Acid Base PH, POH

Question

A shampoo has a pH of 8.39. What is the [H3O^+] in the shampoo?

What is the [OH^−] in the shampoo?

Answer 1

Since pH = -log[H₃O⁺] you can find the answer mathematically:

pH = -log[H₃O⁺]

-pH = log[H₃O⁺]

10^(-pH) = [H₃O⁺]

[H₃O⁺] = 10^(-8.39) = 4.07 x 10^-9 M

In most aqueous solutions, the concentration (in molarity) of H₃O⁺ and OH^- may be related by:

[H₃O⁺] * [OH^-] = 1 x 10^-14 M²

So, you can again find the answer mathematically:

[H₃O⁺] * [OH^-] = 1 x 10^-14 M²

[OH^-] = [1 x 10^-14 M²] / [H₃O⁺]

[OH^-] = [1 x 10^-14 M²] / [4.07 x 10^-9 M] = 2.46 x 10^-6 M

Answer 2

Base on Kw at 25 ^oC --> pH + pOH = 14 OR pH = 14 - pOH OR pOH = 14 - pH.

Given: pH = 8.39 (right the way, you know that it is a weak base)

By definition pH = - log [H⁺]

8.39 = - log [H⁺] => [H⁺] = 10^-8.39 = 4.37 x 10^-9 M //answer 1

pOH = 14- pH = 14 - 8.39 = 5.61

Similar to pH --> [H⁺] pOH = - log [OH^-]

[OH^-] = 10^-5.61 = 2.45 x 10^-6 M //answer 2

----------------

Please notice that:: [H⁺] [OH^-] = 10^-14

Let check if we also have it.

2.45 x 10^-6 x 4.37 x 10^-9 = 1.07 x 10^-14 yes, we have it !!!!