The pKa value of is 5. Calculate the pH of the buffer solution, 1 L of which contains 0.01 M and 0.1 — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

I need to find the pH of a buffer solution containing $NH_4Cl$ (weak acid) and $NH_4OH$ (weak base). **Given Information:** - $pK_a$ of $NH_3$ = 5 - $[NH_4^+]$ from $NH_4Cl$ = 0.01 M - $[NH_3]$ from $NH_4OH$ = 0.10 M - Volume = 1 L **Step 1: Identify the buffer system** This is a buffer of weak base ($NH_3$) and its conjugate acid ($NH_4^+$). **Step 2: Use Henderson-Hasselbalch Equation** For a buffer with weak base and conjugate acid: $$pH = pK_a + \log\frac{[NH_3]}{[NH_4^+]}$$ where $pK_a$ is for the conjugate acid $NH_4^+$. **Step 3: Relate $pK_a$ and $pK_b$** Given: $pK_a(NH_3) = 5$ means this is the $pK_b$ of ammonia. For the conjugate acid $NH_4^+$: $$pK_a(NH_4^+) = 14 - pK_b(NH_3) = 14 - 5 = 9$$ **Step 4: Apply Henderson-Hasselbalch** $$pH = 9 + \log\frac{0.10}{0.01}$$ $$pH = 9 + \log(10)$$ $$pH = 9 + 1 = 10$$ **Answer: pH = 10** The buffer solution is basic (pH > 7) because ammonia (weak base) is in excess compared to its conjugate acid $NH_4^+$. The ratio of base to acid is 10:1, which shifts the pH upward by 1 unit from the $pK_a$ value.