In a given solution, the concentration of hydrogen ions and hydroxide ions are related to each other by the following expression:
pH + pOH = 14
where, pH = - log[H+] and pOH = - log [OH-]
In this case, the concentration of sulfuric acid is given as 2.1 x 10^-4 M. Since each molecule of sulfuric acid (H2SO4) contains 2 atoms of hydrogen, the concentration of hydrogen ions in this solution is twice that of sulfuric acid. That is,
Concentration of H+ ions = 2 x 2.1 x 10^-4
= 4.2 x 10^-4 M
This means, pH = -log (4.2 x 10^-4) = 3.38
Since pH + pOH = 14
pOH = 14 - 3.38 = 10.62
This means, 10.62 = -log [OH-]
Solving the equation, we get [OH-] = 2.4 x 10^-11 M.
Hope this helps.
