Question

A solution is prepared by mixing \(13.00 \mathrm{~mL}\) of \(0.0021 \mathrm{M}\) aqueous \(\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) with \(25.0 \mathrm{~mL}\) of \(0.015 \mathrm{M}\) HCl. Assume that volumes are additive. (a) Will precipitation occur? (b) Calculate [Hg \(\left.2^{2+}\right],\left[\mathrm{Cl}^{-}\right],\) and \(\left[\mathrm{NO}_{3}^{-}\right]\) after equilibrium is established.

Short answer

Solution: 1. Calculate the initial concentrations of Hg2^(2+) and Cl- ions. 2. Determine the reaction quotient (Q) and compare it to the Ksp of HgCl2. If Q > Ksp, precipitation occurs. 3. If precipitation occurs, use an ICE table and the Ksp value to calculate the final concentrations of ions after equilibrium.

Step-by-step solution

Determine the initial concentration of each ion before mixing solutions

The equation for the reaction is as follows: Hg2(2+) + 2Cl- -> HgCl2 (s) First, we need to determine the initial concentration of Hg2(2+) and Cl- ions. We have the following data: 1. Volume of 0.0021 M \(\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) solution: 13 mL 2. Volume of 0.015 M HCl solution: 25 mL To find the concentration of the ions, we'll multiply their molar concentration by their respective volumes and then divide by the total volume (13 mL + 25 mL). [Hg2^(2+)] = (0.0021 mol/L * 13 mL) / (13 mL + 25 mL) [Cl-] = (0.015 mol/L * 25 mL) / (13 mL + 25 mL)

Determine Q and compare it to Ksp

We have the equation: Q = [Hg2^(2+)] * [Cl-]^2 Now calculate Q using the initial concentrations from Step 1. The solubility product constant (Ksp) of HgCl2 is approximately 1.2x10^-18. Compare the calculated Q to Ksp. If Q > Ksp, precipitation will occur.

Calculate the final concentrations of ions after equilibrium (if precipitation occurs)

If precipitation occurs, we need to determine the final concentrations of the ions after equilibrium is established. To do this, we'll use an ICE table (initial, change, and equilibrium concentrations). Hg2^(2+) + 2Cl- -> HgCl2 (s) Initial concentrations: Initial Initial - Change: -x -2x +x Equilibrium concentrations: Initial - x Initial - 2x x Now, using the equilibrium concentrations, we can set up the Ksp expression: Ksp = [Hg2^(2+)] * [Cl-]^2 Substitute the initial concentration minus x for each ion: Ksp = (Initial[Hg2^(2+)] - x) * (Initial[Cl-] - 2x)^2 Now, we need to solve for x using the Ksp value. Having found x, calculate equilibrium concentrations for Hg2^(2+), Cl-, and NO3- ions: [Hg2^(2+)] = Initial[Hg2^(2+)] - x [Cl-] = Initial[Cl-] - 2x [NO3-] = Initial[NO3-] (Doesn't change during reaction)