Question

Calculate the pH of a solution that has [OH^-] = 4.5 × 10^-3 M. Be sure your answer has the correct number of significant figures.

Answer 1

To calculate the pH of a solution when given the hydroxide ion concentration \([OH^-]\), we can follow these steps:

1. **Calculate the pOH**:
The pOH can be calculated using the formula:
\[
\text{pOH} = -\log[OH^-]
\]
Given that \([OH^-] = 4.5 \times 10^{-3} \, M\):
\[
\text{pOH} = -\log(4.5 \times 10^{-3})
\]

Using a calculator, we find:
\[
\text{pOH} \approx -(\log(4.5) + \log(10^{-3}))
\]
\[
\text{pOH} \approx -0.653 + 3 \approx 2.347
\]

2. **Calculate the pH**:
We can use the relationship between pH and pOH:
\[
\text{pH} + \text{pOH} = 14
\]
Solving for pH gives:
\[
\text{pH} = 14 - \text{pOH} = 14 - 2.347 \approx 11.653
\]

3. **Significant Figures**:
The concentration \([OH^-] = 4.5 \times 10^{-3}\) has 2 significant figures, which indicates that we should round our final answer to 2 significant figures.

Therefore, rounding 11.653 to 2 significant figures gives us:
\[
\text{pH} \approx 12
\]

Final answer:
\[
\text{pH} \approx 12
\]