Answer:
a. [Weak acid] = 0.099999949M
[Conjugate base = 5.0119x10⁻⁸M
b. pH = 1.84. Is not a good buffer
c. pH = 6.97
Explanation:
a. To find pH of the buffer we must use Henderson-Hasselbalch formula:
pH = pKa + log [Conjugate base] / [Weak acid]
2.0 = 8.3 + log [Conjugate base] / [Weak acid]
5.01x10⁻⁷ = [Conjugate base] / [Weak acid] (1)
As concentration of the buffer is 0.1M = [Conjugate base] + [Weak acid] (2)
Replacing (2) in (1):
5.01x10⁻⁷ = 0.1M - [Weak acid] / [Weak acid]
5.01x10⁻⁷ [Weak acid] = 0.1M - [Weak acid]
[Weak acid] = 0.099999949M
[Conjugate base] = 5.0119x10⁻⁸M
b. The conjugate base reacts with the HCl. Moles of HCl are:
1.5x10⁻³L * (3.0mol / L) = 4.5x10⁻³ moles HCl
As the conjugate base contains just 5x10⁻⁸ moles. Almost all HCl doesn't react and pH =
[H⁺] = 4.5x10⁻³ moles + 1x10⁻² moles (Initial moles H⁺) / L = 0.0145M
pH = -log [H⁺]
pH = 1.84
As the concentration of the conjugate base is <<< than weak acid. In this pH, Tris is not a good buffer. As general rule a good buffer works pH between pKa ± 1.
c. Now, NaOH reacts with the weak acid producing conjugate base.
The new moles are:
[Weak acid] = [Weak acid] = 0.099999949M - 4.5x10⁻³ = 0.0955
[Conjugate base] = 5.0119x10⁻⁸M + 4.5x10⁻³ = 4.5x10⁻³
pH = pKa + log [Conjugate base] / [Weak acid]
pH = 8.3 + log [4.5x10⁻³] / [0.0955]
pH = 6.97