Final answer:
The effective buffering range for a system containing CH3COOH and CH3COO⁻, given Kb = 5.6 x 10⁻¹⁰, is approximately 3.75 to 5.75, calculated based on the pKa of acetic acid.
Step-by-step explanation:
To calculate the effective range for a buffer system containing acetic acid (CH3COOH) and its conjugate base acetate (CH3COO−), we need to consider the acid dissociation constant (Ka) of acetic acid, as the provided Kb value is for the base dissociation constant of the acetate ion. It's important to recognize that Ka × Kb = Kw, where Kw is the ionic product of water, which is 1.0 × 10−14 at 25 °C.
Given the Kb for acetate is 5.6 x 10−10, we can calculate the Ka of acetic acid using the formula:
Ka = Kw / Kb
Substituting the known values:
Ka = (1.0 × 10−14) / (5.6 x 10−10) = 1.79 x 10−5
The effective range of a buffer is typically within 1 pH unit of the pKa, which is the negative logarithm of Ka. To find the pKa:
pKa = -log(1.79 x 10−5)
This gives us a pKa of approximately 4.75. Therefore, the effective buffering range is roughly 3.75 to 5.75.