Problem 77 - General Chemistry: Principles and Modern Applications

Question

Reaction (18.10), described in the Integrative Example, is called a carbonate transposition. In such a reaction, anions of a slightly soluble compound (for example, hydroxides and sulfates) are obtained in a sufficient concentration in aqueous solution that they can be identified by qualitative analysis tests. Suppose that \(3 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) is used and that an anion concentration of \(0.050 \mathrm{M}\) is sufficient for its detection. Predict whether carbonate transposition will be effective for detecting (a) \(\mathrm{SO}_{4}^{2-}\) from \(\mathrm{BaSO}_{4}(\mathrm{s}) ;\) (b) \(\mathrm{Cl}^{-}\) from \(\mathrm{AgCl}(\mathrm{s}) ;(\mathrm{c}) \mathrm{F}^{-}\) from \(\mathrm{MgF}_{2}(\mathrm{s})\).

Step-by-Step Solution

Answer

The effectiveness of the carbonate transposition for detecting the anions from \(\mathrm{BaSO}_{4}\), \(\mathrm{AgCl}\), and \(\mathrm{MgF}_{2}\) will depend on the relative solubility product constants (Ksp) for the initial compounds and their respective carbonates. If the Ksp of the initial compound is less than that of the carbonate, the reaction will proceed towards right, making the transposition effective.

Step 1: Understand carbonate transposition

In carbonate transposition, a carbonate such as \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is reacted with a slightly soluble compound, the anion of which is to be detected. The carbonate reacts with this compound to produce \(\mathrm{CO}_{2}\) and a soluble salt, thereby increasing the concentration of the particular anion in the aqueous solution.

Step 2: Application to BaSO4

With \(\mathrm{BaSO}_{4}\), the reaction will be: \(\mathrm{BaSO}_{4} + \mathrm{Na}_{2}\mathrm{CO}_{3} \rightarrow \mathrm{BaCO}_{3} + \(\mathrm{Na}_{2}\mathrm{SO}_{4}\). We are interested in the concentration of the \(\mathrm{SO}_{4}^{2-}\) anion. If the solubility product constant (Ksp) for \(\mathrm{BaSO}_{4}\) is less than that for \(\mathrm{BaCO}_{3}\), the reaction will proceed to the right and the \(\mathrm{SO}_{4}^{2-}\) ion will be effectively detected.

Step 3: Application to AgCl

With \(\mathrm{AgCl}\), the reaction will be: \(\mathrm{AgCl} + \(\mathrm{Na}_{2}\mathrm{CO}_{3} \rightarrow \mathrm{AgCO}_{3} + \(\mathrm{NaCl}\). If the \(\mathrm{Ksp}\) for \(\mathrm{AgCl}\) is less than that for \(\mathrm{AgCO}_{3}\), the reaction will proceed to the right, effectively detecting the \(\mathrm{Cl}^{-}\) anion.

Step 4: Application to MgF2

With \(\mathrm{MgF}_{2}\), the reaction will be: \(\mathrm{MgF}_{2} + \(\mathrm{Na}_{2}\mathrm{CO}_{3} \rightarrow \(\mathrm{MgCO}_{3} + 2\(\mathrm{NaF}\). If the \(\mathrm{Ksp}\) for \(\mathrm{MgF}_{2}\) is less than that for \(\mathrm{MgCO}_{3}\), the reaction will proceed to the right, effectively detecting the \(\mathrm{F}^{-}\) anion.

Key Concepts

Qualitative Analysis Chemistry

Qualitative analysis in chemistry refers to the procedures employed to determine the components of a substance or mixture. Unlike quantitative analysis, which reveals how much of a particular substance is present, qualitative analysis focuses on the presence or absence of a specific chemical species.

In the context of the given exercise, qualitative analysis is used to detect the presence of certain anions in a solution. Carbonate transposition comes into play here as a useful technique. By reacting a carbonate with a slightly soluble compound, the resulting increase in the anion's aqueous concentration makes it detectable using various analytical tests such as precipitate formation, color change, or other indicator-based methods. These tests hinge on the sensitivity of the reaction between the target anion and specific reagents or conditions.

Solubility Product Constant

The solubility product constant, denoted as Ksp, is an equilibrium constant that applies to the dissolution of sparingly soluble salts. It quantifies how much a compound will dissolve in water to form a saturated solution and is defined for a reaction at equilibrium.

For a generic salt, represented as AB_n, the solubility product is calculated by the equation \(K_{sp} = [A^+]^m[B^n-]^n\), where [A⁺] and [B^n-] are the molar concentrations of the ions at equilibrium. The Ksp value is critical when analyzing whether a precipitate will form or dissolve in a given reaction, as illustrated in the carbonate transposition exercise. It enables chemists to predict the direction of the reaction and whether a specific anion can be meaningfully detected.

Precipitation Reactions

Precipitation reactions occur when cations and anions of aqueous solutions combine to form an insoluble salt, called a precipitate. They are fundamental to qualitative analysis chemistry and underlie the principle of carbonate transposition.

When a salt exceeds its solubility product constant in a given solution, it will precipitate out of the solution. This reaction is reversible; thus, by altering the concentration of one of the ions in the solution, like introducing a carbonate, it's possible to shift the equilibrium to either promote or reduce the formation of a precipitate. In the exercise, detecting the presence of anions like \(SO_4^{2-}\), \(Cl^-\), and \(F^-\) is tied to their precipitation behavior when reacted with \(Na_2CO_3\). Understanding these relationships helps determine the success of identifying each anion through its respective transposition reaction.