One liter of a 0.1M Tris buffer (pKa=8.3) is adjusted to a pH of 2.0. a. What are the concentrations of the conjugate base and weak acid at this pH? b. What is the pH when 1.5mL of 3.0M HCl is added to this buffer? Is Tris a good buffer at this pH? Why? c. What is the pH when 1.5mL of 3.0M NaOH is added to this buffer?

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