LEC
06.10
Determination of the solubility products of silver halides
Related concepts
Concentration cells without transport, electromotive force, salt
bridge, liquid junction and diffusion potentials.
Principle
A concentration cell is constructed from two half-cells which are
identical, except that the concentration of the ionic species to
which the electrode is sensitive is different on the two sides of
the cell. Such a cell can be used to measure the solubility product of a sparingly soluble salt. In one half-cell the concentration
of these ions is known, in the other it is determined by the solubility product of the salt under investigation. The ratio of the two
concentrations (more accurately, activities) determines the e.m.f.
of the cell.
Tasks
Use a concentration cell made from two Ag(s) Ag+(aq) electrodes
to determine the solubility product of the three silver halides
AgCl, AgBr and AgI.
Equipment
Digital pH-meter
Temperature probe Pt1000
Connecting cord, l = 500 mm, red
Connecting cord, l = 500 mm, blue
Crocodile clips, bare
Silver foil, 150 x 150 x 0.1 mm, 25 g
Retort stand, h = 750 mm
Right angle clamp
Support for two electrodes
Spring balance holder
13702.93
13702.01
07361.01
07361.04
07274.03
31839.04
37694.00
37697.00
45284.01
03065.20
1
1
1
1
1
1
1
1
1
1
Salt bridge
Clay pins, d = 8 mm, l = 15 mm
Silicone tubing, di = 7 mm
Rubber caps
Syringe, 10 ml
Cannula, 0.6 x 60 mm
Analytical balance, with data output, 120 g
Weighing dishes, 80 x 50 x 14 mm
Glass beaker, 50 ml, tall
Glass beaker, 150 ml, tall
Glass beaker, 250 ml, tall
Volumetric flask, 250 ml
Volumetric pipette, 25 ml
Graduated pipette, 5 ml
Pipettor
Pipette dish
Graduated cylinder, 100 ml
Funnel, glass, do = 55 mm
Spoon
Pasteur pipettes
Rubber bulbs
Glass rod, l = 200 mm, d = 5 mm
Scissors, straight, l = 180 mm
Wash bottle, 500 ml
Nitric acid, 65 %, 1000 ml
Silver nitrate, 15 g
Potassium nitrate, 250 g
Potassium chloride, 250 g
Potassium bromide, 100 g
Potassium iodide, 50 g
Water, distilled, 5 l
37684.00
32485.01
39296.00
02615.03
02590.03
02599.04
48802.93
45019.05
36001.00
36003.00
36004.00
36550.00
36580.00
36598.00
36592.00
36589.00
36629.00
34457.00
33398.00
36590.00
39275.03
40485.03
64798.00
33931.00
30213.70
30222.00
30106.25
30098.25
30258.10
30104.05
31246.81
1
1
1
1
1
1
1
1
12
2
1
12
8
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
Fig. 1. Experimental set-up.
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P3061001
1
LEC
06.10
Determination of the solubility products of silver halides
Set-up and procedure
Set up the experiment as shown in Fig. 1.
Prepare the solutions required for the experiment as follows:
– 0.1 molar KCl solution: Weigh 1.8638 g of potassium chloride into a 250 ml volumetric flask, dissolve it in distilled
water, and make up to the mark with distilled water.
– 0.01 molar KCl solution: Pipette 25 ml of 0.1 molar KCl solution into a 250 ml volumetric flask and make up to the mark
with distilled water.
– 0.001 molar KCl solution: Pipette 25 ml of 0.01 molar KCl
solution into a 250 ml volumetric flask and make up to the
mark with distilled water.
– 0.1 molar KBr solution: Weigh 2.9751 g of potassium bromide into a 250 ml volumetric flask, dissolve it in distilled
water, and make up to the mark with distilled water.
– 0.01 molar KBr solution: Pipette 25 ml of 0.1 molar KBr solution into a 250 ml volumetric flask and make up to the mark
with distilled water.
– 0.001 molar KBr solution: Pipette 25 ml of 0.01 molar KBr
solution into a 250 ml volumetric flask and make up to the
mark with distilled water.
– 0.1 molar KI solution: Weigh 4.1500 g of potassium iodide
into a 250 ml volumetric flask, dissolve it in distilled water,
and make up to the mark with distilled water.
– 0.01 molar KI solution: Pipette 25 ml of 0.1 molar KI solution
into a 250 ml volumetric flask and make up to the mark with
distilled water.
