Transcript pH measurements - Cornell Engineering

V
+
+
pH measurements
The probe, from chemistry to voltage
to a number
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
pH probe
Buffered KCl solution
4 M KCl solution
Reference electrode
Silver/silver chloride electrode
Sensing electrode
V
+
+
+
+
++ +
+ +
++ +
++ +
+
+ +
+
+
+
+
+ + + +
+ +
+ + +
+ ++ + +
+ + +
++ + + +
+ +
+ +
+ +
+ + +
+
+ ++ + +
+ + +
+
+ +
+
++ +
++ +
+ ++
+
+
Porous reference junction
Glass bulb (insulator) with
anionic sites
Glass membrane (Insulator)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+
Reference Voltage +
+
+
+
+
+
+
+
Call it+ zero!
+
+
+
+
+
+
+
+
++
+
+
+
+ ++
+
+
++
++
+
+
+++ +
+
+
+
+
+
+
+
+
+
+ +++ + +
+
+
+
+ + +
 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 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
__________
impedance 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
+
+
Difficult Measurements?
pH is difficult to measure in poorly buffered
solutions
Distilled water
Rain
Between pKs of dilute buffers
Nernst Equation: Voltage = f(pH)
E E 0
E E 0
RT FH
 lnG
nF G
HH
I
JJ
K
RT ln(10) FH

logG
G
nF
HH

éH + ù Reference (known) [H+]
ë
û
0
0


0
I
JJ
K
RT ln(10)
0
é
E=E +
pH
- pH ù
ë
û
nF
E - E ) nF
(
0
pH = pH 0
RT ln(10)
F
Faraday constant
R
Gas constant
0

0
E0
+
é
H
Voltage at ë ùû
J
R 8.314
mol K
Coulombs
F 96500
mol e 
n 1 mol e 
Nernst Equation
E (mV)
pH = pH 0 -
0
E
E
(
) nF
æE 0 E ö nF
pH = pH + ç 0 - ÷
èT
T ø R ln(10)
0
RT ln(10)
250
200
150
100
50
0
-50
-100
-150
-200
-250
J
R 8.314
mol K
E at 0 C
E at 25 C
E at 35 C
E at 100 C
Coulombs
F 96500
mol e 
n 1 mol e 
4
5
6
7
pH
8
9
10
Slope vs. Temperature
mV/pH
E 
0.000198T pH 7
75
70
65
60
55
50
0
50
100
Temperature (C)
 Temperature compensation is important when
temperature changes between samples!
pH 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
The Challenge
0 to 3 known buffers used as standards
Temperature compensation optional
E
T
Buffer pH
pH
Current measurement (E, T)
Calibration Cases
0 or 1 standards w/ Temperature
nF æE 0 E ö
0
pH =
+
pH
÷
R ln(10) çèT 0 T ø
æE E ö
0
+
pH
çèT 0 T ÷
ø
0
ideal
pH = k pH
pH = - k ideal
pH
E
+7
T
1
æ
E
Eö
ideal
pH = k pH ç 1 - ÷ + pH 1
èT T ø
ideal
k pH
ideal
k pH
nF
=
R ln(10)
K
= 5040.8
Volt
No standards (assume ideal
slope and intercept)
Single standard (assume
ideal slope)
Multiple Point Calibrations w/
Temperature Compensation
How would you use
this information to
calculate pH?
Calculate E/T
Piecewise linear fit
E
(mV)
T (C)
Buffer
pH
8
23
7
185
24
4
-170
20
10
Current measurement (E, T)
pH