Question

Suppose the concentration of a solution is \(0.10 M \mathrm{Ba}^{2+}\) and \(0.10 \mathrm{M} \mathrm{Sr}^{2+}\). Which sulfate, \(\mathrm{BaSO}_{4}\) or \(\mathrm{SrSO}_{4}\), will precipitate first when a dilute solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added dropwise to the solution? Show evidence for your answer. \(\left(K_{\mathrm{sp}}=1.5 \times 10^{-9}\right.\) for \(\mathrm{BaSO}_{4}\) and \(K_{\mathrm{sp}}=3.5 \times 10^{-7}\) for \(\mathrm{SrSO}_{4}\) )

Short answer

\(\mathrm{BaSO}_4\) will precipitate first since it has a lower solubility product constant \(K_{\mathrm{sp}}\) than \(\mathrm{SrSO}_4\).

Step-by-step solution

- Write the Ionic Equations

Start by writing the balanced chemical equations for the dissociation of the two possible sulfates:For Barium Sulfate: \( \mathrm{BaSO}_4 (s) \rightleftharpoons \mathrm{Ba}^{2+} (aq) + \mathrm{SO}_4^{2-} (aq) \).For Strontium Sulfate: \( \mathrm{SrSO}_4 (s) \rightleftharpoons \mathrm{Sr}^{2+} (aq) + \mathrm{SO}_4^{2-} (aq) \).

- Calculate the Ions' Product

Calculate the ionic product (Q) for both sulfates using the initial concentrations of the ions. This is done by multiplying the concentration of the metal ion by the expected concentration of the sulfate ion, which would initially be zero, but will start to increase as the sulfuric acid is added:\(Q_{\mathrm{BaSO}_4} = [\mathrm{Ba}^{2+}] \times [\mathrm{SO}_4^{2-}]\)\(Q_{\mathrm{SrSO}_4} = [\mathrm{Sr}^{2+}] \times [\mathrm{SO}_4^{2-}]\)

- Determine the Saturation Point

For precipitation to occur, the ionic product (Q) must exceed the solubility product constant \(K_{\mathrm{sp}}\). The lower the \(K_{\mathrm{sp}}\), the sooner the salts will precipitate as the concentration of \(\mathrm{SO}_4^{2-}\) ions increase. In this case, since \(K_{\mathrm{sp}}(\mathrm{BaSO}_4) < K_{\mathrm{sp}}(\mathrm{SrSO}_4)\), \(\mathrm{BaSO}_4\) will reach its saturation point and precipitate first.

Key concepts

Chemical Equilibrium

In chemistry, chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, leading to no overall change in the concentrations of the reactants and products. This principle is essential when discussing reactions in solution, such as when salts dissolve or precipitate.

In the equilibrium state for a reversible reaction, like the dissolution of a salt in water, there is a dynamic balance. This means that while the individual ions are still moving between the solid phase and the solution, the amount of solid and the concentration of dissolved ions remain constant over time.

An equilibrium constant, expressed as either a dissociation constant (Kd) for dissolution or a solubility product constant (Ksp) for precipitation, quantifies this balance. The equilibrium constant is specific for a given compound at a particular temperature. Therefore, understanding the concept of chemical equilibrium is crucial for predicting the behavior of substances in a solution and for figuring out which compound will precipitate first in a mixture.

Solubility Equilibrium

Solubility equilibrium refers to the physical state in which a chemical compound has dissolved in a solvent to the extent that its rate of dissolution is in a dynamic balance with its rate of precipitation. This equilibrium is represented by the solubility product constant (Ksp), a key concept when analyzing solubility and precipitation reactions.

The Ksp value is used to determine whether a salt will precipitate under certain conditions. A solution is unsaturated if the product of the ion concentrations is below the Ksp, meaning more salt can dissolve. When the product equals the Ksp, the solution is saturated, and any additional salt added will remain undissolved, establishing a dynamic equilibrium. If the product exceeds the Ksp, the solution is supersaturated, and precipitation is favored.

In the exercise provided, the concept of solubility equilibrium allows us to predict which sulfate will precipitate first upon adding sulfuric acid to the mixture of barium and strontium ions, based on the comparative Ksp values.

Ionic Product

The ionic product (Q) of a salt in a solution is the product of the molar concentrations of its ions, each raised to the power of their stoichiometric coefficient in the dissolution reaction. It is a useful concept for understanding the possible behavior of ions in a solution with respect to precipitation.

The ionic product is often compared with the solubility product constant (Ksp) of the salt. If Q is less than Ksp, the solution can still dissolve more of the salt without precipitation. If Q equals Ksp, the solution is at equilibrium and is saturated with salt. If Q exceeds Ksp, the solution is supersaturated, and precipitation of the salt is likely.

In the context of the provided exercise, calculating the ionic product for both barium sulfate (BaSO4) and strontium sulfate (SrSO4) helps us identify the point at which each salt will begin to precipitate. Thus, this concept is crucial for predicting precipitation outcomes in a variety of chemical contexts.

Precipitation Reaction

A precipitation reaction is a type of chemical reaction where a solid, known as a precipitate, forms when two aqueous solutions combine. Precipitation occurs when the ionic product of the dissolved ions exceeds the solubility product constant (Ksp) for that particular solid at a given temperature.

To predict the formation of a precipitate, one must know the solubility rules and the Ksp values ​​of potential precipitates. A lower Ksp means that the compound is less soluble and will precipitate more readily. Hence, a solid with a smaller Ksp will form first in a solution that contains multiple potential precipitates.

The exercise demonstrates this principle with two possible sulfates, barium sulfate and strontium sulfate. By comparing their Ksp values and calculating the ionic product as sulfuric acid is added, one can determine which sulfate will precipitate first. This specific concept of precipitation reaction is essential for students studying reactions in aqueous solutions, particularly in fields such as environmental engineering, where controlling the formation of precipitates is often a key concern.