Calculate the pH of a buffer system composed of 0.880 M C5H5N and 0.660 M C5H5NHNO3. The Kb for C5H5N is 1.70 x 10^-9.
Convert Kb to Ka by KaKb = Kw and change that to pKa; then
Use the Henderson-Hasselbalch equation.
To calculate the pH of a buffer system, you need to consider the dissociation of the weak base and the acid in the buffer solution. In this case, C5H5N is a weak base and C5H5NHNO3 is its conjugate acid.
Firstly, let's write down the chemical equation for the dissociation of C5H5N (the weak base):
C5H5N + H2O ⇌ C5H5NH⁺ + OH⁻
The Kb expression for the dissociation of C5H5N is:
Kb = [C5H5NH⁺][OH⁻] / [C5H5N]
Since we're given the concentration of C5H5N (0.880 M) and the Kb value (1.70 × 10^-9), we can rearrange the equation to solve for [OH⁻].
[C5H5NH⁺][OH⁻] = Kb[C5H5N]
[OH⁻] = (Kb[C5H5N]) / [C5H5NH⁺]
Now, we can calculate [OH⁻]:
[OH⁻] = (1.70 × 10^-9)(0.880 M) / (0.660 M)
[OH⁻] ≈ 2.27 × 10^-9 M
Since the buffer system contains a weak base and its conjugate acid, we can assume that the concentration of [H⁺] is equal to [OH⁻] at equilibrium.
Therefore, [H⁺] ≈ 2.27 × 10^-9 M
Now, we can calculate the pH using the formula:
pH = -log[H⁺]
pH = -log(2.27 × 10^-9)
pH ≈ 8.64
So, the pH of the given buffer system is approximately 8.64.