Monday, April 29, 2013

Relations between pH, pOH, pKa, pKb, and pKw

In a previous post the terms pH, pOH, pKa, pKb, and pKw were defined. Additionally, there is a relation between pH and pOH and a relation between pKa and pKb which are summarized by the following equations:

                                                                   pH + pOH = pKw........(equation 1)
                                                                   pKa + pKb = pKw.......(equation 2)

 The above equations can also be written as the following:

                                                                    [H3O+][OH-]=Kw........(equation 3)
                                                                       Ka × Kb = Kw..........(equation 4)

How to use these equations:
- Equations 1 or 3: If we know the pH (or hydronium ion concentration) then we can calculate pOH (or hydroxyl ion concentration) and vis versa. for example if the pH of a given solution is 3.0 ([H3O+] = 0.001 M) at 25 °C then: 

                                                                   3.0 + pOH = 14.0
                                                                      pOH = 11.0

And [OH-] can also be calculated to be equal to  1 × 10-11 M.

- Equations 2 or 4: can be applied on a weak acid and its conjugate base (e.g. acetic acid and sodium acetate) or on a base and its conjugate acid (e.g. ammonia and ammonium chloride). Thus, we can use equations 2 or 4 to find pKb (or Kb) for the conjugate base of the weak acid and we can find pKa (or Ka) of the conjugate acid of the weak base.

For example, pKa for acetic acid is equal to 4.76 so pKb of sodium acetate is calculated as the following:
                                                             4.76 + pKb = 14.00
                                                                   pKb = 9.24
                                                              Kb = 5.75 × 10-10

Feel free to write comments, or questions?


  1. is Pkw always 14?

    1. It depends on temperature. The value of pKw is equal to 14.0 at 25 °C and it decreases as temperature increases. For example, pKw = 14.5 at 10 °C and pKw = 13.6 at 37 °C.

  2. Thanks, this was very helpful.

  3. Sir please help. I am not getting to find out the value of pH from the value of Kb

    1. In order to make the calculation you need to know the concentration of the base. Then use the equations on the following linked-post:
      Examples are also available on this linked-post.
      I hope this helps.

  4. ow did it go from pkb 9.24 to kb 5.75*10^-10?

    1. pKb = - log Kb
      Kb = 10^(-pKb)
      Kb = 10^(-9.24) = 5.75*10^(-10)

  5. Excuse me sir, How did you calculate the pKw at different temperatures, temperatures like 140 C, 200 C, and 310 C.

    1. There are some mathematical models that can be used to make such calculations or may be find the values in published tables. You can see the following scientific article entitled "The Ionization Constant of Water over Wide Ranges of Temperature and Density" by Andrei V. Bandura and Serguei N. Lvova published in J. Phys. Chem. Ref. Data, Vol. 35, No. 1, 2006 at the following address:

  6. what will be the value for pkw at 100 degree centigrade? plz ans


Thank you for your comment.