Question

Interpret Data What compound would precipitate first if a 0.500M sodium fluoride solution were added gradually to a solution already containing 0.500M concentrations of both barium ions and magnesium ions? Use the data in Table 17.6. Write the solubility equilibrium equations and solubility product constant expressions for both compounds. Explain your answer.

Short answer

Upon adding 0.500M sodium fluoride solution to a solution containing 0.500M concentrations of both barium ions and magnesium ions, barium fluoride (BaF2) would precipitate first before magnesium fluoride (MgF2). This is determined by comparing their Qsp values to their respective Ksp values found in Table 17.6. The solubility product constant expressions are \(K_{sp_{BaF2}} = [Ba^{2+}][F^-]^2\) and \(K_{sp_{MgF2}} = [Mg^{2+}][F^-]^2\), with Ksp values of 1.7x10^(-6) and 6.4x10^(-9) respectively.

Step-by-step solution

Write the solubility equilibrium equations and solubility product constant expressions for both compounds

First, let's write the solubility equilibrium equations and solubility product constant expressions for the formation of barium fluoride (BaF2) and magnesium fluoride (MgF2) using the chemical equations. Barium fluoride (BaF2) formation: \(Ba^{2+}(aq) + 2F^-(aq) \rightleftharpoons BaF2(s)\) Solubility product constant expression for barium fluoride: \(K_{sp_{BaF2}} = [Ba^{2+}][F^-]^2 \) Magnesium fluoride (MgF2) formation: \(Mg^{2+}(aq) + 2F^-(aq) \rightleftharpoons MgF2(s)\) Solubility product constant expression for magnesium fluoride: \( K_{sp_{MgF2}} = [Mg^{2+}][F^-]^2 \)

Find the solubility product constants for both compounds

Now let's look up the solubility product constants in Table 17.6 for both barium fluoride and magnesium fluoride. For barium fluoride (BaF2), Ksp = 1.7x10^(-6) For magnesium fluoride (MgF2), Ksp = 6.4x10^(-9)

Determine the Qsp (Reaction Quotient) for both compounds

Now we'll determine and compare the Qsp (reaction quotient) for both compounds when a 0.500M sodium fluoride solution is added gradually to a solution containing 0.500M concentrations of both barium and magnesium ions. For Barium Fluoride: Qsp = [Ba^2+][F^-]^2 = [0.500][0.500]^2 = 6.25x10^(-2) For Magnesium Fluoride: Qsp = [Mg^2+][F^-]^2 = [0.500][0.500]^2 = 6.25x10^(-2)

Compare Qsp values to Ksp values for both compounds

Finally, let's compare the Qsp values to their respective Ksp values for both compounds. For Barium Fluoride: Qsp(6.25x10^(-2)) > Ksp(1.7x10^(-6)), indicating precipitation would occur. For Magnesium Fluoride: Qsp(6.25x10^(-2)) > Ksp(6.4x10^(-9)), indicating precipitation would also occur. However, since the Qsp for barium fluoride exceeds the Ksp by a larger margin than the Qsp of magnesium fluoride, barium fluoride precipitates first.

Conclusion

Upon adding 0.500M sodium fluoride solution to a solution containing 0.500M concentrations of both barium ions and magnesium ions, barium fluoride (BaF2) would precipitate first before magnesium fluoride (MgF2), as determined by comparing their Qsp values to their respective Ksp values found in Table 17.6.

Key concepts

Precipitation

Precipitation occurs when ions in a solution react to form a solid compound, known as a precipitate, that is insoluble or less soluble than the initial compounds. This process is crucial in chemistry for separating substances or driving reactions to completion. When a precipitate forms, it indicates that the concentration of ions has exceeded the solubility limit in the solution. This is where solubility product constant expressions, denoted as \(K_{sp}\), become useful. For instance, in the case where sodium fluoride is added to a solution containing barium and magnesium ions, the formation of solid barium fluoride or magnesium fluoride can occur if the concentration of fluoride ions surpasses the respective solubility limits.

To predict which compound precipitates first, we compare the reaction quotient \(Q_{sp}\) for each potential precipitate against its \(K_{sp}\). If \(Q_{sp}\) exceeds \(K_{sp}\), the solution favors the formation of a solid precipitate. This sequential precipitation strategy helps chemists isolate compounds selectively.

Chemical Equilibrium

Chemical equilibrium is a dynamic state in which the rate of the forward reaction equals the rate of the reverse reaction. When a solution reaches equilibrium, the concentrations of reactants and products remain constant over time as long as the system remains closed. In the case of precipitation reactions, equilibrium applies to the solubility of ionic compounds.

Consider the dissolution of barium fluoride: when equilibrium is reached, the dissolution and precipitation processes of barium ions and fluoride ions balance at the same rate. The constant that describes this balance is the solubility product, \(K_{sp}\). This is specific to each compound and is essential for predicting solubility under given conditions. For example, barium fluoride has a \(K_{sp}\) of \(1.7 \times 10^{-6}\), indicating how much barium and fluoride ions will be present at equilibrium. Thus, equilibrium is not a static condition but a balance of dynamic processes.

Reaction Quotient

The reaction quotient, \(Q_{sp}\), is a tool used to predict the direction of a reaction by comparing it to the solubility product constant \(K_{sp}\). The \(Q_{sp}\) is calculated using the initial concentrations of the reacting ions, just as the \(K_{sp}\) is calculated at equilibrium. By comparing these two values, one can determine whether a precipitate will form.

If \(Q_{sp}\) is greater than \(K_{sp}\), the solution has more ions in solution than it can handle at equilibrium, leading to precipitation until \(Q_{sp}\) decreases to match \(K_{sp}\). If \(Q_{sp}\) equals \(K_{sp}\), the system is at equilibrium and no further net precipitation occurs. If \(Q_{sp}\) is less than \(K_{sp}\), insufficient ions are present to reach equilibrium, and no precipitation occurs.

• For the precipitation problem, both barium fluoride and magnesium fluoride had the same initial \(Q_{sp}\), but since barium fluoride had a much higher \(K_{sp}\), it precipitated first.

Understanding \(Q_{sp}\) allows chemists to predict precipitation processes and manipulate them for applications in separation and purification.