$buffer-constant-A(T)¶
Constant \(A(T)\) used for buffer calculations: The \({\text p}K_{\text a}\) value depends on the ionic strength.
$buffer-constant-A(T) optional
constant-Centigrade-to-Kelvin double required
T_A(T) double_array required
$end_buffer-constant-A(T) optional
Example
!-------------------------------------------------------------!
$buffer-constant-A(T) !
constant-Centigrade-to-Kelvin = 273.15 ! Kelvin = Celsius + 273.15
!
!============================================================!
! first column: T[C] second column: A(T) !
!============================================================!
T_A(T) = 0.0 0.4918 ! 0° C = 273.15 K
10.0 0.4989 ! 10° C = 283.15 K
20.0 0.5070 ! 20° C = 293.15 K
25.0 0.5114 ! 25° C = 298.15 K
30.0 0.5161 ! 30° C = 303.15 K
37.0 0.5321 ! 37° C = 310.15 K
40.0 0.5262 ! 40° C = 313.15 K
50.0 0.5373 ! 50° C = 323.15 K
60.0 0.5494 ! 60° C = 333.15 K
70.0 0.5625 ! 70° C = 343.15 K
80.0 0.5767 ! 80° C = 353.15 K
90.0 0.5920 ! 90° C = 363.15 K
100.0 0.6086 ! 100° C = 373.15 K
$end_buffer-constant-A(T) !
!-------------------------------------------------------------!
The left column of the specifier T_A(T) contains the temperature in degrees of Centigrade (Celsius) between 0° C and 100° C.
The right column of the specifier T_A(T) contains the corresponding value of the constant A as a function of temperature T, i.e. A(T).
The values are taken from page 30 of [Beynon1996].
They can also be approximated by a second-order polynomial ([Beynon1988]):
\(A(T) = 0.4918 + 0.0006614 T + 0.000004975 T^2\)
If the keyword $buffer-constant-A(T) is present in the input file, the values for this keyword in the database are overwritten.
Physical significance of this parameter
The ionic strength of an electrolyte influences the \({\text p}K_{\text a}\) value of the buffer. This dependence can be described by the following equation (sometimes known as the Debye-Hückel relationship) where the constant A(T) enters.
\({\text p}K_{\text a}'={\text p}K_{\text a} + ( 2 z_a - 1) [A I^{1/2} / (1 + I^{1/2})-0.1 I]\)
where \(I\) is the ionic strength and \(z_a\) is the charge on the conjugate acid species. \({\text p}K_{\text a}'\) is the modified \({\text p}K_{\text a}\) value. The value of \(A\) (sometimes called Debye-Hückel parameter) is about 0.5 but it is temperature dependent.
Internally, the program takes the temperature \(T_0\) that is given in the input file under the keyword $global-parameters (in units of Kelvin) and
interpolates linearly between the two appropriate neighboring \(A(T)\) values to find the value for \(A(T_0)\).
The conversion between temperature in Kelvin and Centigrade is done by the constant: constant-Centigrade-to-Kelvin = 273.15
Example
lattice-temperature = 288.15 ! 288.15 [K] = 15° [C] + 273.15 [K]
A(T = 10° C) = 0.4989
A(T = 20° C) = 0.5070
=> Internally the program calculates the value for A(T = 15° C) = (0.4989 + 0.5070)/2 = 0.50295.
The following interpolation formula is used:
A(T = x°C) = A(T_i) + slope * ('lattice-temperature' - 'constant-Centigrade-to-Kelvin' - Ti) =
= A(T_i) + slope * ('lattice-temperature' - '273.15' - Ti) =
where
slope = ( A(T_(i+1)) - A(T_i) ) / ( T_(i+1) - T_i )
and it holds:
T_i < 'lattice-temperature' - '273.15'T_i < T_(i+1)
\(T_{i+1}\) and \(T_{i}\) are the closest temperature points above and below the specified temperature lattice-temperature.
If the
lattice-temperatureis smaller than the smallest value of A(T), the smallest A(T) value is taken.If the
lattice-temperatureis larger than the largest value of A(T), the largest A(T) value is taken.
The value of A always depends on temperature. This can only be switched off by specifying only one value of T and A(T) in the database or in the input file. The values for T and A(T) that are specified in the database can be overwritten in the input file. For details, have a look at the input file keyword $buffer-constant-A(T).