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  buffer-solutions

 

 

 
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Buffer solutions: To control pH values in electrolytes.

 

!------------------------------------------------------!
$buffer-solutions                          optional    !
 buffer-name             character         required    !
 number-of-ions          integer           required    !
 ion-valency             double_array      required    !
 ion-name-1              character         required    !
 ion-name-2              character         required    !
 ion-name-3              character         optional    !
(only necessary for some buffers, e.g. PBS)
 ion-name-4              character         optional    !
(only necessary for some buffers, e.g. PBS)
 pKa                     double_array      required    !
pKa at 25 C ( = 298.15 K)
 dpKa_dT                 double_array      required    !
d pKa / d T
 z_acid                  double_array      required    !
charge on the conjugate acid species
$end_buffer-solutions                      optional    !
!------------------------------------------------------!

 

Syntax

                                                 ! name of buffer
 buffer-name    = ACETATE                        !
Acetate (sodium acetate + acetic acid) (CH3COO-Na+ + CH3COOH)
                = HEPES                          !
HEPES (C8H18N2O4S)
                = TRIS                           !
TRIS     (C4H11NO3)
                = MOPS                           !
MOPS  (C7H15NO4S)
                = PBS                            !
PBS (phosphate buffer)
 

                                                 ! number of ions that are contained in the buffer
 number-of-ions = 2                              ! 2
for ACETATE, HEPES, TRIS and MOPS
                = 4                              ! 4
for PBS
 

                                                 ! valency of the ions that are contained in the buffer
 ion-valency    = -1d0  +1d0                     !
for ACETATE:  (CH3COO)-          Na+
                = +1d0  -1d0                     ! for TRIS:        TrisH+                    (OH)-
                = -1d0  +1d0                     ! for MOPS:        (C7H14NO4S)-   Na+
                = -1d0  -2d0  -3d0  1d0          ! for PBS:          (H2PO4)-   (HPO4)2-    (PO4)3-    Na+
                                                 ! (the number of expected entries corresponds to number-of-ions)
 

                                                 ! name of the ions that are contained in the buffer
                                                 !
                                                 !
CH3COOH  <==> (CH3COO)- + H+
 ion-name-1     = CH3COO^-                       !
name of ion no. 1 (for ACETATE)
 ion-name-2     = Na^+                           !
name of ion no. 2 (for ACETATE)
                                                 !
                                                 !
TrisH+     <==> Tris   + H+           (  "NH3+"      <==> "NH2"  + H+       )
                                                 ! Tris + H20 <==> TrisH+ + (OH)-       (  "NH2" + H20 <==> "NH3+" + (OH)-  )
 ion-name-1     = TrisH^+                        !
name of ion no. 1 (for TRIS)
 ion-name-2     = OH^-                           !
name of ion no. 2 (for TRIS)
                                                 !                             ("SO3H" <==> "(SO3)-"      + H+)
 ion-name-1     = Mops^-                         !
name of ion no. 1 (for MOPS)   C7H15NO4S <==> (C7H14NO4S)- + H+
 ion-name-2     = Na^+                           !
name of ion no. 2 (for MOPS)

 ion-name-1     = H2PO4^-                        !
name of ion no. 1 (for PBS)     NaH2PO4 <==> (H2PO4)- +   Na+
 ion-name-2     = HPO4^2-                        !
name of ion no. 2 (for PBS)     Na2HPO4 <==> (HPO4)2- + 2 Na+
 ion-name-3     = PO4^3-                         !
name of ion no. 3 (for PBS)      (HPO4)2- <==> (PO4)3-  +   H+
 ion-name-4     = Na^+                           !
name of ion no. 4 (for PBS)
 

                                                 ! pKa value(s) of buffer reactions
                                                 !
One can calculate the pH value from the pKa value and
                                                 ! the concentrations of acid and base (Henderson-Hasselbalch equation):
                                                 !         pH =
pKa + log10 ([base]/[acid])
                                                 !
Example: pH = pKa + log10 ([ Cl- ]/[ HCl ])
                                                 !        
HCl + H20 <==> Cl- + H30+
 pKa            = 4.76d0                         !
for ACETATE: pKa                                      at 25 C ( = 298.15 K)
                = 7.66d0                         !
for HEPES:     pKa                                      at 25 C ( = 298.15 K)
                = 8.06d0                         !
for TRIS:       pKa                                      at 25 C ( = 298.15 K)
                = 7.31d0                         !
for MOPS:       pKa                                      at 25 C ( = 298.15 K)
                = 2.15d0     7.21d0    12.33d0   !
for PBS:         pKa,1    pKa,2    pKa,3    at 25 C ( = 298.15 K)
 

