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The problem asks to calculate the pH of a solution with a hydroxide ion concentration \([OH^-] = 4.2 \times 10^{-4} \, M\). To solve for the pH, we can follow these steps:

### Step 1: Calculate the pOH
The pOH is calculated using the formula:
\[
pOH = -\log[OH^-]
\]
Substituting the given concentration of \([OH^-]\):
\[
pOH = -\log(4.2 \times 10^{-4})
\]

### Step 2: Calculate the pH from pOH
Next, recall the relationship between pH and pOH:
\[
pH + pOH = 14
\]
Thus, once we find the pOH, we can calculate the pH as:
\[
pH = 14 - pOH
\]

### Step 3: Significant Figures
Since the given hydroxide concentration \([OH^-]\) has two significant figures (4.2), our final pH value should be reported with the same number of significant figures.

Let me calculate this for you:

1. \[
pOH = -\log(4.2 \times 10^{-4}) = 3.38
\]
2. Then, \[
pH = 14 - 3.38 = 10.62
\]

So, the pH of the solution is **10.62**.

Would you like more details on any step, or have further questions?

Here are some related questions you might consider:
1. What is the relationship between pH and acidity?
2. How do strong acids and strong bases affect pH and pOH values?
3. What is the significance of using logarithms in pH calculations?
4. How do you determine significant figures in logarithmic calculations?
5. How does temperature affect the pH of a solution?

**Tip:** Always double-check the number of significant figures in logarithmic operations. The mantissa (decimal part) of the result should reflect the same number of significant figures as the original concentration.

Calculate the pH of a solution that has [OH-] = 4.2 x 10^-4 M. Be sure your answer has the correct number of significant figures.

Learn how to calculate the pH of a solution with a hydroxide ion concentration of 4.2 x 10^-4 M. Follow detailed steps using logarithmic functions and the relationship between pH and pOH, ensuring the correct number of significant figures. Ideal for students in Grades 10-12.

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