Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering pH measurements The probe, from chemistry to voltage to a number + + V.

Monroe L. Weber-Shirk

School of Civil and

Environmental Engineering

pH measurementspH measurements

The probe, from chemistry to voltage to a number

The probe, from chemistry to voltage to a number

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pH probepH probe

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Silver/silver chloride electrode

Porous reference junction

4 M KCl solution

Glass bulb (insulator) with anionic sites

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Sensing electrode

Reference electrode

Buffered KCl solution

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Glass membrane (Insulator)Glass membrane (Insulator)

pH 4 solution (high H+) Voltage across glass membrane Solution voltage is 180 mV higher than reference! We need a way to measure the solution voltage

pH 4 solution (high H+) Voltage across glass membrane Solution voltage is 180 mV higher than reference! We need a way to measure the solution voltage

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Reference VoltageCall it zero!Reference VoltageCall it zero!

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pH MeasurementspH Measurements

The porous frit provides electrical contact between the solution and the electrolyte Must be in contact with the sample solution Probe won’t work well if frit is clogged (fouled)

The voltage measurement requires a very high __________ circuit (high resistance) because a pH probe can’t produce much current

Gentle stirring keeps the solution next to the glass bulb from being depleted of protons

The porous frit provides electrical contact between the solution and the electrolyte Must be in contact with the sample solution Probe won’t work well if frit is clogged (fouled)

The voltage measurement requires a very high __________ circuit (high resistance) because a pH probe can’t produce much current

Gentle stirring keeps the solution next to the glass bulb from being depleted of protons

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impedance

Difficult Measurements?Difficult Measurements?

pH is difficult to measure in poorly buffered solutions Distilled water Rain Between pKs of dilute buffers

pH is difficult to measure in poorly buffered solutions Distilled water Rain Between pKs of dilute buffers

Nernst Equation: Voltage = f(pH)Nernst Equation: Voltage = f(pH)

E ERTnF

H

H

FHGG

IKJJ

0 100

ln( )log

E ERTnF

H

H

FHGG

IKJJ

00ln

0

H +é ùë û

0E

R

F

Reference (known) [H+]

Voltage at 0

H +é ùë û

Faraday constant

Gas constant

0 0ln(10)RTE E pH pH

nFé ù= + -ë û

( )00

ln(10)

E E nFpH pH

RT

-= -

RJ

mol K

8 314.

FCoulombsmol e

96500

n mol e 1

Nernst EquationNernst Equation

RJ

mol K

8 314.

FCoulombsmol e

96500

n mol e 1

( )00

ln(10)

E E nFpH pH

RT

-= -

00

0 ln(10)E E nF

pH pHT T R

æ ö= + -ç ÷è ø

-250

-200

-150

-100

-50

0

50

100

150

200

250

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pH

E (

mV

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E at 0 C

E at 25 C

E at 35 C

E at 100 C

Slope vs. TemperatureSlope vs. Temperature

Temperature compensation is important! Temperature compensation is important!

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55

60

65

70

75

0 50 100

Temperature (C)

mV

/pH

E T pH 0 000198 7.

pH CalibrationpH Calibration

It would be possible to make a pH measurement without any calibration Based on theoretical values This is how the software recognizes buffers!

Calibration accounts for non-ideal probe behavior (fouling) as well as electronic measurement errors

It is important that buffers be used covering the range of pH measurements

It would be possible to make a pH measurement without any calibration Based on theoretical values This is how the software recognizes buffers!

Calibration accounts for non-ideal probe behavior (fouling) as well as electronic measurement errors

It is important that buffers be used covering the range of pH measurements

The ChallengeThe Challenge

E T Buffer pH

Current measurement (E, T)

pH

0 to 3 known buffers used as standardsTemperature compensation optional

Calibration Cases0 or 1 standards w/ Temperature

Calibration Cases0 or 1 standards w/ Temperature

00

0ln(10)nF E E

pH pHR T T

æ ö= - +ç ÷è ø

7pH

ideal EpH kT

=- + No standards (assume ideal slope and intercept)

ln(10)pH

ideal nFk

R=

Single standard (assume ideal slope)

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1pH

ideal E EpH k pH

T T

æ ö= - +ç ÷è ø

00

0pH

ideal E EpH k pH

T T

æ ö= - +ç ÷è ø

5040.8pH

ideal Kk

Volt=

Multiple Point Calibrations w/ Temperature Compensation

Multiple Point Calibrations w/ Temperature Compensation

How would you use this information to calculate pH?

How would you use this information to calculate pH?

E (mV) T (C)Buffer

pH

8 23 7

185 24 4

-170 20 10

Current measurement (E, T)

pH

Piecewise linear fit

Calculate E/T