Solved Examples: Ka and Kb Calculations for Weak Acids and Bases

📚 Quick Study Guide

• ⚗️ $K_a$ is the acid dissociation constant, measuring the strength of an acid in solution. A larger $K_a$ indicates a stronger acid.
• ⚖️ The equilibrium reaction for a weak acid HA is: $HA(aq) + H_2O(l) \rightleftharpoons A^-(aq) + H_3O^+(aq)$, and $K_a = \frac{[A^-][H_3O^+]}{[HA]}$.
• 💧 $K_b$ is the base dissociation constant, measuring the strength of a base in solution. A larger $K_b$ indicates a stronger base.
• 🧪 The equilibrium reaction for a weak base B is: $B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq)$, and $K_b = \frac{[BH^+][OH^-]}{[B]}$.
• 🌡️ The relationship between $K_a$ and $K_b$ for a conjugate acid-base pair is: $K_a \times K_b = K_w$, where $K_w = 1.0 \times 10^{-14}$ at 25°C.
• 🔢 To calculate pH from $K_a$, use an ICE table to find $[H_3O^+]$, then $pH = -log[H_3O^+]$.
• 💡 Similarly, to calculate pOH from $K_b$, use an ICE table to find $[OH^-]$, then $pOH = -log[OH^-]$, and $pH = 14 - pOH$.

Practice Quiz

1. Question 1: The $K_a$ of a weak acid HA is $2.0 \times 10^{-5}$. What is the pH of a 0.1 M solution of HA?
   1. pH = 2.35
   2. pH = 5.00
   3. pH = 3.40
   4. pH = 2.87
2. Question 2: A 0.2 M solution of a weak base B has a pH of 11.0. What is the $K_b$ of the base?
   1. $5.0 \times 10^{-3}$
   2. $5.0 \times 10^{-11}$
   3. $2.5 \times 10^{-6}$
   4. $2.5 \times 10^{-3}$
3. Question 3: What is the conjugate base of $H_2PO_4^-$?
   1. $H_3PO_4$
   2. $HPO_4^{2-}$
   3. $H^+$
   4. $PO_4^{3-}$
4. Question 4: The $K_b$ for $NH_3$ is $1.8 \times 10^{-5}$. What is the $K_a$ for $NH_4^+$?
   1. $1.8 \times 10^{-5}$
   2. $5.6 \times 10^{-10}$
   3. $1.0 \times 10^{-14}$
   4. $5.6 \times 10^{-1}$
5. Question 5: A 0.1 M solution of a weak acid has a pH of 4.0. What is the approximate percent dissociation of the acid?
   1. 0.01%
   2. 1%
   3. 0.1%
   4. 10%
6. Question 6: Which of the following acids is the strongest, given their $K_a$ values?
   1. Acid A: $K_a = 1.0 \times 10^{-7}$
   2. Acid B: $K_a = 1.0 \times 10^{-5}$
   3. Acid C: $K_a = 1.0 \times 10^{-3}$
   4. Acid D: $K_a = 1.0 \times 10^{-9}$
7. Question 7: What is the pOH of a 0.05 M solution of a base with $K_b = 2.0 \times 10^{-6}$?
   1. 2.65
   2. 11.35
   3. 3.35
   4. 10.65