A 0.135 M solution of a weak base has a pH of 11.23. Determine Kb for the base.

Verified step by step guidance

1. Identify the relationship between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Use this to find pOH from the given pH.
2. Calculate the hydroxide ion concentration \([\text{OH}^-]\) using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\).
3. Set up the expression for the base dissociation constant \(K_b\) using the formula \(K_b = \frac{[\text{OH}^-]^2}{[\text{Base}] - [\text{OH}^-]}\).
4. Assume that \([\text{Base}] - [\text{OH}^-] \approx [\text{Base}]\) if \([\text{OH}^-]\) is much smaller than the initial concentration of the base.
5. Substitute the values into the \(K_b\) expression and solve for \(K_b\).