                                                 ! d pKa / d T value(s) of pKa value(s), i.e. temperature dependence of pKa value(s)
                                                 !
(temperature coefficient, i.e. the rate of change of pKa with temperature)
                                                 !
If the buffer solution warms up, the pKa value drops.
                                                 !
For further details, see $electrolyte.
 dpKa_dT        = -0.0002d0                      !
for ACETATE:  d pKa   / d T
                = -0.014d0                       !
for HEPES:      d pKa   / d T
                = -0.028d0                       !
for TRIS:        d pKa   / d T
                = -0.011d0                       !
for MOPS:        d pKa   / d T
                =  0.0044d0  -0.0028d0  -0.026d0 !
for PBS:          d pKa,1 / d T      d pKa,2 / d T      d pKa,3 / d T
 

                                                 ! charge on the conjugate acid species
                                                 !
Note:   'conjugate acid'  + H20 <==> 'conjugate base'  + H30+
                                                 !
This value enters the equation for the ionic strength dependence
                                                 ! of the pKa value (modified pKa value: pKa' ).
 z_acid         =  0d0                           !
for ACETATE:   0 = CH3COOH
                =  0d0                           !
for MOPS:      0 = C7H15NO4S
                = +1d0                           !
for TRIS:     +1 = TrisH+
                =  0d0       -1d0       -2d0     !
for PBS:        0 = H3PO4, -1 = (H2PO4)- , -2 = (HPO4)2-
 

 

 

Examples: Acetate, MOPS and PBS (phosphate buffer)

The phosphate buffer is special (and thus more complicated) because it consists of three pKa values (and it thus has four different ions).

!------------------------------------------------!
$buffer-solutions                                !
                                                 !
 buffer-name    = ACETATE                        !
Acetate (sodium acetate + acetic acid) (CH3COO-Na+ + CH3COOH)
 number-of-ions = 2                              !
CH3COOH  <==> (CH3COO)- + H+
 ion-valency    = -1d0 +1d0                      !
 ion-name-1     = CH3COO^-                       !
(CH3COO)-
 ion-name-2     = Na^+                           !
Na+
 pKa            = 4.76d0                         !
pKa at 25 C ( = 298.15 K)
 dpKa_dT        = -0.0002d0                      !
d pKa   / d T
 z_acid         = 0d0                            !
charge on the conjugate acid species (0 = CH3COOH)
                                                 !
                                                 !
 buffer-name    = MOPS                           !
MOPS  (C7H15NO4S)  +  NaOH
 number-of-ions = 2                              !
 ion-valency    = -1d0  +1d0                     !
(C7H14NO4S)-  Na+
 ion-name-1     = Mops^-                         !  C7H15NO4S <==> (C7H14NO4S)- + H+
 ion-name-2     = Na^+                           !
 pKa            = 7.31d0                         !
pKa at 25 C ( = 298.15 K)
                                                 ! (Note: This pKa is thermodynamic value. The working pKa' is 7.20.)
 dpKa_dT        = -0.011d0                       !
d pKa   / d T
 z_acid         = 0d0                            !
charge on the conjugate acid species (0 = C7H15NO4S)
                                                 !
                                                 !
 buffer-name    = PBS                            !
PBS (phosphate buffer)
 number-of-ions = 4                              !
 ion-valency    = -1d0  -2d0  -3d0  1d0          !
(H2PO4)-     (HPO4)2-     (PO4)3-     Na+
 ion-name-1     = H2PO4^-                        ! NaH2PO4 <==> (H2PO4)- +   Na+
 ion-name-2     = HPO4^2-                        !
Na2HPO4 <==> (HPO4)2- + 2 Na+
 ion-name-3     = PO4^3-                         !
 ion-name-4     = Na^+                           !
 pKa            = 2.15d0     7.21d0    12.33d0   !
pKa,1    pKa,2    pKa,3    at 25 C ( = 298.15 K)
 dpKa_dT        = 0.0044d0  -0.0028d0  -0.026d0  !
d pKa   / d T
 z_acid         = 0d0       -1d0       -2d0      !
charge on the conjugate acid species (0 = H3PO4, -1 = (H2PO4)- , -2 = (HPO4)2-)
                                                 !
$end_buffer-solutions                            !
!------------------------------------------------!
 

