Method for determining the acidity of an acidic aqueous solution
Methods for determining the acidity of an acidic aqueous solution. These methods make it possible to measure the total acidity of an aqueous solution comprising a strong acid or a mixture of strong acids and, if this solution contains one or more hydrolysable cations, to also measure its free acidity.
1 . A method for determining a free acidity of an aqueous solution A1 comprising a strong acid or a mixture of strong acids and one or more hydrolysable cations, wherein the free acidity is determined without neutralization of the strong acid by an acid-base titration, the method comprising at least the following steps:
a) forming an aqueous solution A3 comprising a volume V1 of the solution A1 and a volume V2 of an aqueous solution A2 having pH pHA2, wherein A2 comprises a compound selected from the group consisting of a weak acid, a weak base, a salt of a weak acid and a salt of a weak base, and an agent complexing the hydrolysable cation(s), wherein the agent complexing the hydrolizable cation(s) having a concentration of C2;
b) measuring a UV-visible absorbance spectrum of the hydrolysable cation(s) present in the solution A3 by using the solution A2 as a measuring blank using a spectrophotometer;
c) determining a concentration C3 of the hydrolysable cation(s) in the solution A3 from the absorbance spectrum obtained in step b);
d) forming an aqueous solution A5 by mixing the solution A3 and a volume V4 of a solution A4 wherein A4 comprises a pH-sensitive dye having an acid form and a base form, and a transition range between a first pH and a second pH, the second pH being higher than the first pH but lower than pHA2;
e) measuring a UV-visible absorbance spectrum of the dye present in the solution A5 by using the solution A2 or the solution A3 as a measuring blank using a spectrophotometer;
f) determining a concentration of at least one of the acid form or the base form of the dye in the solution A5 from the absorbance spectrum obtained in step e);
g) determining a pH pHA5 of the solution A5 from the concentration determined in step f); then h) determining the free acidity of the solution A1 from the concentration C3 determined in step c) and from the pHA5 determined in step g),
wherein no alkaline titrant is added to solution A1, A3, or A5 to neutralize the strong acid during determination of the free acidity,
and wherein
pHA2 and the volumes V1 and V2 are such that the solution A3 has a pH, pHA3 which is within the dye transition range; and wherein
the concentration C2 and the volumes V1 and V2 are such that the complexing agent is in excess with respect to the hydrolysable cation(s) in the solution A3.
2 . The method of claim 1 , wherein the compound present in the aqueous solution A2 is the complexing agent.
3 . The method of claim 1 , wherein step b) comprises:
acquiring a light intensity spectrum of the solution A2 in a UV-visible range, whereby light intensity values are obtained for the solution A2;
acquiring a light intensity spectrum of the solution A3 in the UV-visible range, whereby light intensity values are obtained for the solution A3; and
calculating a decimal logarithm of a ratio between the light intensity values obtained for the solution A3 and the light intensity values obtained for the solution A2.
4 . The method of claim 3 , wherein step c) comprises applying the Beer-Lambert law.
5 . The method of claim 3 , wherein step e) comprises:
acquiring a light intensity spectrum of the solution A5 in a UV-visible range, whereby light intensity values are obtained for the solution A5; and
calculating a decimal logarithm of a ratio between the light intensity values obtained for the solution A5 and the light intensity values obtained for the solution A3.
6 . The method of claim 5 , wherein step f) comprises applying the Beer-Lambert law.
7 . The method of claim 1 , wherein step g) comprises applying equation (1):
10
-
pHA
5
=
K
HC
×
[
HC
]
[
C
-
]
(
1
)
wherein:
K HC is a dissociation constant of the acid form of the dye in the solution A5;
[HC] is a concentration of the acid form of the dye in the solution A5 in mol/L; and
[C − ] is a concentration of the base form of the dye in the solution A5 in mol/L.
8 . The method of claim 1 , wherein step g) comprises
pHA
5
=
-
log
{
K
HC
(
1
R
-
1
)
)
(
2
)
wherein:
K HC is a dissociation constant of the acid form of the dye in the solution A5; and
R is a ratio between a concentration of the base form of the dye in the solution A5 and a concentration of the dye in the solution A5.
9 . The method of claim 1 , wherein the free acidity of solution A1, expressed in molar concentration of H + protons, denoted [H + ], is determined by equation (3):
[
H
+
]
=
10
-
pHA
5
×
(
V
1
+
V
2
)
-
10
-
pHA
2
×
V
2
+
Y
V
1
(
3
)
wherein:
V1 and V2 are expressed in L; and
Y is determined by equation (7):
Y
=
1
0
-
p
HA
5
×
(
[
A
-
]
×
V
2
-
n
m
C
3
×
V
1
)
-
K
H
A
×
[
HA
]
1
×
V
1
K
H
A
+
1
0
-
p
HA
5
(
7
)
wherein:
m is a stoichiometric coefficient of the hydrolysable cation(s) in a complexing reaction of the hydrolysable cation(s) by the complexing agent;
n is a stoichiometric coefficient of the complexing agent in the complexing reaction of the hydrolysable cation(s) by the complexing agent;
if the solution A2 comprises a weak acid or a salt of a weak acid, then:
K HA is an acid dissociation constant of the weak acid in the solution A5;
[A − ] is a concentration of a conjugate base of the weak acid in the solution A2 in mol/L;
[HA] is the concentration of the weak acid in the solution A2 in mol/L;
if the solution A2 comprises a weak base or a salt of a weak base, then:
K HA is an acid dissociation constant of a conjugate acid of the weak base in the solution A5;
[A − ] is a concentration of the weak base in the solution A5 in mol/L;
[HA] is a concentration of the conjugate acid of the weak base in the solution A5 in mol/L;
V1 and V2 are expressed in L and C3 is expressed in mol/L.
