# Given an aqueous solution in which the [H^+]=5.0*10^-3 M, what is the molar hydroxide ion concentration?

Feb 20, 2017

$\left[H {O}^{-}\right] = {10}^{- 11.7} = 2.0 \times {10}^{-} 12 \cdot m o l \cdot {L}^{-} 1$

#### Explanation:

The easiest way to approach this problem is to use logarithms, and use the relationship:

$p H + p O H = 14$

This is specified for aqueous solution under standard conditions.

So $\left[{H}_{3} {O}^{+}\right] = 5 \times {10}^{-} 3 \cdot m o l \cdot {L}^{-} 1$, and thus,

$p H = - {\log}_{10} \left(5 \times {10}^{-} 3\right) = 2.30$

And thus $p O H = 11.70$,

and thus $\left[H {O}^{-}\right] = {10}^{- 11.7} = 2.0 \times {10}^{-} 12 \cdot m o l \cdot {L}^{-} 1$