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The problem asks to calculate the \([OH^-]\) and pH given \([H^+]\) = \(1 \times 10^{-4}\) M for an aqueous solution.

### Step 1: Relationship between \([H^+]\) and \([OH^-]\)
In water, the concentrations of \([H^+]\) and \([OH^-]\) are related through the ion product of water (\(K_w\)):

\[
K_w = [H^+] \times [OH^-] = 1 \times 10^{-14} \, \text{at 25°C}
\]

Given \([H^+] = 1 \times 10^{-4} \, M\), we can solve for \([OH^-]\):

\[
[OH^-] = \frac{K_w}{[H^+]} = \frac{1 \times 10^{-14}}{1 \times 10^{-4}} = 1 \times 10^{-10} \, M
\]

### Step 2: Calculate the pH
pH is calculated as:

\[
\text{pH} = -\log [H^+]
\]

Substitute \([H^+] = 1 \times 10^{-4} \, M\):

\[
\text{pH} = -\log(1 \times 10^{-4}) = 4
\]

### Final Answer:
- \([OH^-] = 1 \times 10^{-10} \, M\)
- \(\text{pH} = 4\)

Let me know if you'd like further details or have any questions.

Here are five related questions:
1. How does the pH scale relate to acidity and basicity of solutions?
2. What happens to the \([OH^-]\) concentration if \([H^+]\) increases?
3. How is the pOH calculated from \([OH^-]\)?
4. What is the difference between strong acids and weak acids in terms of dissociation?
5. How does temperature affect the value of \(K_w\)?

**Tip:** For acidic solutions (\(pH < 7\)), the \([H^+]\) concentration is greater than \([OH^-]\).

An aqueous solution has an [H⁺] = 1 × 10⁻⁴ M. Calculate [OH⁻] and pH.

Learn how to calculate the hydroxide ion concentration [OH⁻] and the pH for an aqueous solution with [H⁺] = 1 × 10⁻⁴ M. This problem covers the relationship between [H⁺], [OH⁻], and pH using the ion product of water and logarithms. Suitable for high school students in Grades 9-12.

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