An aqueous solution contains 10% ammonia by mass and has a density of . If in this solution is '', t — Ionic Equilibrium Chemistry Question
Question
An aqueous solution contains 10% ammonia by mass and has a density of $0.85\text{ g/ml}$. If $[\text{H}_3\text{O}^+]$ in this solution is '$x\text{ M}$', then the value of '$x \times 10^{12}$' is ($K_a$ for $\text{NH}_4^+ = 5.0 \times 10^{-10}\text{ M}$)
💡 Solution & Explanation
1 L of the solution weighs $850\text{ g}$. Mass of ammonia = 10% of $850 = 85\text{ g}$. Moles of $\text{NH}_3 = 85 / 17 = 5\text{ moles}$. Molarity $C = 5\text{ M}$. The base dissociation constant is $K_b = K_w / K_a = 10^{-14} / (5.0 \times 10^{-10}) = 2.0 \times 10^{-5}$. $[\text{OH}^-] = \sqrt{K_b C} = \sqrt{2.0 \times 10^{-5} \times 5} = \sqrt{10^{-4}} = 10^{-2}\text{ M}$. $[\text{H}_3\text{O}^+] = 10^{-14} / 10^{-2} = 10^{-12}\text{ M}$. Thus $x = 10^{-12}$, making $x \times 10^{12} = (10^{-12}) \times 10^{12} = 1$. Therefore, correct answer is 1.