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 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 ‘grid’ below: