To find the concentration of the hydroxide ion $[OH^-]$ in an aqueous solution at 25 °C, we use the water dissociation constant $K_w$, which is the product of the concentrations of the hydronium and hydroxide ions:

[ K_w = [H_3O^+][OH^-] ]

At 25 °C, $K_w$ is $1.0 \times 10^{-14}$.

Given: $[H_3O^+] = 0.0076 \, \text{M}$

Now, we can rearrange the equation to solve for $[OH^-]$:

[ [OH^-] = \frac{K_w}{[H_3O^+]} ]

Substitute the values:

$[OH^-] = \frac{1.0 \times 10^{-14}}{0.0076}$

Calculating this:

$[OH^-] = 1.3158 \times 10^{-12} \, \text{M}$

Thus, the concentration of the hydroxide ion $[OH^-]$ is approximately:

$[OH^-] \approx 1.32 \times 10^{-12} \, \text{M}$

Would you like more details or have any questions?

Related Questions

1. How does temperature affect the value of $K_w$ and the concentrations of $[H_3O^+]$ and $[OH^-]$?
2. What is the pH of this solution, given the concentration of $[H_3O^+]$?
3. How would you calculate $[OH^-]$ concentration if the $[H_3O^+]$ concentration were different?
4. What does it mean if $[H_3O^+]$ and $[OH^-]$ are equal in a solution?
5. How can you determine if a solution is acidic, basic, or neutral based on $[H_3O^+]$ or $[OH^-]$ concentrations?

Tip: Remember that the relationship $K_w = [H_3O^+][OH^-]$ holds true at 25 °C.