Calculating the pOH of an Aqueous Buffered Solution
To calculate the pOH of an aqueous buffered solution of the weak acid HA, where 50% of the acid is ionized, we can follow these steps:

Step 1: Determine the pH of the solution
Since 50% of the weak acid HA is ionized, we can assume that the concentration of [HA] = [A-]. This means that [HA] = [A-] = x (let's assume).
The equilibrium expression for the ionization of the weak acid is:
HA ⇌ H+ + A-
Using the equation for the ionization of a weak acid, we can write:
Ka = [H+][A-] / [HA]
Ka = x*x / (c-x) (where c is the initial concentration of HA)
Given that the pk of HA is 4.5, we know that:
pk = -log(Ka)
4.5 = -log(Ka)
Solving for Ka, we get:
Ka = 10^(-4.5)
Now, we can plug in the value of Ka into the equation and solve for x to find the concentration of [H+] in the solution.

Step 2: Calculate the pOH of the solution
The pOH of a solution is defined as:
pOH = -log[OH-]
Since the solution is buffered, we can assume that the concentration of [OH-] is equal to the concentration of [H+]. Therefore, we can calculate the pOH of the solution using the concentration of [H+] we found in step 1.

Step 3: Conclusion
By following these steps, we can determine the pOH of an aqueous buffered solution of the weak acid HA, where 50% of the acid is ionized. This calculation helps us understand the basic principles of acid-base equilibrium and buffered solutions.