Final answer:
To calculate the Kb value of a weak base, we can use the percent protonation of the base. By setting up an expression using the molarities of the base and its conjugate acid, we can solve for Kb.
Step-by-step explanation:
The percent protonation of a weak base can be used to calculate the Kb value. In this case, the 0.5 M solution of the weak base is 2% protonated. This means that 2% of the base is converted to the conjugate acid. The remaining 98% is still the base. We can use this information to calculate the Kb value.
Let's assume the molarity of the conjugate acid is x. Since 2% of the base is converted, the molarity of the base is (0.5 - x).
From there, we can set up an expression for the Kb value:
Kb = (x)(0.5 - x)/0.5
By plugging in the given values, we can solve for x and find the Kb.