Calculate the pH of a solution that contains 7.8 × 10-6 M OH⁻ at 25°C.

To calculate the pH of a solution containing \(7.8 \times 10^{-6} \, \text{M} \, \text{OH}^-\) at \(25^\circ C\), we follow these steps:

1. **Calculate the pOH**:
   The concentration of hydroxide ions (\(\text{OH}^-\)) can be used to find the pOH using the formula:

   \[
   \text{pOH} = -\log [\text{OH}^-]
   \]

   Substituting the given value of \([\text{OH}^-]\):

   \[
   \text{pOH} = -\log (7.8 \times 10^{-6})
   \]

   First, calculate the logarithm:

   \[
   \log (7.8 \times 10^{-6}) = \log(7.8) + \log(10^{-6}) = 0.8928 - 6 = -5.1072
   \]

   Therefore:

   \[
   \text{pOH} = -(-5.1072) = 5.1072
   \]

2. **Use the relationship between pH and pOH**:
   At \(25^\circ C\), the relationship between pH and pOH is:

   \[
   \text{pH} + \text{pOH} = 14
   \]

   Substituting the calculated pOH:

   \[
   \text{pH} = 14 - 5.1072 = 8.8928
   \]

   Rounding to two decimal places:

   \[
   \text{pH} \approx 8.89
   \]

### Final Answer:
The pH of the solution is approximately **8.89**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the pH of a solution given the \(\text{H}^+\) concentration instead of \(\text{OH}^-\)?
2. What is the significance of the pH scale and its range?
3. How would the pH change if the \(\text{OH}^-\) concentration were halved?
4. How does temperature affect the relationship between pH and pOH?
5. What is the difference between a strong base and a weak base in terms of pH?

**Tip**: Remember that pH values below 7 are acidic, while values above 7 are basic (alkaline).

Calculate the pH of a solution that contains 7.8 × 10^-6 M OH⁻ at 25°C.

Learn how to calculate the pH of a solution with a hydroxide ion concentration of 7.8 × 10^-6 M at 25°C. This problem involves logarithms and the relationship between pH and pOH, perfect for students in Grades 10-12.

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