Calculating Kb from pOH: Formula and Examples

📚 Quick Study Guide

• 🧪 The relationship between $pOH$ and $[OH^-]$ is given by: $pOH = -\log_{10}[OH^-]$.
• ➗ To find $[OH^-]$ from $pOH$, use: $[OH^-] = 10^{-pOH}$.
• ⚖️ For a weak base B, the equilibrium is: $B + H_2O \rightleftharpoons BH^+ + OH^-$.
• ➮ The base dissociation constant, $K_b$, is expressed as: $K_b = \frac{[BH^+][OH^-]}{[B]}$.
• 📝 If you know the initial concentration of the base and the $pOH$, you can calculate $[OH^-]$ and then $K_b$.
• 💡 Use an ICE table (Initial, Change, Equilibrium) to organize the concentrations and solve for $K_b$.
• ➕ Remember that $pK_b = -\log_{10}(K_b)$, and $K_b = 10^{-pK_b}$.

Practice Quiz

1. Question 1: If the $pOH$ of a solution is 3, what is the hydroxide ion concentration, $[OH^-]$?
   1. $1 \times 10^{-3} M$
   2. $1 \times 10^{3} M$
   3. $3 M$
   4. $-3 M$
2. Question 2: For a weak base with a concentration of 0.1 M, the $[OH^-]$ is $1 \times 10^{-3} M$. What is the $K_b$?
   1. $1 \times 10^{-5}$
   2. $1 \times 10^{-6}$
   3. $1 \times 10^{-4}$
   4. $1 \times 10^{-2}$
3. Question 3: What is the relationship between $pOH$ and $[OH^-]$?
   1. $pOH = \log[OH^-]$
   2. $[OH^-] = -\log(pOH)$
   3. $pOH = -\log[OH^-]$
   4. $[OH^-] = 10^{pOH}$
4. Question 4: A solution has a $pOH$ of 2. What is the $pK_b$ if $K_b$ is $1 \times 10^{-4}$?
   1. 2
   2. 4
   3. -4
   4. -2
5. Question 5: If $K_b = 1 \times 10^{-5}$, what is the $pK_b$ value?
   1. 5
   2. -5
   3. 10
   4. -10
6. Question 6: Which formula is used to calculate $K_b$ for a weak base B?
   1. $K_b = \frac{[B]}{[BH^+][OH^-]}$
   2. $K_b = \frac{[BH^+][OH^-]}{[B]}$
   3. $K_b = [BH^+][OH^-][B]$
   4. $K_b = \frac{[B]}{[BH^+] + [OH^-]}$
7. Question 7: A 0.2 M solution of a weak base has a $pOH$ of 4. Calculate the $K_b$.
   1. $5 \times 10^{-8}$
   2. $5 \times 10^{-7}$
   3. $5 \times 10^{-6}$
   4. $5 \times 10^{-5}$