$buffer-constant-A(T)

Constant $A (T)$ used for buffer calculations: The $p K_{a}$ 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 $p K_{a}$ 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.

$p K_{a}^{'} = p K_{a} + (2 z_{a} - 1) [A I^{1 / 2} / (1 + I^{1 / 2}) - 0.1 I]$

where $I$ is the ionic strength and $z_{a}$ is the charge on the conjugate acid species. $p K_{a}^{'}$ is the modified $p K_{a}$ 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-temperature is smaller than the smallest value of A(T), the smallest A(T) value is taken.
If the lattice-temperature is 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).