10 . The method of claim 1 , wherein the solution A2 comprises oxalic acid or a salt thereof.
11 . The method of claim 1 , wherein the dye is bromocresol green.
12 . The method of claim 1 , wherein the solution A1 is an aqueous solution of nitric acid.
13 . A method for determining a free acidity of an aqueous solution A1 comprising a strong acid or a mixture of strong acids and one or more hydrolysable cations, the method comprising:
a) forming an aqueous solution A3 comprising a volume V1 of the solution A1 and a volume V2 of an aqueous solution A2 having a pH pH_A2,
wherein the solution A2 comprises a compound selected from the group consisting of a weak acid, a weak base, a salt of a weak acid, and a salt of a weak base,
and an agent for complexing the hydrolysable cation(s), the complexing agent being present at a concentration C2;
b) measuring a UV-visible absorbance spectrum of the hydrolysable cation(s) present in the solution A3 using a spectrophotometer, after complexation of the hydrolysable cation(s), with the solution A2 used as a measuring blank;
c) determining a concentration C3 of the hydrolysable cation(s) in the solution A3 from the absorbance spectrum measured in step b);
d) forming an aqueous solution A5 by mixing the solution A3 with a volume V4 of a solution A4,
wherein the solution A4 comprises a pH-sensitive dye having an acid form and a base form and a transition range between a first pH and a second pH, the second pH being higher than the first pH and lower than pH_A2;
e) measuring a UV-visible absorbance spectrum of the pH-sensitive dye present in the solution A5 using a spectrophotometer, with the solution A2 or the solution A3 used as a measuring blank,
wherein the absorbance spectrum reflects relative concentrations of the acid form and the base form of the pH-sensitive dye after complexation of the hydrolysable cation(s);
f) determining a concentration of at least one of the acid form or the base form of the pH-sensitive dye in the solution A5 from the absorbance spectrum measured in step e);
g) determining a pH pH_A5 of the solution A5 from the concentration determined in step f); and
h) determining the free acidity of the solution A1 from the concentration C3 determined in step c) and from the pH pH_A5 determined in step g),
wherein pH_A2 and the volumes V1 and V2 are selected such that the solution A3 has a pH pH_A3 within the transition range of the pH-sensitive dye; and
wherein the concentration C2 and the volumes V1 and V2 are selected such that the complexing agent is present in excess with respect to the hydrolysable cation(s) in the solution A3.
14 . A method for determining a free acidity of an aqueous solution A1 comprising a strong acid or a mixture of strong acids and one or more hydrolysable cations, wherein the method is configured to determine the free acidity independently of proton release caused by hydrolysis of the hydrolysable cation(s), the method comprising:
a) forming an aqueous solution A3 comprising a volume V1 of the solution A1 and a volume V2 of an aqueous solution A2 having a pH pH_A2,
wherein the solution A2 comprises a compound selected from the group consisting of a weak acid, a weak base, a salt of a weak acid, and a salt of a weak base,
and an agent for complexing the hydrolysable cation(s), the complexing agent being present at a concentration C2;
b) measuring a UV-visible absorbance spectrum of the hydrolysable cation(s) present in the solution A3 using a spectrophotometer, after complexation of the hydrolysable cation(s), with the solution A2 used as a measuring blank;
c) determining a concentration C3 of the hydrolysable cation(s) in the solution A3 from the absorbance spectrum measured in step b);
d) forming an aqueous solution A5 by mixing the solution A3 with a volume V4 of a solution A4,
wherein the solution A4 comprises a pH-sensitive dye having an acid form and a base form and a transition range between a first pH and a second pH, the second pH being higher than the first pH and lower than pH_A2;
e) measuring a UV-visible absorbance spectrum of the pH-sensitive dye present in the solution A5 using a spectrophotometer, with the solution A2 or the solution A3 used as a measuring blank,
wherein the absorbance spectrum reflects relative concentrations of the acid form and the base form of the pH-sensitive dye after complexation of the hydrolysable cation(s);
f) determining a concentration of at least one of the acid form or the base form of the pH-sensitive dye in the solution A5 from the absorbance spectrum measured in step e);
g) determining a pH pH_A5 of the solution A5 from the concentration determined in step f); and
h) determining the free acidity of the solution A1 from the concentration C3 determined in step c) and from the pH pH_A5 determined in step g),
wherein pH_A2 and the volumes V1 and V2 are selected such that the solution A3 has a pH pH_A3 within the transition range of the pH-sensitive dye; and
wherein the concentration C2 and the volumes V1 and V2 are selected such that the complexing agent is present in excess with respect to the hydrolysable cation(s) in the solution A3.