Question

\(\begin{array}{llll}\text { Solubility } & \text { products of } & \mathrm{Mg}(\mathrm{OH})_{2} \text { , }\end{array}\) \(\mathrm{Cd}(\mathrm{OH})_{2}, \mathrm{Al}(\mathrm{OH})_{3}\) and \(\mathrm{Zn}(\mathrm{OH})_{2}\) are \(4 \times 10^{-11}, 8 \times 10^{-6}, 8.5 \times 10^{-23}\) and \(1.8 \times 10^{-14}\), respectively. The cation that will precipitate first as hydroxide, on adding limited quantity of \(\mathrm{NH}_{4} \mathrm{OH}\) in a solution containing equimolar amount of metal cations, is (a) \(\mathrm{Al}^{3+}\) (b) \(\mathrm{Zn}^{2+}\) (c) \(\mathrm{Mg}^{2+}\) (d) \(\mathrm{Cd}^{2+}\)

Short answer

Al^3+ will precipitate first.

Step-by-step solution

Understanding the Solubility Product

The solubility product (Ksp) represents the product of the concentrations of the ions in a saturated solution of a salt, each raised to the power of their respective stoichiometry in the salt's formula. A lower solubility product indicates a less soluble compound. This means that, when comparing different salts, the one with the lowest solubility product is the first to precipitate when a common ion is added to the solution.

Determining the cation that will precipitate first

To ascertain the cation that will precipitate first from a solution containing equimolar amounts of different metal cations upon adding NH4OH, we need to compare the solubility products (Ksp values) of their corresponding hydroxides. The cation forming the least soluble hydroxide (with the smallest Ksp value) will precipitate first.

Comparing the Ksp values

The given solubility products are: Mg(OH)2: 4 x 10^-11, Cd(OH)2: 8 x 10^-6, Al(OH)3: 8.5 x 10^-23, Zn(OH)2: 1.8 x 10^-14. Therefore, Al(OH)3 with the Ksp of 8.5 x 10^-23 is the least soluble compound among the ones given. Hence, Al^3+ will precipitate first when NH4OH is added.

Key concepts

Chemistry Competitive Examinations

Preparing for chemistry competitive examinations requires a deep understanding of various chemical concepts, one of which is the solubility product constant (Ksp). This particular topic often appears in the form of problems that ask to predict precipitation reactions or compare solubility of different compounds. To excel in this area, it's essential to comprehend the meaning of Ksp and its role in predicting the formation of a precipitate.

Competitive exams test a student's ability to apply concepts to new situations. In the context of solubility, a student must not only remember the numerical value of solubility products but also understand how these values affect the saturation level of a solution and the likelihood of a precipitate forming when reacting with another compound or ion. Mastering calculations involving the solubility product constant can significantly improve a student's performance in the inorganic chemistry section of these exams.

Solubility Product Constant

The solubility product constant, symbolized as Ksp, is an essential quantitative measure in chemistry that indicates the solubility of sparingly soluble ionic compounds. It is the constant for the equilibrium between a solid substance and its ions in a saturated solution. The formula for the solubility product is derived from the equilibrium expression for the dissociation of the compound into its constituent ions.

For instance, for the general dissolution of a compound AxBy into x A^y+ ions and y B^x- ions, the solubility product expression is:
Ksp = [A^y+]^x * [B^x-]^y.
Here, [A^y+] and [B^x-] represent the molar concentrations of the ions at equilibrium. The powers of x and y reflect the stoichiometry of the dissociation reaction. A high Ksp value indicates higher solubility, while a lower Ksp signifies a compound that is less likely to dissolve. Understanding Ksp is vital for predicting whether a precipitate will form in a reaction.

Precipitation Reactions

Precipitation reactions occur when two solutions containing soluble salts are mixed, resulting in the formation of an insoluble product or precipitate. These reactions are represented by the solubility rules, which predict whether a compound will remain in solution or form a precipitate based on the constituent ions' solubility.

In an equimolar solution containing multiple cations, the one that forms the least soluble hydroxide upon addition of a common anion will precipitate first. In our example, when NH4OH is added to a solution containing equimolar amounts of Mg²⁺, Cd²⁺, Al³⁺, and Zn²⁺, Al³⁺ will precipitate first due to its lowest Ksp value of 8.5 x 10^-23 for Al(OH)₃. This tends to be a frequent type of question in competitive examinations, where understanding the concept of solubility product and its application to predict the sequence of precipitation is critical.