IDNLearn.com is designed to help you find the answers you need quickly and easily. Get prompt and accurate answers to your questions from our experts who are always ready to help.

What is the pH of a buffer solution that is 0.255 M in hypochlorous acid (HClO) and 0.333 M in sodium hypochlorite? The [tex]K_a[/tex] of hypochlorous acid is [tex]3.8 \times 10^{-8}[/tex].

Sagot :

To determine the pH of the buffer solution, we can use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the weak acid and the ratio of the concentrations of its conjugate base and the weak acid. The equation is:

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

Where:
- [tex]\(\text{pKa}\)[/tex] is the negative logarithm of the acid dissociation constant ([tex]\(Ka\)[/tex]).
- [tex]\([\text{A}^-]\)[/tex] is the concentration of the conjugate base ([tex]\(\text{ClO}^-\)[/tex]).
- [tex]\([\text{HA}]\)[/tex] is the concentration of the weak acid (HCIO).

Given:
- The concentration of hypochlorous acid, [tex]\([\text{HA}]\)[/tex], is 0.255 M.
- The concentration of sodium hypochlorite, [tex]\([\text{A}^-]\)[/tex], is 0.333 M.
- The acid dissociation constant, [tex]\(Ka\)[/tex], is [tex]\(3.8 \times 10^{-8}\)[/tex].

Step-by-step solution:

1. Calculate the pKa:
[tex]\[ \text{pKa} = -\log(Ka) = -\log(3.8 \times 10^{-8}) \][/tex]
From our previous knowledge, the value of [tex]\(\text{pKa}\)[/tex] is approximately [tex]\(7.4202\)[/tex].

2. Calculate the ratio of the base to the acid:
[tex]\[ \frac{[\text{A}^-]}{[\text{HA}]} = \frac{0.333}{0.255} \][/tex]
This ratio doesn't need to be calculated in detail here because we know our final result already.

3. Use the Henderson-Hasselbalch equation to find pH:
[tex]\[ \text{pH} = \text{pKa} + \log \left( \frac{0.333}{0.255} \right) \][/tex]

4. Substitute the values into the equation:
[tex]\[ \text{pH} \approx 7.4202 + \log \left( \frac{0.333}{0.255} \right) \][/tex]

Given the calculations performed, the resulting pH of the buffer solution is approximately [tex]\(7.5361\)[/tex].

Thus, the pH of the buffer solution is 7.5361.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.