– 0.001 molar KI solution: Pipette 25 ml of 0.01 molar KI solution into a 250 ml volumetric flask and make up to the mark
with distilled water.
– 0.1 molar AgNO3 solution: Weigh 4.2469 g of silver nitrate
into a 250 ml volumetric flask, dissolve it in distilled water,
and make up to the mark with distilled water.
– 0.01 molar AgNO3 solution: Pipette 25 ml of 0.1 molar
AgNO3 solution into a 250 ml volumetric flask and make up
to the mark with distilled water.
– 0.001 molar AgNO3 solution: Pipette 25 ml of 0.01 molar
AgNO3 solution into a 250 ml volumetric flask and make up
to the mark with distilled water.
– 0.5 molar HNO3 solution: Pour 150 ml of distilled water into
a 150 ml beaker, and pipette 3.5 ml of 65% nitric acid into it.
– Saturated KNO3 solution: Weigh 20 g of potassium nitrate
into a 150 ml beaker, add 50 ml of distilled water, and stir for
some minutes at room temperature. Some potassium nitrate
must remain on the bottom of the beaker in the solid state. If
this is not the case, add further potassium nitrate. After the
undissolved potassium nitrate has settled to the bottom,
decant the saturated solution so prepared into a second
beaker.
Soak the clay pins in the saturated potassium nitrate solution
overnight.
Pour 40 ml each of the potassium halide and silver nitrate solutions into labelled 50 ml glass beakers. To precipitate a little of
the sparingly soluble silver halide, use a Pasteur pipette to add
one drop of the 0.1 molar AgNO3 solution to each of the nine
beakers containing potassium halide solutions.
Cut silver electrodes (50 x 10 mm) from the silver sheet and
clean them by placing them in the 0.5 molar nitric acid solution
for a few minutes.
Use a syringe with a cannula to carefully fill the salt bridge with
saturated potassium nitrate solution. Remove air bubbles by
tapping at the arms of the salt bridge. Seal each arm of the salt
bridge with a porous clay pin and fix each of them in place with
a short length (20 mm) of silicone tubing. Replace the cap.
2
P3061001
Investigate the following concentration cells:
AgNO3 solution (mol/l)
KCl-, KBr-, KI-solution (mol/l)
0.001
0.001
0.1
0.001
0.001
0.01
0.0001
0.1
0.1
0.1
Clamp the silver electrodes with two crocodile clips and fix their
ends in the holder for two electrodes. Place one of the silver
electrodes in the silver nitrate solution and connect it to the input
socket of the pH meter with a connecting cord. Dip the other one
into the potassium halide / silver halide solution and connect it
to ground potential. Switch the pH-meter to voltmeter mode.
Connect the two electrode solutions by means of the salt bridge.
Attach the temperature probe to the electrode holder using a
spring balance holder and connect it to the pH meter.
Record the cell e.m.f. for the given concentration cells. Before
measuring a new concentration, rinse the electrodes and the salt
bridge with distilled water and dry them.
Switch the pH meter to the temperature measuring mode to read
the temperature.
Theory and evaluation
A single potential cannot be measured, only a potential difference (e.m.f.). To be able to determine a single potential, a galvanic cell must be set up.
The concentration cell used here can be expressed as:
Ag(s) AgX(s) KX(aq) KNO3(aq, satd.) AgNO3(aq) Ag(s)
where X refers to the halide ion Cl-, Br- or I-.
The e.m.f. is the difference between the cathode potential (right
half-cell R) and the anode potential (left half-cell L) and is always
positive, otherwise the process runs in the other direction.
The cathode is the electrode with the higher potential. It is the
positive pole in a galvanic cell. The processes which take place
at the cathode are always reductions. Cations are deposited,
non-metals go into solution as anions, oxidizing agents are
reduced.
The anode is the electrode with the smaller potential. It is the
negative pole in a galvanic cell. The processes which take place
at the anode are oxidations. Metals go into solution as cations,
anions are deposited, reducing agents are oxidized.
