Instrumental Measurements with Carbon Paste Electrodes, Sensors, and Detectors - Electroanalysis with Carbon Paste Electrodes - page 136

TABLE 6.1
Limiting Current Responses of Electrodes
of Various Geometry in Flow-Through Cells
Electrode Geometry Limiting Current

2 3 /

A
R

*

1 61 . ⋅ n F D ⋅ ⋅ ⋅ ⋅ V

1 3 /

⋅ C

Tubular

f

2 3 /

D A
d

⋅

*

Planar.(parallel.low)

1 3 /

0 68 . ⋅ n F ⋅ ⋅ ⋅ V ⋅ C

f

2 3 /

D A
d

⋅

*

1 3 /

Thin-layer.cell 1 47 . ⋅ n F ⋅ ⋅ ⋅ V ⋅ C

f

*

Planar.(perpendicular)

2 3 / − 1 6 / 3 4 / 1 2 /

0 93 . ⋅ n F D ⋅ ⋅ ⋅ v ⋅ A ⋅ u ⋅ C

Source: . Assembled. after. Wang,. J.,. Analytical Electrochemistry ,.
1st.edn.,.New.York:.VCH.publishers,.1994.
d ,.thickness.of.the.channel;. u ,.velocity.(cm.s −1 );. C *,.concentration.
(mM);.other.symbols.with.their.usual.meaning.

standard.solution.of.the.analyte..If.the.indicator.electrode.response.is.speciic.for.the.analyte.and.
independent.of.the.matrix,.no.preliminary.steps.are.required..In.addition,.although.discontinuous.
measurements. are. mainly. carried. out,. direct. potentiometry. is. readily. adapted. to. continuous. and.
automated.monitoring.
In.pH.measurements,.an.electrochemical.pH-cell.consists.essentially.of.a.measuring.(indicator).
electrode.together.with.a.reference.electrode,.both.in.contact.with.the.solution.to.be.studied..For.
precise.measurements,.it.has.been.suggested.to.use.two.standard.buffers,.pH( S 1 ).and.pH( S 2 ),.which.
straddle.the.pH( X ).value..The.pH( X ).value.is.then.given.as

[ pH ( X ) −

−

pH ( S )] [ E X ( ) −

−

E S ( )]

1 1

= . (6.20)

[ pH ( S ) pH ( S )] [ E S ( ) E S ( )]

.

2 1 2 1

This.equation.represents.the.so-called.practical.deinition.of.the.pH.scale.[1956-1958]..Evidently,.
in.practice.the.voltage.differences.expressed.on.the.right.side.of.the.aforementioned.equation.are.
not.measured.inasmuch.as.the.present.meters.provide.direct.pH.readings..Hence,.instead.of.the. E ( S ).
values,.the.pH( S ).values.are.adjusted.directly.on.the.instrument.scale..The.Nernst.equation.contains.
a.temperature.term.that.can.be.corrected.by.automatic.temperature.compensation;.detailed.instruc-
tions.are.attached.to.each.pH.meter.
For.direct.concentration.measurements.with.ion-selective.electrodes,.measurements.of.p X ,.dif-
ferent.methods.are.available,.although.none.is.as.well.organized.as.pH.measurements..The.simplest.
procedure.is.to.measure.the.voltage.of.the.cell.containing.an.ion-selective.electrode.in.solutions.of.
graduated.concentrations,.usually.between.10 −1 .and.10 −6 .mol.L −1 .(or.similar.to.the.pH.scale,.in.an.
interval.of.p X .1-6)..A.typical.calibration.graph.is.usually.linear.between.p X .1.and.5,.deined.for.
p X .=.−log. a i .(see.Figure.6.8).
In.practice,.however,.the.determination.of.concentration.is.more.frequently.requested;.it.is.pos-
sible.and.more.often.used..In.this.case,.the.cell.voltage.values.are.plotted.against.the.logarithms.
of.the.concentration. of.the.ion.determined,.p X .=.−log. c i ..Such.a.calibration. graph,.however,. dif-
fers. from. that. obtained. by. measuring. the. activity. at. higher. concentrations,. when. y i . (the. activity.