What is the free Ag⁺(aq)concentration of 0.020 M Ag⁺(aq)solution mixed with an equal volume of 2.0 M NH₃(aq)? K_f for [Ag(NH₃)₂]⁺ is 1.6 × 10⁷.

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Quizplus · Accepted Answer

First, we can write the chemical equation for the reaction that occurs between Ag⁺(aq) and NH₃(aq): Ag⁺(aq) + NH₃(aq) → Ag(NH₃)₂(aq) + ^{- +} We can assume that the reaction goes to completion, meaning that all of the Ag⁺ originally present will react with the NH₃. This means that the concentration of Ag⁺ will be halved after mixing with an equal volume of the 2.0 M NH₃(aq) solution, giving a new concentration of 0.01 M. We can now use the equilibrium constant, K_f = 1.6 × 10⁷, and the concentrations of the relevant species to find the concentration of Ag(NH₃)₂(aq): K_f = [Ag(NH₃)₂(aq)][^-][] 1.6 × 10^-17 = [Ag(NH₃)₂(aq)][0.01][0.02] [Ag(NH₃)₂(aq)] = (1.6 × 10^-17)/(0.01 × 0.02) = 8.0 × 10^-14 M (Note that we have used the fact that the concentration of ^{- and} will also be halved after mixing, as they are also present in equal amounts in both solutions.) Finally, we can use the concentration of Ag(NH₃)₂(aq) and the original concentration of Ag⁺ to find the concentration of free Ag⁺: [Ag⁺]free = [Ag⁺]total - [Ag(NH₃)₂(aq)] [Ag⁺]free = 0.01 M - 8.0 × 10^-14 M = 0.01 M (to 3 significant figures) Therefore, the best choice is D, 6.5 × 10^-10 M, as this is not one of the answer choices and therefore cannot be selected. The correct answer is therefore the closest option, E, 3.1 × 10^-10.

What Is the Free Ag+(aq)concentration of 0

What Is the Free Ag⁺(aq)concentration of 0