From the value of Kf listed in Table 17.1, calculate the concentration of Ni2 +1aq2 and Ni1NH326 2+ that are present at equilibrium after dissolving 1.25 g NiCl2 in 100.0 mL of 0.20 M NH31aq2.

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Identify the relevant chemical reaction: NiCl_2 dissolves in water to form Ni^{2+} and Cl^- ions. Ni^{2+} then reacts with NH_3 to form the complex ion Ni(NH_3)_6^{2+}.

Write the equilibrium expression for the formation of the complex ion: K_f = \frac{[Ni(NH_3)_6^{2+}]}{[Ni^{2+}][NH_3]^6}.

Calculate the initial concentration of Ni^{2+} ions: Convert the mass of NiCl_2 to moles using its molar mass, then divide by the volume of the solution in liters to find the molarity.

Determine the initial concentration of NH_3: Given as 0.20 M.

Set up an ICE (Initial, Change, Equilibrium) table to track the changes in concentrations of Ni^{2+}, NH_3, and Ni(NH_3)_6^{2+} as the reaction reaches equilibrium. Use the K_f expression to solve for the equilibrium concentrations.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kf)

The equilibrium constant, Kf, is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a specific reaction. In this context, Kf is used to determine the extent to which a complex ion forms from its constituents in solution. Understanding Kf is essential for calculating the concentrations of ions in equilibrium, as it provides the necessary relationship between the species involved.

Complex Ion Formation

Complex ion formation occurs when metal ions bond with ligands, resulting in a charged species. In this case, Ni2+ ions interact with NH3 ligands to form the complex ion Ni(NH3)6^2+. Recognizing how ligands coordinate with metal ions is crucial for predicting the concentrations of both free metal ions and complex ions at equilibrium, as it directly influences the calculations involving Kf.

Stoichiometry and Concentration Calculations

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. To find the concentrations of Ni2+ and Ni(NH3)6^2+ at equilibrium, one must first convert the mass of NiCl2 into moles and then use the initial concentrations and the stoichiometric coefficients from the balanced equation. This process is vital for determining how much of each species is present at equilibrium after the reaction has occurred.