D þ H 3 O
þ
⇄DH
þ
þ H 2 O
ð7Þ
K a ¼
a DH
þ
a D
a H 2 O
a H 3 O
þ
ð8Þ
Solving Eq. (8) for the proton activity and expressing the result in terms of
concentrations and activity coefficients γ, we obtain:
a H 3 O
þ ¼
DH
þ
½
D
½
H 2 O
½
K a
γ DH
þ γ H 2 O
γ D
ð9Þ
This means that proton activity inside of the zeolite channels can be obtained by
measuring the ratio [DH
+
]/[D] by means of electronic absorption spectroscopy. The
change of the number of water molecules in the protonation reaction (Eq. (7)) can be
taken into account. It is not so important for fully hydrated zeolite but can become
very important in partially hydrated materials. The ratio of the activity coefficients γ
is not known. It is, however, reasonable to assume that it is essentially constant if
different dyes are used for probing the proton activity so that a meaningful comparison of the values is possible. This procedure has many applications in different
fields, including biology [176]. It is well known that positive metal ion gives acidic
solutions in water according to Eq. (10) [183]:
M OH 2
ð
Þ m
Â
à nþ þ H 2 O Ð M OH 2
ð
Þ mÀ1 OH
ð Þ
À
Â
à nÀ1
ð
Þþ þ H 3 O
þ
ð10Þ
A consequence of this is that the proton activity inside of the ZL channels
depends on the nature of the charge compensation cations. Values for some cations
have been measured using the spectral response of pH-sensitive dyes [172, 184],
typically the reaction of DSMI in Eq. (11); see Table 7:
DSM
þ
þ H
þ
Ð DSMH
2þ
ð11Þ
The influence of the charge compensating metal cations is large [83, 172,
178]. Table 7 shows that the high acidity inside the channels cannot be controlled
Table 7 pK a values of aqueous solutions of metal ions and pH values measured inside the channels
of ZL, using Dsm
+ as indicator
a
Cation
pK a
b cation in water
pH inside the channels of ZL
Li
+
13.6
3.4
K
+ % Na
+
14.0
3.4
Cs
+
–
3.7
Mg
2+
11.2
2.8
Ca
2+
12.7
3.1
a Loading of Dsm
+ : 0.06 per u.c., T ¼ 298 K, [172]
b
[183], 3.6 equivalents of the corresponding cations per u.c. were in the main channel of ZL
40
G. Calzaferri
þ
⇄DH
þ
þ H 2 O
ð7Þ
K a ¼
a DH
þ
a D
a H 2 O
a H 3 O
þ
ð8Þ
Solving Eq. (8) for the proton activity and expressing the result in terms of
concentrations and activity coefficients γ, we obtain:
a H 3 O
þ ¼
DH
þ
½
D
½
H 2 O
½
K a
γ DH
þ γ H 2 O
γ D
ð9Þ
This means that proton activity inside of the zeolite channels can be obtained by
measuring the ratio [DH
+
]/[D] by means of electronic absorption spectroscopy. The
change of the number of water molecules in the protonation reaction (Eq. (7)) can be
taken into account. It is not so important for fully hydrated zeolite but can become
very important in partially hydrated materials. The ratio of the activity coefficients γ
is not known. It is, however, reasonable to assume that it is essentially constant if
different dyes are used for probing the proton activity so that a meaningful comparison of the values is possible. This procedure has many applications in different
fields, including biology [176]. It is well known that positive metal ion gives acidic
solutions in water according to Eq. (10) [183]:
M OH 2
ð
Þ m
Â
à nþ þ H 2 O Ð M OH 2
ð
Þ mÀ1 OH
ð Þ
À
Â
à nÀ1
ð
Þþ þ H 3 O
þ
ð10Þ
A consequence of this is that the proton activity inside of the ZL channels
depends on the nature of the charge compensation cations. Values for some cations
have been measured using the spectral response of pH-sensitive dyes [172, 184],
typically the reaction of DSMI in Eq. (11); see Table 7:
DSM
þ
þ H
þ
Ð DSMH
2þ
ð11Þ
The influence of the charge compensating metal cations is large [83, 172,
178]. Table 7 shows that the high acidity inside the channels cannot be controlled
Table 7 pK a values of aqueous solutions of metal ions and pH values measured inside the channels
of ZL, using Dsm
+ as indicator
a
Cation
pK a
b cation in water
pH inside the channels of ZL
Li
+
13.6
3.4
K
+ % Na
+
14.0
3.4
Cs
+
–
3.7
Mg
2+
11.2
2.8
Ca
2+
12.7
3.1
a Loading of Dsm
+ : 0.06 per u.c., T ¼ 298 K, [172]
b
[183], 3.6 equivalents of the corresponding cations per u.c. were in the main channel of ZL
40
G. Calzaferri