To calculate the pH of a buffer system containing 1.5 M HClO and 1.7 M NaClO, we will apply the Henderson-Hasselbalch equation, which is useful for buffer solutions:

[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) ]

Where:

• $\text{pKa}$ is the negative logarithm of the acid dissociation constant $K_a$,
• $[\text{A}^-]$ is the concentration of the conjugate base (in this case, NaClO),
• $[\text{HA}]$ is the concentration of the weak acid (HClO).

Steps:

1. Identify the concentrations:

   • $[\text{HA}] = 1.5 \, \text{M}$ (HClO, the weak acid).
   • $[\text{A}^-] = 1.7 \, \text{M}$ (NaClO, the conjugate base).

2. Find the $K_a$ of HClO: You would need to reference the table of $K_a$ values at 25°C, but typically the $K_a$ for hypochlorous acid (HClO) is around $2.9 \times 10^{-8}$. We can calculate the $\text{pKa}$ from this value:

   $\text{pKa} = -\log (2.9 \times 10^{-8}) \approx 7.54$

3. Apply the Henderson-Hasselbalch equation:

   $\text{pH} = 7.54 + \log \left( \frac{1.7}{1.5} \right)$

4. Calculate the ratio: $\log \left( \frac{1.7}{1.5} \right) \approx \log (1.133) \approx 0.054$

5. Final pH: $\text{pH} = 7.54 + 0.054 = 7.59$

Final Answer:

The pH of the buffer system is approximately 7.59.

Would you like any further details or clarification on this calculation?

Related Questions:

1. How does the concentration of the acid and base affect the buffer's pH?
2. What would happen to the pH if the concentrations of HClO and NaClO were reversed?
3. How would the pH change if the $K_a$ of the acid was larger?
4. What is the significance of the Henderson-Hasselbalch equation in buffer systems?
5. How do you calculate the pH of a solution when you know the $K_a$ but not the concentrations?

Tip:

When dealing with buffer problems, always verify that the $K_a$ is appropriate for the acid involved and ensure the concentrations of acid and base are correct before applying the equation.