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To calculate the concentration of \( \text{H}_3\text{O}^+ \) in the solution, we can use the following relation at 25°C:

\[
K_w = [\text{H}_3\text{O}^+][\text{OH}^-]
\]

Where \( K_w \) is the ionization constant of water at 25°C, which is \( 1.0 \times 10^{-14} \, \text{M}^2 \).

Given that the hydroxide ion concentration, \( [\text{OH}^-] \), is \( 2.0 \times 10^{-6} \, \text{M} \), we can rearrange the equation to solve for \( [\text{H}_3\text{O}^+] \):

\[
[\text{H}_3\text{O}^+] = \frac{K_w}{[\text{OH}^-]} = \frac{1.0 \times 10^{-14}}{2.0 \times 10^{-6}}
\]

Performing the division:

\[
[\text{H}_3\text{O}^+] = 5.0 \times 10^{-9} \, \text{M}
\]

So, the concentration of \( \text{H}_3\text{O}^+ \) is \( 5.0 \times 10^{-9} \, \text{M} \).

Would you like more details or have any questions?

Here are some related questions:
1. How is \( K_w \) affected by temperature changes?
2. What happens to the pH if the \( [\text{OH}^-] \) increases?
3. Can \( K_w \) ever change its value?
4. What is the relationship between pH and \( [\text{H}_3\text{O}^+] \)?
5. How does the solution's neutrality relate to the concentrations of \( \text{H}_3\text{O}^+ \) and \( \text{OH}^- \)?

**Tip:** Always check the significant figures in both your given values and your final answer to ensure accuracy in chemistry problems.

An aqueous solution at 25°C has a OH− concentration of 2.0 × 10−6 M. Calculate the H3O+ concentration.

This example demonstrates how to calculate the concentration of H3O+ given a hydroxide ion concentration of 2.0 × 10−6 M at 25°C using the ionization constant of water (Kw).

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