Download E b

Home Reading
Skoog et al. Fundamentals of Analytical Chemistry.
Chapter 10, 21
Eb  E2  E1  L  0.0592pH
Include EIRE, EERE, Ej
Ecell  E
0
cell
 0.0592pH
Calibration plot
Ecell
(250C)
slope = - 0.0592
0
Ecell
0
Ecell  Ecell
 0.0592log CH
pH
Concentration and activity
0
Ecell  Ecell
 0.0592pH
pH = -logCH+
Diluted solutions
0
Ecell  Ecell
 0.0592 log CH
[C] = mole/L
Concentration and activity
0
Ecell  Ecell
 0.0592pH
pH = -logCH+
Diluted solutions
Concentrated
solutions
0
Ecell  Ecell
 0.0592 log CH
0
Ecell  Ecell
 0.0592 log CH
0
Ecell  Ecell
 0.0592 log aH
Activity
(Apparent concentration)
Concentration and activity
0
 0.0592pH
By convention we accept that equation Ecell  Ecell
is true at any concentration.
0
Ecell  Ecell
 0.0592 log aH
Ecell  E
0
cell
 0.0592pH
pH = -logaH+
Operational definition of pH
pH   log aH 
0
Ecell  Ecell

0.0592
Concentration and activity
0
Ecell  Ecell
 0.0592 log aH
aH    H  C H 
H  activity coefficient
 1 C 0
For diluted solutions a = C
Activity coefficient of an individual ion is a theoretical quantity.
Ions exist in solutions only in combinations with oppositely charged
co-ions. Therefore we cannot experimentally measure the activity
coefficient of an individual ion. In experiment, we can only able to
determinate the mean activity coefficient, averaged by all the ions
in the solution.
The mean activity coefficient of the electrolyte KmAn is defined as
    

m n 1 m n 
 
Experimental
Value
Theoretical value
    

m n 1 m n 
 
For a 1:1 electrolyte KA the mean activity coefficient is
equal to
       
12
Calculation of the activity coefficient
The total concentration of ions in a solution is characterized by a
quantity called ionic strength (I)
1
I   Ci zi2
2 i
Ci = molar concentration of ionic species i
zi = charge of ionic species i
Example: Calculate ionic strength of 1M solution of HCl
1
I   Ci zi2
2 i
CH = 1M;
CCl = 1 M; zH = 1;


1
I  112  112  1
2
zCl = 1
Debay – Hückel equation
Azi2 I
 log  i 
1  Bri I
A and B are coefficients depending on the solvent and temperature.
For water solutions at T = 25 oC A = 0.51, B = 3.3
ri = effective diameter of the hydrated ion i in nanometers.
It is close to 0.3 nm for most single charged ions.
Ion-selective electrode
Ion-selective electrodes measure the activity of ions. Correspondingly the
potentiometric equation for them reads
0
Ecell  Ecell
 0.0592pX
pX = -logCX
Ion-selective electrode
Glass electrodes
Liquid membrane electrodes
Solid-state crystalline electrodes
Li+, Na+, K+, NH4+
Ca2+, K+, Water hardness (Ca2+ +
Mg2+), Cl-, NO3-
Cu2+, Cd2+, Pb2+, Ag+/S2-,
Cl-, F-, I-, CN-
Ion-sensitive glass electrodes
H+ responsive glass
Na+ responsive glass
H+
Na+
H+
Na+
H+
Na+
H+
Na+
Ion-sensitive glass electrodes
Cole-Parmer® potassiumselective electrode
Ion-sensitive glass electrodes
Ion conductive glasses are ion-exchangers. When such glass is brought to contact
with a solution of electrolyte, equilibrium is established:
Glass-A+ + B+ = Glass-B+ +A+
soln
soln
Any aqueous solution contains hydrogen-ions. So, most frequently, this ion- exchange
equilibrium is between H+ and a metal cation.
Glass-H+ + B+ = Glass-H+ +A+
soln
soln
Ion-sensitive glass electrodes
Eb = L‘ + 0.0592log(a+kH,Bb)
Ej
EIRE
Eb = E2 – E1
EERE
a, b = activity of hydrogen-ion and
the cation in the solution
kH,B = selectivity coefficient
The selectivity coefficient is a measure
of the response of an ion-selective
electrode to other ions.
Eb = L‘ + 0.0592log(a+kH,Bb)
1. kH,B ≈ 0
Eb ≈ L‘ + 0.0592log(a)=L‘ - 0.0592pH
pH-glass
2. kH,B >> 0
Eb ≈ L‘ + 0.0592log(kH,Bb)=L‘‘ - 0.0592pB
L ‘‘ = L ‘ + 0.0592*log(kH,B)
Ion-selective glass
Ion-sensitive glass electrodes
Liquid membrane electrodes
Ag wire
Plastic tubing
Liquid ionexchanger
Aqueous
solution sat’d
AgCl + B+
Porous plastic membrane
holding liquid ion-exchanger
Liquid membrane electrodes
Solid-state electrodes
Solid-state electrode has principally the same design as glass membrane
electrodes except the membrane is made from cast pellets of crystalline
material rather than from conducting glass.
Solid membrane must contain mobile ions, to which it is responsive.
Material
Selective ion
AgF, LaF
F-
AgCl
Cl-
AgI
I+
Ag2S
S2+, Ag+
CdS/Ag2S
Cd2+
PbS/Ag2S
Pb2+
Solid-state electrode
Potentiometric titration
Potentiometric titration is a titration technique. It differs from classic
titration only in a method of indicating the titration endpoint.
Can be used for
Benefits:
1. Acid/base titration
1. More sensitive
2. Red/Ox titration
2. Can be automated
3. Complexometry
3. Can be used for turbid or
strongly coloured solutions
4. Can be used if there is no
suitible indicator
Set-up for potentiometric titration
Burette
Potentiometer
Electrode
Automatic titration
Pump-burette
Electrodes
Reservoirs
Cell
There are two distinguishable situation in
potentiometric acid/base titration:
1. Titration of a strong electrolyte by a strong electrolyte
2. Titration of a weak electrolyte by a strong electrolyte
Titration of a strong acid by a strong base
13
12
11
10
pH
9
Veq
8
7
6
5
4
3
0
5
10
15
20
Volume NaOH (mL)
25
30
35
Titration of a weak acid by a strong base
Consider the following graph:
13
12
11
10
Veq
pH
9
8
7
6
pKa
5
Veq/2
4
3
0
5
10
15
20
Volume NaOH (mL)
25
30
35
Consider the following graph:
13
12
11
10
pH
9
8
7
6
5
4
3
0
5
10
15
20
25
30
35
Volume NaOH (mL)
In this region H+ dominates, the small change in pH is the result
of relatively small changes in H+ concentration.
Consider the following graph:
13
12
11
10
pH
9
8
7
6
5
4
3
0
5
10
15
20
25
30
35
Volume NaOH (mL)
In this region, relatively small changes in H+ concentration cause
large changes in pH, The midpoint of the vertical region is the
equivalence point.
Consider the following graph:
13
12
11
10
pH
9
8
7
6
5
4
3
0
5
10
15
20
25
30
35
Volume NaOH (mL)
In this region OH- dominates, the small change in pH is the result
of relatively small changes in OH- concentration.