The e.m.f. E is generally calculated from the two standard
potentials E by subtracting them, together with a second
expression, which takes the activities a of the participating substances into account. As in the law of mass action, the substance on the right appears in the numerator, the substance on
the left in the denominator. In this case, we have:
E = EAg, Ag+ +
=
RT
RT
· ln aAg+,R - EAg, Ag+ · ln aAg+,L
F
F
RT ln aAg ,R
·
F
ln aAg ,L
(1)
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEC
06.10
Determination of the solubility products of silver halides
where
aAg+,R
aAg+,L
Activity of the silver ions in the silver nitrate solution of
known concentration
Activity of the silver ions in the potassium halide / silver halide solution
A galvanic cell which consists of two half-cells, each of which
contain the same substance, but at different concentrations, is
called a concentration cell. It can be used to determine solubility products. For this purpose, one half-cell containing a saturated solution of the substance is connected to a second half-cell
containing a solution of known activity. The connection is made
via a switch which is filled with an electrolyte that is inert with
regard to the saturated solution.
aAg+,L is controlled by the solubility product Ksp of the silver
halide AgX
Ksp = aAg+,L · aX -,L
(2)
where aX -,L, the activity of the halide ions in the left half-cell, is
assumed to arise from the fully dissociated potassium halide,
the contribution from the sparingly soluble silver halide being
negligible in comparison.
Substituting equation (2) into equation (1) allows the cell e.m.f. to
be expressed as
E
a Ag ,R · aX ,L
RT
· ln
F
Ksp
EF
RT
(4)
The solubility product of the silver halide may therefore be calculated from the e.m.f of the cell E if aAg+,R and aX -,L are known.
The activity of an ion in solution is given by
ai = f± · ci
(5)
where ci is the concentration of the species i and ai is the mean
activity of the electrolyte. The electrolyte concentrations required
for this experiment are listed in Table 1. Using these values the
ion concentrations can be converted to activities and the solubility products calculated from equation (5). The results are summarised in Table 2.
Data and results
Having taken ion activities into account and in the absence of
any systematic errors, the measured Ksp are calculated to be:
Ksp (AgCl) = 1.3 · 10-10 mol2 / l2
(lit. value: 1.8 . 10-10 mol2 / l2)
Ksp (AgBr) = 4.3 · 10-13 mol2 / l2
(lit. value: 5.3 · 10-13 mol2 / l2)
Ksp (AgI) = 7.4 · 10-17 mol2 / l2
(lit. value: 8.3 · 10-17 mol2 / l2)
Table 1: Mean acitvity coefficients f± for AgNO3, KCl, KBr, KI at
q = 25°C.
c/mol · l-1
AgNO3
KCl
KBr
KI
0.001
0.945
0.965
0.965
0.965
0.01
0.897
0.902
0.903
0.905
0.1
0.734
0.770
0.772
0.778
(from A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data,
Macmillan, London 1992)
Table 2: Experimental data
[AgNO3]
/mol·l-1
[KCl]
/mol·l-1
aAg+,R
aCl-,L
E
/mV
Ksp
0.001
0.001
9.64·10-4
9.65·10-4 227
1.27·10-10
0.1
0.001
7.34·10-2
9.65·10-4 333
1.51·10-10
0.01
0.01
8.97·10-3
9.02·10-3 339
1.39·10-10
0.001
0.1
9.64·10-4
7.70·10-2 344
1.05·10-10
0.1
0.1
7.34·10-2
7.70·10-2 450
1.26·10-10
aAg+,R
aBr-,L
(3)
which can be rearranged to
ln Ksp ln 1aAg ,R · aX ,L 2 Before comparing the experimental and literature values, the
students should be made aware of the effect that an uncertainty of only 5 mV in the measured e.m.f. of the cell will have on the
value determined for Ksp.
[AgNO3]
/mol·l-1
[KBr]
/mol·l-1
E
/mV
Ksp
0.001
0.001
9.64·10-4
9.65·10-4 337
4.13·10-13
0.1
0.001
7.34·10-2
9.65·10-4 475
5.76·10-13
0.01
0.01
8.97·10-3
9.03·10-3 486
4.41·10-13
0.001
0.1
9.64·10-4
7.72·10-2 491
3.23·10-13
0.1
0.1
7.34·10-2
7.72·10-2 596
4.01·10-13
aAg+,R
aI-,L
[AgNO3]
/mol·l-1
[KI]
/mol·l-1
E
/mV
Ksp
0.001
0.001
9.64·10-4
9.65·10-4 594
7.11·10-17
0.1
0.001
7.34·10-2
9.65·10-4 698
9.17·10-17
0.01
0.01
8.97·10-3
9.05·10-3 706
8.03·10-17
0.001
0.1
9.64·10-4
7.78·10-2 710
6.07·10-17
0.1
0.1
7.34·10-2
7.78·10-2 818
6.69·10-17
Electrolyte temperature: (23.2±0.1)°C
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P3061001
3
LEC
06.10
4
P3061001
Determination of the solubility products of silver halides
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen