Question

What is the pH of an aqueous solution with a hydrogen ion concentration of [H ] = 4.9 × 10–8 M?

Answer 1

With the known equation pH = – log [H₃O⁺],

We get pH equal to 8. But this is not correct as an acidic solution cannot have pH > 7. It may be noted that in very dilute acidic solution, when H⁺ concentrations from acid and water are comparable, the concentration of H⁺ from water cannot be ignored.

Therefore, [H⁺] _total = [H⁺] _acid + [H⁺] _water
Since HCl is a strong acid and is completely ionized
[H⁺] _HCl = 4.9 x 10^-8

The concentration of H⁺ from ionization is equal to the [OH^–] from water,
[H⁺] _H2O = [OH^–] _H2O= x (say)

[H⁺] _total = 4.9 x 10^-8 + x

But [H⁺] [OH^–] = 1.0 x 10^-14
(4.9 x 10^-8 + x) (x) = 1.0 x 10^-14
X²+4.9×10^-8X-10^-14 = 0

Solving for x, using ax²+bx+c =o quadratic expression

we get x = 4.70×10^-8 (only plus is taken in the solution of the quadratic expression. For the better solution, if the student desired, he/she can take the other value also.

Therefore,
[H⁺] = 1.0 x 10^-8 + 4.70 x 10^-8
= 5.70 x 10^-8
= 0.57 x 10^-7
pH = – log [H⁺] = – log (0.57 x 10^-7)