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###### Lessons
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
##### Examples
###### Lessons
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.
###### 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.

Notes:

• 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: