HOW TO CALCULATE BICARBONATE, CARBONATE AND HYDROXIDE FROM TOTAL ALKALINITY

 

Bicarbonate, carbonate and hydroxide alkalinity can be calculated from total alkalinity (TA) if the pH is known.  These concentrations are often calculated, especially for carbonate and hydroxide ion concentrations which are generally low and difficult to measure.  The ion concentrations must be given in molar (M) concentrations, which are indicated by parentheses in this article.  For most natural situations Equation 5, which takes into account charge differences, is adequate for determination of the various sources of alkalinity. 

 

            2TA = () + 2() +                                                             eq. 5

 

TA is commonly expressed as mg/L  and must be converted to moles/L (M) in order to make the following calculations.  The conversion of mg/L to M  is accomplished by use of Equation 6

 

            (TA moles/L ) =                                                    eq. 6

 

Rearranging the second disassociation constant for carbonic acid (eq. 7) in terms of

() yields Equation 8

           

                                                                                         eq. 7

 

                                                                                                 eq. 8

 

Substitution of Equation 8 for () in Equation 5 and expressing (OH) in terms of  based on Equation 9 yields Equation 10.

 

            () = =                                                                                  eq. 9

 

            2TA = () + 2() +                                                     eq. 10

 

Rearranging Equation 10 to solve for  (eq. 12) is carried out by the following step (eq. 11).

 

            2TA -  = () (1 + )                                                              eq. 11

 

            =                                                                              eq. 12

 

Once () has been calculated (or determined by titration), this concentration can be substituted into Equation 8 and () can be calculated.  To determine the hydroxide alkalinity, requires that only the pH be known (eq. 9).

 

To convert these molar alkalinity concentrations (eqs. 8, 9 and 12) to mg/L, the molar concentrations must be multiplied by the molecular weight of  (100,000 mg/mole) and in the case of () and () a factor of ½ is required because 1 mole of  is equivalent to 2 moles of  and 2 moles of , whereas 1 mole of  is equivalent to 1 mole of ()

 

The equations necessary for calculation of bicarbonate, carbonate and hydroxide alkalinities as  mg/L are:

 

            Bicarbonate alkalinity ( mg/L) = 50,000 ()                   eq. 13

 

            Carbonate alkalinity ( mg/L) = 100,000 (                 eq. 14

 

            Hydroxide alkalinity ( mg/L) = 50,000 (10)                             eq. 15