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 (acid component) - $[NH_3]$ or $[NH_4OH]$ = 0.10 M (base component) - Volume = 1 L **Step 1: Identify the buffer system** This is an $NH_4^+/NH_3$ buffer (or $NH_4Cl/NH_4OH$ buffer). The $pK_a$ given (5) refers to $NH_4^+$ ionization: $$NH_4^+ \rightleftharpoons NH_3 + H^+$$ **Step 2: Apply Henderson-Hasselbalch equation** $$pH = pK_a + \log\frac{[Base]}{[Acid]}$$ $$pH = pK_a + \log\frac{[NH_3]}{[NH_4^+]}$$ **Step 3: Substitute values** $$pH = 5 + \log\frac{0.10}{0.01}$$ $$pH = 5 + \log(10)$$ $$pH = 5 + 1 = 6$$ **Answer: pH = 6** The buffer works because $NH_4OH$ is the weak base and $NH_4Cl$ provides $NH_4^+$ (weak acid). Since the ratio of base to acid is 10:1, the pH is one unit above the $pK_a$, giving pH = 6.