# $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
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-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).