Dissolution of 5.0 x 10^-3 mol of Cr(OH)3 in 1.0 L of 1.0 M NaOH gives a solution of the complex ion [Cr(OH)4]- (Kf = 8 x10^29). What fraction of the chromium in such a solution is present as uncomplexed Cr3+?

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Identify the relevant chemical equilibrium: Cr(OH)_3 + OH^- \(\rightleftharpoons\) [Cr(OH)_4]^-. The formation constant (K_f) for this reaction is given as 8 \(\times\) 10^{29}.

Write the expression for the formation constant (K_f): K_f = \(\frac{[[Cr(OH)_4]^-]}{[Cr^{3+}\)][OH^-]^4}. This expression relates the concentrations of the complex ion, uncomplexed Cr^{3+}, and hydroxide ions.

Assume that the initial concentration of Cr^{3+} is equal to the amount of Cr(OH)_3 dissolved, which is 5.0 \(\times\) 10^{-3} \(\text{ mol/L}\).

Since the solution is 1.0 M in NaOH, the concentration of OH^- is 1.0 M. Substitute this value into the K_f expression.

Solve the K_f expression for the concentration of uncomplexed Cr^{3+} and use it to find the fraction of chromium present as uncomplexed Cr^{3+} by dividing the concentration of Cr^{3+} by the initial concentration of Cr(OH)_3.

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Key Concepts

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

Complex Ion Formation

Complex ions are formed when metal ions bond with ligands, which are molecules or ions that can donate electron pairs. In this case, Cr(OH)3 reacts with NaOH to form the complex ion [Cr(OH)4]-. The stability of this complex is indicated by its formation constant (Kf), which quantifies the extent to which the complex forms in solution.

Equilibrium and Kf

The formation constant (Kf) is a measure of the stability of a complex ion in solution. A high Kf value, such as 8 x 10^29 for [Cr(OH)4]-, indicates that the complex is favored over the uncomplexed ions. Understanding how to apply Kf in equilibrium calculations is essential for determining the concentrations of species in the solution.

Stoichiometry and Concentration Calculations

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this scenario, calculating the fraction of uncomplexed Cr3+ requires determining the initial concentration of Cr(OH)3 and how it changes upon dissolution and complex formation. This involves using molarity and the stoichiometric coefficients from the balanced chemical equations.

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