Ionic EquilibriumhardNUMERICAL

A basic buffer of pH is manufactured by dissolving of solid ammonium sulphate and of ammonia into enIonic Equilibrium Chemistry Question

Question

A basic buffer of pH $9.26$ is manufactured by dissolving $x \text{ moles}$ of solid ammonium sulphate and $0.1 \text{ mole}$ of ammonia into enough water to make exactly $100 \text{ mL}$ of solution. If $pK_b$ of ammonia is $4.74$, find the exact value of $x \times 100$.

Answer: 5

💡 Solution & Explanation

Given $pH = 9.26$, the $pOH = 14 - 9.26 = 4.74$. The Henderson equation gives $pOH = pK_b + \log\frac{[Salt]}{[Base]}$. Since $pOH = pK_b$, $\log\frac{[NH_4^+]}{[NH_3]} = 0$, meaning $[NH_4^+] = [NH_3] = \frac{0.1}{0.1\text{L}} = 1.0 \text{ M}$. $x \text{ moles}$ of $(NH_4)_2SO_4$ in $100 \text{ mL}$ gives an $[NH_4^+]$ of $\frac{2x}{0.1} \text{ M}$. Equating them: $\frac{2x}{0.1} = 1.0 \Rightarrow 2x = 0.1 \Rightarrow x = 0.05$. Therefore, $x \times 100 = 5$.

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