For more details on buffers, please have a look at the excellent book of
R.J. Beynon, J.S. Easterby, "Buffer solutions: The basics", Oxford University Press (1996).

Rob Beynon also provides a web interface "A recipe calculator for thermodynamically correct buffers for pH control" at: http://www.liv.ac.uk/buffers/

 

 

Example: Acetate buffer (sodium acetate + acetic acid)

  • The following figure shows the pH value as a function of the concentration of the (CH3COO)- ions. Note that this number is equal to the concentration of Na+ ions (see equations above).

    The concentration of the acetate buffer is 0.1 M, i.e. it consists of
    - 0.1 M CH3COOH (acetic acid) and
    - 0.1 M CH3COO-Na+ (sodium acetate).
    The temperature was set to 298.15 K ( = 25 C).
    The pKa value at 25 C is 4.76. Note that the pKa value depends on temperature and ionic strength. Thus for each pH value a different value of pKa had been calculated self-consistently => pKa'.

    The nextnano calculations were performed by looping over the pH values. Note that the code adds the appropriate concentrations of Cl- ions (originating from the acid HCl) and Na+ ions (originating from the base NaOH) automatically.

         CH3COO-   +   H3O+   +   Cl-   <==>  CH3COOH   +   H2O   +   Cl-
         CH3COOH  +   Na+     +   OH-  <==>  CH3COO-    +   H2O   +   Na+

    The acetate buffer has the best buffering range (i.e. pH = +-1) at around pKa = 4.76, i.e. it buffers nicely between pH = 3.76 and pH = 5.76.

    Below the pH value of 3, the concentration of (CH3COO)- is negligible and only CH3COOH  exists.
    Above the pH value of 8, the concentration of CH3COOH  is negligible and only (CH3COO)- exists.

                                 pH value vs. [CH3COO-]


    The relation between the pH value, the pKa' value and the concentration of CH3COO- ions is governed by the Henderson-Hasselbalch equation.

          pH = pKa'  +  log (  [CH3COO-] / [CH3COOH] )

    The concentration of all ions (not only the buffer ions), the ionic strength, as well as the pKa' value(s) as a function of pH are contained in this file:
    BufferIonConc_vs_pH1D.dat

    If you want to obtain the nextnano input file (1DAcetate_Buffer.in) that calculates the above figure, please contact stefan.birner@nextnano.de.

 

Details on the calculations:

  • ACETATE (sodium acetate + acetic acid)

    [CH3COOH]  = [ACETATE] / ( 1 + 10pH-pKa )
    [(CH3COO)-] = [CH3COOH] * 10pH-pKa       !  Henderson-Hasselbalch equation
    [Na+]            = [(CH3COO)-]
     
  • MOPS

    [C7H15NO4S]     = [MOPS] / ( 1 + 10pH-pKa )
    [(C7H14NO4S)-] = [C7H15NO4S] * 10pH-pKa    !  Henderson-Hasselbalch equation
    [Na+]                 = [(C7H14NO4S)-]

    (analogous for HEPES and TRIS)
     
  • PBS (phosphate buffer)

    [H3PO4]    = [PBS] / ( 1 + 10pH-pKa,1 * ( 1 + 10pH-pKa,2  * ( 1 + 10pH-pKa,3 ) ) )
    [(H2PO4)-] = [H3PO4]    * 10pH-pKa,1        !  Henderson-Hasselbalch equation
    [(HPO4)2-] = [(H2PO4)-] * 10pH-pKa,2        !  Henderson-Hasselbalch equation
    [(PO4)3-]   = [(HPO4)2-] * 10pH-pKa,3        !  Henderson-Hasselbalch equation
    [Na+]         = (1 * [(H2PO4)-] + 2 * [(HPO4)2-] + 3 * [(PO4)3-]

    The following figure shows the pH value as a functions of the Na+ concentration for a PBS buffer. Note that there are three buffer ranges.



    In this figure, we plot the concentration of the PBS buffer ions, and the resulting ionic strength as a function of pH.


    If you want to obtain the nextnano input file (1DPBS_Buffer.in) that calculates the above figure, please contact stefan.birner@nextnano.de.

 

The entries for $buffer-solutions that are specified in the database can be overwritten in the input file. For details, have a look at the input file keyword $buffer-solutions.