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  1. Relating pH, H3O+ and Kw.
  2. Defining pH and pOH.
  3. Antilogs: Using pH and pOH to find [H3O+] and [OH-].
  4. Connecting pH → [H3O+] → [OH-] → pOH → pH
  1. Find the concentration of acidic and basic solutions when given from the pH.
    1. A solution of HCl, a strong acid, has a pH of 1.74. What is the H3O+(aq) concentration of this solution? Give your answer to three significant figures.
    2. A solution of potassium hydroxide, KOH, has a pH of 12.89. Find the concentration of OH-(aq) ions in this solution. Give your answer to three significant figures.
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Topic Notes

In this lesson, we will learn:

  • To recall the expressions for pH and pOH.
  • To use the antilog to relate pH and pOH back to aqueous ion concentration.
  • How pH and pOH are related to the Kw expression.


  • We learned earlier in Introduction to acid-base theory , that pH is defined by the concentration of H3O+ ions in solution:

    pH = -log[H3O+]

  • In the same way, pOH can be measured, which is defined by the concentration of OH- ions in solution:

    pOH = -log[OH-]

    Be careful with significant figures – with logarithms, only the values in decimal places are considered significant figures.

  • The reverse of the logarithm is known as the antilog, so the antilog can be used to convert pH into [H3O+] and pOH into [OH-]. The antilog is found by rising 10 to the value for which you are getting the antilog:

    Antilog (x) = 10 x

    Make sure your calculator gives antilogs in scientific notation, or standard form. As stated above, the decimal places are the significant figures in a logarithm value. The first digit represents the order of magnitude. For example, log(10) = 2.0 and log(100) = 3.0; 3 is one greater than 2, so 3 as a logarithm is one order of magnitude (10x) greater than 2 as a logarithm.

    With this, we can show expressions to find [H3O+] and [OH-] using pH and pOH:

    [H3O+] = 10 -pH
    [OH-] = 10 -pOH

  • Because [H3O+] and [OH-] in aqueous solution at 25oC are related to Kw, pH and pOH are related to pKw – which is just the negative log of the Kw constant!
    • pH and pOH give logarithmic expressions of the aqueous ion concentration. Recall that:

      Kw = [H3O+(aq)] [OH-(aq)] = 1.00 βˆ—* 10 -14 at 25oC

      Taking the negative log of these aqueous ion concentrations, we can determine:

      pH + pOH = pKw = 14

      With these we can relate the four expressions in a β€˜grid’ below: