Problem 74 - Chemistry: The Central Science in SI Units, Global Edition

Question

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}(a q)\) and \(0.010 \mathrm{M}\) in \(\mathrm{Sr}^{2+}(a q) .(\mathbf{a}) \mathrm{What}\) concentration of \(\mathrm{SO}_{4}^{2-}\) is necessary to begin precipitation? (Neglect volume changes. \(\mathrm{BaSO}_{4}: K_{s p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}:\) \(K_{s p}=3.2 \times 10^{-7} .\) ) (b) Which cation precipitates first? (c) What is the concentration of \(\mathrm{SO}_{4}^{2-}(a q)\) when the second cation begins to precipitate?

Step-by-Step Solution

Answer

(a) The necessary concentration of $\mathrm{SO}_{4}^{2-}$ to begin precipitation is \(1.1\times10^{-9}\,M\). (b) $\mathrm{Ba}^{2+}$ will precipitate first. (c) The concentration of $\mathrm{SO}_{4}^{2-}$ needed for the second cation, $\mathrm{Sr}^{2+}$, to precipitate is \(3.2\times10^{-6}\,M\).

Step 1: Write solubility product expressions.

The solubility products expressions can be written as: For BaSO4: \[K_{sp}(BaSO_4) = [Ba^{2+}][SO_4^{2-}]\] For SrSO4: \[K_{sp}(SrSO_4) = [Sr^{2+}][SO_4^{2-}]\]

Step 2: Find saturation concentrations for each cation.

The concentration of Ba^2+ and Sr^2+ ions are both given as 0.010 M. Now, let's solve for the saturation concentration of SO4^2- for each cation using the solubility products: For Ba^2+: \[[SO_4^{2-}]_{sat}(Ba^{2+}) = \frac{K_{sp}(BaSO_4)}{[Ba^{2+}]} = \frac{1.1\times10^{-10}}{0.010} = 1.1\times10^{-9}\,M\] For Sr^2+: \[[SO_4^{2-}]_{sat}(Sr^{2+}) = \frac{K_{sp}(SrSO_4)}{[Sr^{2+}]} = \frac{3.2\times10^{-7}}{0.010} = 3.2\times10^{-6}\,M\]

Step 3: Determine which cation precipitates first.

Since we are looking for the minimum concentration of SO4^2- to start precipitation, we should compare the saturation concentrations calculated in step 2. The cation with the lower saturation concentration will precipitate first: \(1.1\times10^{-9}\,M < 3.2\times10^{-6}\,M\), therefore Ba^2+ will precipitate first. Answer (b): Ba^2+ will precipitate first.

Step 4: Calculate the concentration of SO4^2- when the second cation begins to precipitate.

After Ba^2+ has precipitated, it is now out of the solution and does not affect the solution anymore. The concentration of SO4^2- required to make Sr^2+ precipitate can be found using the saturation concentration we calculated for Sr^2+: Answer (c): The concentration of SO4^2- when the second cation (Sr^2+) begins to precipitate is \(3.2\times10^{-6}\,M\). In summary: (a) The necessary concentration of sulfate ions to begin precipitation is \(1.1\times10^{-9}\,M\). (b) Ba^2+ will precipitate first. (c) The concentration of sulfate ions needed for the second cation, Sr^2+, to precipitate is \(3.2\times10^{-6}\,M\).

Key Concepts

Precipitation Reaction

A precipitation reaction occurs when two aqueous solutions are mixed together, leading to the formation of an insoluble solid known as a precipitate. This happens when the product of the ions in solution exceeds the solubility product constant (K_{sp}), which is essentially the threshold concentration beyond which a compound begins to form a solid and precipitate out of solution. In the provided exercise, the precipitation reaction involves the mixing of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) with a solution containing \(\mathrm{Ba}^{2+}\) and \(\mathrm{Sr}^{2+}\). The \(\mathrm{SO}_{4}^{2-}\) ions from \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) interact with the metal cations in the solution to possibly form \(\mathrm{BaSO}_{4}\) or \(\mathrm{SrSO}_{4}\) precipitates.

• Reactants in Solution: These are the substances that dissolve in water to form respective ions. Here, \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) breaks down into \(\mathrm{Na}^{+}\) and \(\mathrm{SO}_{4}^{2-}\) ions.
• Formation of Precipitate: When the \(\mathrm{SO}_{4}^{2-}\) concentration is sufficiently high, either \(\mathrm{BaSO}_{4}\) or \(\mathrm{SrSO}_{4}\) will begin to form as a solid.
• Order of Precipitation: Through the calculation in the exercise, it was shown that \(\mathrm{Ba}^{2+}\) precipitates first as \(\mathrm{BaSO}_{4}\).

Understanding precipitation reactions is crucial for predicting which compounds will form solids when two or more solutions are combined. This concept is particularly important in chemistry fields such as analytical chemistry, environmental chemistry, and industrial applications.

Saturation Concentration

Saturation concentration is a key term used to describe the maximum concentration of a solute that can dissolve in a solvent at a given temperature before the solute starts to precipitate. In the exercise given, you were tasked with identifying the saturation concentrations of \(\mathrm{SO}_{4}^{2-}\) in the presence of \(\mathrm{Ba}^{2+}\) and \(\mathrm{Sr}^{2+}\). These values are crucial for determining when each metallic sulfate will start to precipitate from the solution.

• BaSO₄ Saturation Concentration: We calculated it to be \(1.1\times10^{-9} \mathrm{M}\).
• SrSO₄ Saturation Concentration: Was found to be \(3.2\times10^{-6} \mathrm{M}\).
• Comparing Saturations: A lower saturation concentration indicates a higher tendency to precipitate. Hence, BaSO₄ precipitates at a lower concentration of \(\mathrm{SO}_{4}^{2-}\), showing BaSO₄ is less soluble in water compared to SrSO₄.

Saturation concentration allows chemists to predict the solubility of substances and conduct calculations to maintain balanced solutions, ensuring no unwanted precipitates form during experiments or manufacturing processes.

Solubility Constants

Solubility constants, represented as \(K_{sp}\), are values that express the equilibrium between the dissolution and precipitation processes of a slightly soluble compound in solution. These constants help in predicting how much of a compound can dissolve before it starts forming a precipitate. In the context of the exercise, we dealt with the solubility constants of two compounds: \(\mathrm{BaSO}_{4}\) with a \(K_{sp}\) of \(1.1 \times 10^{-10}\) and \(\mathrm{SrSO}_{4}\) with a \(K_{sp}\) of \(3.2 \times 10^{-7}\).

• Using \(K_{sp}\): These values allow us to determine the concentrations at which particular ions will start precipitating out whenever their product exceeds the \(K_{sp}\) value.
• Precise Calculations: From the solubility constants, we derive the necessary formulas to calculate when precipitation occurs, and, importantly, the conditions needed for selective precipitation.
• Interpreting \(K_{sp}\) Values: A smaller \(K_{sp}\) indicates a less soluble compound. In our case, BaSO₄ is less soluble than SrSO₄, evidenced by its lower solubility constant.

Understanding solubility constants is essential for predicting and controlling precipitation reactions, particularly in scenarios requiring fine separations or purification of compounds.