# What is the pH of a 0.0067 M KOH solution?

Jun 3, 2016

$p H = 11.83$

#### Explanation:

Potassium hydroxide fully ionizes when dissolved in water according to the following equation:

$K O H \to {K}^{+} + O {H}^{-}$

Now, let's find the relationship between $K O H$ and $O {H}^{-}$

$\text{ " 1 " : "1 " ratio } \implies \left[K O H\right] = \left[O {H}^{-}\right] = 6.7 \times {10}^{-} 3 M$

In any aqueous solution, $\left[{H}_{3} {O}^{+}\right]$and $\left[O {H}^{-}\right]$ must satisfy the following condition:

$\left[{H}_{3} {O}^{+}\right] \left[O {H}^{-}\right] = {K}_{w}$

$\left[{H}_{3} {O}^{+}\right] = {K}_{w} / \left(\left[O {H}^{-}\right]\right)$

$\left[{H}_{3} {O}^{+}\right] = \frac{1.0 \times {10}^{-} 14}{6.7 \times {10}^{-} 3}$

$\left[{H}_{3} {O}^{+}\right] = 1.5 \times {10}^{-} 12 M$

Now, after finding the concentration of the hydronium ion, the pH of the solution is determined:

$p H = - \log \left[{H}_{3} {O}^{+}\right]$

$p H = - \log \left[1.5 \times {10}^{-} 12\right]$

$p H = 11.83$

Other Method
Find the pOH using the concentration of the hydroxide ion, then use the formula $\text{ } p H + P O H = 14$ to find the pH.