Calculate Hydroxide Concentration

The concentration of hydroxide ions ($[OH^-]$) in an aqueous solution is related to the concentration of hydrogen ions ($[H^+]$) through the ion product constant of water ($K_w$).

The fundamental relationship is:

$K_w = [H^+][OH^-]$

At 25$^\circ$ C, the value of $K_w$ is:

$K_w = 1.0 \times 10^{-14} M^2$

Determine OH- Concentration

We are given the concentration of hydrogen ions:

$[H^+] = 2 \times 10^{-4} M$

To find the hydroxide concentration, we rearrange the $K_w$ expression:

$[OH^-] = \frac{K_w}{[H^+]}$

Now, substitute the known values into the equation:

$[OH^-] = \frac{1.0 \times 10^{-14} M^2}{2 \times 10^{-4} M}$

Final Calculated OH- Concentration

Perform the calculation:

$[OH^-] = \left(\frac{1.0}{2}\right) \times \left(\frac{10^{-14}}{10^{-4}}\right) M$

$[OH^-] = 0.5 \times 10^{(-14 - (-4))} M$

$[OH^-] = 0.5 \times 10^{-10} M$

Expressing this in standard scientific notation:

$[OH^-] = 5 \times 10^{-11} M$

This result matches one of the provided options.