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To calculate the pH and pOH of a phosphate solution containing 0.220 M \( \text{HPO}_4^{2-} \) and 0.220 M \( \text{PO}_4^{3-} \), we can use the Henderson-Hasselbalch equation. Given the \( K_a \) value for \( \text{HPO}_4^{2-} \) is \( 4.2 \times 10^{-13} \) at 25°C, we'll first need to determine the pK_a.

The Henderson-Hasselbalch equation is:

\[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \]

### Step 1: Determine pK_a
\[ \text{p}K_a = -\log (K_a) \]
\[ \text{p}K_a = -\log (4.2 \times 10^{-13}) \]
\[ \text{p}K_a = 12.38 \]

### Step 2: Apply the Henderson-Hasselbalch equation
Here, the base is \( \text{PO}_4^{3-} \) and the acid is \( \text{HPO}_4^{2-} \).

\[ \text{pH} = 12.38 + \log \left( \frac{0.220}{0.220} \right) \]
\[ \log \left( \frac{0.220}{0.220} \right) = \log (1) = 0 \]
\[ \text{pH} = 12.38 + 0 = 12.38 \]

### Step 3: Calculate pOH
Since \( \text{pH} + \text{pOH} = 14 \):

\[ \text{pOH} = 14 - \text{pH} \]
\[ \text{pOH} = 14 - 12.38 \]
\[ \text{pOH} = 1.62 \]

So, the pH of the solution is 12.38 and the pOH is 1.62.

Would you like further details or have any questions?

Here are 5 questions you might be interested in:

1. How do you use the Henderson-Hasselbalch equation to find pH?
2. What is the relationship between pH and pOH?
3. How does the value of \( K_a \) affect the pH of a solution?
4. What are some common buffer systems and how are they used?
5. How can you prepare a buffer solution with a desired pH using phosphates?

**Tip:** The Henderson-Hasselbalch equation is useful for buffer calculations, but it's essential to ensure the concentrations of the acid and base are accurate for precise pH determination.

Learn how to calculate the pH and pOH of a phosphate solution containing HPO4^2- and PO4^3- using the Henderson-Hasselbalch equation. Includes step-by-step solution and explanation of acid-base chemistry principles.

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