I@DN<NOMJIBAPI>ODJIJAO@HK@M<OPM@NO@HK@M<OPM@
DI>M@<N@N OC@ DHK@?<I>@ ?@>M@<N@N $JM < >C<IB@ DI
BG<NN DHK@?<I>@ OJ C<Q@ <IT H@<IDIB OC@ DHK@?<I>@
H@<NPM@H@IOHPNO=@>JMM@>O@?OJ<M@A@M@I>@O@HK@M<
OPM@2C@DHK@?<I>@JA<OTKD><GBG<NN@G@>OMJ?@<OY!DN
N@Q@M<GCPI?M@?H@BJCHNNC<MK?@>M@<N@DIOC@O@H
K@M<OPM@>JMM@>O@? DHK@?<I>@ DHKGD@N OC<O OC@ BG<NN DN
>M<>F@?>M<>F@?BG<NN@G@>OMJ?@KMJ?P>@N@MMJI@JPNK&
M@<?DIBN2C@@G@>OMJ?@NCJPG?=@M@KG<>@?DHH@?D<O@GT
CDBC O@HK@M<OPM@>JMM@>O@? BG<NN DHK@?<I>@ DHKGD@N OC@
N@INJMDNI@<MDIBOC@@I?JADONGDA@<I?NCJPG?=@M@KG<>@?
<NNJJI<NKJNND=G@
,!"%,"',.%-"(''
)+&)%""+,
K
& H@<NPM@H@IO NTNO@HN >@GG <I? H@O@M C<Q@ CDBC
DHK@?<I>@2C@CDBCDHK@?<I>@>DM>PDODHKJN@NDHKJMO<IO
M@NOMD>ODJIN JI CJR K& H@<NPM@H@IO NTNO@HN <M@
?@NDBI@?
2C@G@<?RDM@AMJHOC@BG<NN@G@>OMJ?@>JII@>ONORJCDBC
M@NDNO<I>@N <=JPO +W <O OC@ @G@>OMJ?@ <I? <=JPO
+W <O OC@ H@O@M 2C@M@AJM@ @G@>OMJNO<OD>
>C<MB@NRCD>C<>>PHPG<O@JIOC@RDM@AMJH@IQDMJIH@I
O<GDIAGP@I>@N><IIJOM@<?DGT?M<DI<R<T PDG?PKJA>C<MB@
M@NPGONDI?@BM<?@?IJDNTM@<?DIBN1CD@G?DIBOC@RDM@RDOC
H@O<G=M<D?>JII@>O@?OJBMJPI?<OOC@DINOMPH@IODNJI@
R<TOJDHKMJQ@OC@NDBI<G'ODN<GNJC@GKAPGOJF@@KOC@N@I
NJM><=G@<NA<M<R<T<NKJNND=G@AMJH!KJR@M><=G@N
2C@CDBCDIKPODHK@?<I>@JAOC@K&H@O@MM@LPDM@NOC<OOC@
G@<?DINPG<ODJI<I?OC@DINPG<ODJI=@OR@@IOC@H@O@MDIKPON
=@JACDBCLP<GDOT2JKMJQD?@APMOC@MKMJO@>ODJIAMJH@IQD
MJIH@IO<G DIO@MA@M@I>@ OC@ @IODM@ N@INJM ><=G@ ><I =@
@I>GJN@?DI>JI?PDO
2J<QJD?OC@I@@?AJM@SK@INDQ@><=G@<I?><=G@DINO<GG<
ODJIN<KM@<HKGDAD@M=PDGODIOJOC@N@INJMJMDINO<GG@?DI<
EPI>ODJI=JSI@<MOC@N@INJM><I=@PN@?2C@KM@<HKGDAD
@M>JIQ@MONOC@CDBCDHK@?<I>@NDBI<GDIOJ<GJRDHK@?
<I>@NDBI<GOC<O><I=@N@IO<NA<M<NA@@ORDOCJPONK@
>D<G><=G@
" .+ %=EI=8#IB7H=CB)CH9BH=5@&=GA5H7<
The dashed vertical lines are the measured cell voltages
for the buffers and the sample. The contribution from each
term in equation 4 is shown. The buffers are are assumed
to have identical liquid junction potentials. Because most
buffers are equitransferant, i.e., the mobilities of the ions
making up the buffer are nearly equal, assuming equal liq-
uid junction potentials is reasonable. In the figure, the liq-
uid junction potential of the sample is greater than the
buffers. The difference gives rise to an error in the meas-
ured pH.