Does a precipitate form if you mix 175.0 mL if a 0.0055 M KCl aqueous solution with 145.0 mL of 0.0015 M aqueous AgNO3 solution? Ksp = 1.77 10–10 for AgCl.

Question

Does a precipitate form if you mix 175.0 mL if a 0.0055 M KCl aqueous solution with 145.0 mL of 0.0015 M aqueous AgNO3 solution?  Ksp = 1.77  10–10 for AgCl.

BlackTom AI · Accepted Answer

To tackle this precipitation question, I’ll start by identifying the reacting species and the stoichiometry involved.

- The relevant reaction is Ag+ + Cl− → AgCl(s).
- We have 175.0 mL of 0.0055 M KCl, giving moles Cl− = 0.1750 L × 0.0055 mol/L = 0.0009625 mol.
- We have 145.0 mL of 0.0015 M AgNO3, giving moles Ag+ = 0.1450 L × 0.0015 mol/L = 0.0002175 mol.
- Upon mixing, the total volume becomes 175.0 mL + 145.0 mL = 320.0 mL = 0.320 L.

Next, assess whether precipitation occurs by comparing the ion product with the solubility product.

- Initial concentrations after mixing (before any precipitation) would be:
  [Ag+]0 = 0.0002175 mol / 0.320 L ≈ 6.80×10^−4 M
  [Cl−]0 = 0.0009625 mol / 0.320 L ≈ 3.01×10^−3 M
- The reaction quotient (ion product) is Q = [Ag+][Cl−] ≈ (6.80×10^−4)(3.01×10^−3) ≈ 2.05×10^−6.

Compare Q to Ksp for AgCl, which is Ksp = 1.77×10^−10. Since Q ≈ 2.05×10^−6 is much larger than Ksp, the solution is supersaturated with respect to AgCl. This means solid AgCl will begin to form to reduce the product [Ag+][Cl−] down to the level dictated by Ksp.

When precipitation occurs, Ag+ is the limiting ion (it is the smaller initial amount in moles), so most, if not all, Ag+ will precipitate as AgCl until the ionic concentrations satisfy [Ag+][Cl−] = Ksp. After precipitation, there will be substantially less Ag+ in solution, and the remaining Cl− will be higher than in the initial mixture, but still above the threshold needed to maintain Ksp at equilibrium depending on the exact solid–solution balance.

In summary, because the initial ion product greatly exceeds Ksp, precipitation occurs; the correct conclusion is that a precipitate forms.

Chem 1C General Chemis... Self Assessment Quiz 19

Does a precipitate form if you mix 175.0 mL if a 0.0055 M KCl aqueous solution with 145.0 mL of 0.0015 M aqueous AgNO3 solution? Ksp = 1.77 10–10 for AgCl.

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