If a buffer solution is 0.160 M in a weak base (Kb = 2.3 × 10-5) and 0.550 M in its conjugate acid, what is the pH?
To determine the pH of a buffer solution, you need to consider the equilibrium between the weak base and its conjugate acid. In this case, the weak base is partially dissociating to produce hydroxide ions (OH-) while the conjugate acid is partially dissociating to produce hydronium ions (H3O+).
To solve this problem, you can use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log([Conjugate Acid] / [Weak Base])
The pKa for a weak acid is determined by taking the negative logarithm (base 10) of its acid dissociation constant (Ka). For a weak base and its conjugate acid, you can use the following relation:
Kw = Ka × Kb
where Kw is the ionization constant of water (1.0 × 10^-14 at 25°C), and Kb is the base dissociation constant.
Now, let's break down the problem step by step:
Step 1: Find the pKa value using the Kb value.
Since we are given the Kb value for the weak base (Kb = 2.3 × 10^-5), we can calculate the pKa using the equation:
pKa = 14 - pKb
pKa = 14 - (-log10(2.3 × 10^-5))
Step 2: Calculate the ratio of [Conjugate Acid] / [Weak Base] using the given concentrations.
Given that the buffer solution is 0.160 M in the weak base and 0.550 M in its conjugate acid, the ratio can be calculated as:
[Conjugate Acid] / [Weak Base] = 0.550 / 0.160
Step 3: Plug the calculated values into the Henderson-Hasselbalch equation.
Using the pKa value from Step 1 and the ratio from Step 2, you can now calculate the pH:
pH = pKa + log([Conjugate Acid] / [Weak Base])
Plug in the values obtained in the previous steps to calculate the pH of the buffer solution.
Note: Make sure to double-check the units of the given concentrations and convert them if necessary to ensure they are consistent in the equation.
By following these steps and performing the calculations, you can determine the pH of the buffer solution.