Question

What is the minimum concentration of \(\mathrm{SO}_{4}^{2-}\) required to precipitate \(\mathrm{BaSO}_{4}\) in a solution containing \(1 \times 10^{-4}\) mole of \(\mathrm{Ba}^{2+} ?\left(K_{i p}\right.\) for \(\left.\mathrm{BaSO}_{4}=4 \times 10^{-10}\right)\) (a) \(4 \times 10^{-10} \mathrm{M}\) (b) \(2 \times 10^{-10} \mathrm{M}\) (c) \(4 \times 10^{-6} \mathrm{M}\) (d) \(2 \times 10^{-3} \mathrm{M}\)

Short answer

The minimum concentration of SO42- required to precipitate BaSO4 is 4 x 10^-6 M.

Step-by-step solution

Identify the Ksp Expression

Write down the solubility product constant (Ksp) expression for the precipitation reaction of barium sulfate (BaSO4), which is given by: Ksp = [Ba2+][SO42-].

Insert Known Values

Insert the known values into the Ksp expression. We have Ksp = 4 x 10^-10 and the concentration of Ba2+ which is 1 x 10^-4 M. The equation will look like this: 4 x 10^-10 = (1 x 10^-4)[SO42-].

Solve for [SO42-]

Rearrange the equation from step 2 to solve for the sulfate ion concentration [SO42-]. Divide the Ksp value by the concentration of Ba2+ to find the minimum concentration of [SO42-] required to start precipitating BaSO4.

Calculate [SO42-]

Calculate the concentration of [SO42-] by dividing the Ksp by the concentration of Ba2+: [SO42-] = 4 x 10^-10 / 1 x 10^-4 = 4 x 10^-6 M.

Key concepts

Precipitation Reaction

A precipitation reaction is a chemical process where two soluble ionic compounds in solution are combined to form an insoluble solid, known as a precipitate. This kind of reaction is driven by the formation of a product that has a very low solubility in water. When the product of a reaction has a solubility that falls below the concentrations of its ions in solution, a solid will start to form.

The reaction generally follows the pattern of AB + CD → AD + CB, where AB and CD are the reactants in solution, and AD is the precipitate that forms, while CB remains in the solution. In the context of the given exercise, when aqueous solutions of barium ions (\r\(Ba^{2+}\)) and sulfate ions (\r\(SO_4^{2-}\)) are mixed, barium sulfate (\r\(BaSO_4\)) forms as a precipitate if the product of the ionic concentrations exceeds the solubility product constant (\r\(K_{sp}\)).

Barium Sulfate (BaSO4)

Barium sulfate (\r\(BaSO_4\)) is a white crystalline solid that is largely insoluble in water. Its low solubility makes it a common example when discussing precipitation reactions. It is noteworthy that \r\(BaSO_4\) is used extensively in medical imaging as a radiocontrast agent and also in various industrial applications. However, in a chemical reaction, the minimal solubility is represented by the solubility product constant (\r\(K_{sp}\)), which is the product of the molar concentrations of the constituent ions at equilibrium.

The importance of \r\(BaSO_4\) in educational exercises lies in understanding solubility equilibria and the factors that influence them, such as temperature and the presence of other ions that can shift the equilibrium or participate in secondary reactions.

Ion Concentration

Ion concentration refers to the amount of an ion in a given volume of solution, generally expressed in molarity (M), which is moles per liter. In the context of solubility product, the ion concentrations are crucial for predicting whether a precipitate will form when solutions containing different ions are mixed.

The solubility product constant (\r\(K_{sp}\)) is a specific kind of equilibrium constant that applies to the solubility of sparingly soluble compounds. It quantifies the level at which a compound’s ions are saturated in solution, thereby enabling the calculation of the concentrations at which a precipitate will begin to form. In the exercise, understanding the relationship between \r\(Ba^{2+}\) and \r\(SO_4^{2-}\) ion concentrations allows us to predict the formation of \r\(BaSO_4\) precipitate under certain conditions.