What is the concentration of Ni²⁺ if 0.223 g of NiCl₂ is dissolved in 250.0 mL of 0.760 M NH₃? Kf ([Ni(NH₃)₆]²⁺) = 5.5 × 10⁸ A) 6.9 × 10^-3 M B) 7.6 × 10^-11 M C) 1.3 × 10^-11M D) 9.7 × 10^-11 M E) 1.4 × 10^-11 M

Question

Quizplus · Accepted Answer

First, we need to write out the balanced equilibrium equation for the dissolution of NiClS1U1B12S1U1B0 in water:
NiClS1U1B12S1U1B0(s) → NiS1U1P12+S1S1P0(aq) + 2ClS1U1B1-(aq)
Then, we need to write the equilibrium constant expression for this reaction in terms of the formation of NiNHS1U1B13S1U1B0 complexes:
Kf = [Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0 / [NiS1U1P12+S1S1P0][NHS1U1B13S1U1B0]S1U1B2[ClS1U1B1-]S1U1B2
We are given the value of Kf, which allows us to solve for the concentration of NiNHS1U1B13S1U1B0 complexes at equilibrium:
Kf = 5.5 × 10S1U1P18S1S1P0
[Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0 = (5.5 × 10S1U1P18S1S1P0)([NHS1U1B13S1U1B0]S1U1P2[ClS1U1B1-]S1U1B2) / [NiS1U1P12+S1S1P0]
Next, we need to calculate the molar quantity of NiClS1U1B12S1U1B0 that was dissolved in the solution:
moles of NiClS1U1B12S1U1B0 = 0.223 g / (58.69 g/mol) = 0.0038 mol
We also need to calculate the number of moles of NHS1U1B13S1U1B0 that were present in the solution:
moles of NHS1U1B13S1U1B0 = (0.760 mol/L) (0.250 L) = 0.190 mol
Using the stoichiometry of the balanced equilibrium equation, we can see that 1 mol of NiClS1U1B12S1U1B0 produces 1 mol of NiS1U1P12+S1S1P0, meaning that:
moles of NiS1U1P12+S1S1P0 = 0.0038 mol
Now, we can plug in all of the values into the equation for Kf and solve for [Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0:
(5.5 × 10S1U1P18S1S1P0) = [Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0 / (0.0038)(0.190)(2)
[Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0 = 9.7 × 10S1U1P1-11S1S1P0 M
Therefore, the concentration of NiS1U1P12+S1S1P0 in the solution is equal to 0.0038 mol / 0.250 L = 0.0152 M. Finally, we can use the equilibrium constant expression to solve for the concentration of NiS1U1P12+S1S1P0:
Kf = [Ni(NHS1U1B13S1U1B0)S1U1B16S1U1B0]S1U1P12+S1S1P0 / [NiS1U1P12+S1S1P0][NHS1U1B13S1U1B0]S1U1B2[ClS1U1B1-]S1U1B2
5.5 × 10S1U1P18S1S1P0 = (9.7 × 10S1U1P1-11S1S1P0) / (0.0152)(0.190)(22)
[NiS1U1P12+S1S1P0] = 9.7 × 10S1U1P1-11S1S1P0 M (rounded to 2 significant figures)

Therefore, the best choice is D) 9.7 × 10S1U1P1-11S1S1P0 M, since that is the calculated concentration of NiS1U1P12+S1S1P0 in the solution.

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