pH, pOH and antilogs  AcidBase Theory
pH, pOH and antilogs
Lessons
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 K_{w} expression.
Notes:
 We learned earlier in Introduction to acidbase theory , that pH is defined by the concentration of H_{3}O^{+} ions in solution:
pH = log[H_{3}O^{+}]  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 [H_{3}O^{+}] 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 [H_{3}O^{+}] and [OH^{}] using pH and pOH:[H_{3}O^{+}] = 10 ^{pH} [OH^{}] = 10 ^{pOH}  Because [H_{3}O^{+}] and [OH^{}] in aqueous solution at 25^{o}C are related to K_{w}, pH and pOH are related to pK_{w} – which is just the negative log of the K_{w} constant!
 pH and pOH give logarithmic expressions of the aqueous ion concentration. Recall that:
K_{w} = [H_{3}O^{+}_{(aq)}] [OH^{}_{(aq)}] = 1.00 $*$ 10 ^{14} at 25^{o}C Taking the negative log of these aqueous ion concentrations, we can determine: pH + pOH = pK_{w} = 14
With these we can relate the four expressions in a ‘grid’ below:
 pH and pOH give logarithmic expressions of the aqueous ion concentration. Recall that:

Intro Lesson
Relating pH, H_{3}O^{+} and K_{w}.

1.
Find the concentration of acidic and basic solutions when given from the pH.