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.
