Question

Can \(\mathrm{Fe}^{2+}\) and \(\mathrm{Mn}^{2+}\) be separated by precipitating \(\mathrm{FeS}(\mathrm{s})\) and not \(\mathrm{MnS}(\mathrm{s}) ?\) Assume \(\left[\mathrm{Fe}^{2+}\right]=\left[\mathrm{Mn}^{2+}\right]=\) \(\left[\mathrm{H}_{2} \mathrm{S}\right]=0.10 \mathrm{M} .\) Choose a \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) that ensures maximum precipitation of \(\mathrm{FeS}(\mathrm{s})\) but not \(\mathrm{MnS}(\mathrm{s}) .\) Will the separation be complete? For \(\mathrm{FeS}, K_{\mathrm{spa}}=6 \times 10^{2} ;\) for \(\mathrm{MnS}, K_{\mathrm{spa}}=3 \times 10^{7}\).

Short answer

For the conditions given, it's feasible to precipitate FeS while MnS remains in solution by adjusting the [H3O+]. This can be achieved by finding a range of hydronium ion concentrations that would trigger FeS precipitation but not MnS. Evaluation of completeness of separation would depend on comparison of hs needed for precipitation for both ions. However, this doesn't guarantee an absolute separation due to the close proximity of the solubility constants.

Step-by-step solution

Write the solubility product expression for FeS and MnS

The general form for a solubility product expression is \(Ksp = [M^z+][A^y-]\), where M is the cation, A is the anion, z and y are their charges. For FeS, \(Ksp = [Fe^{2+}][HS^-]\). Since H2S is a weak acid, the concentration of HS- can be approximated as concentration of H2S. Therefore, for FeS, \(Ksp = [Fe^{2+}][H2S]\). Similarly, for MnS, \(Ksp = [Mn^{2+}][H2S]\).

Calculate the minimum hydronium ion concentration

From the expressions above, it can be seen that the [H2S] needed to begin precipitation of each metal is just \(Ksp/M^{2+}\) . It is given in the problem statement that [Fe^{2+}] = [Mn^{2+}] = [H2S] = 0.1 M . We want to find a [H_{3}O^+] that ensures maximum precipitation of FeS and not MnS. Let's denote [H_{3}O^+] as h, and [HS^-] as hs. The equilibrium concentration of HS^- can be estimated using the equilibrium constant expression for the ionization of H2S in water, which is \(Kws = [HS^-][H_{3}O^+]/ [H2S]\). Substituting, we get hs = \(Kws \cdot [H2S]/ h\). As the [HS^-] need for precipitation is bigger for FeS, set hs to match the [HS^-] needed for precipitation for both ions, that is \(Ksp_{Fe}/[Fe^{2+}] = Ksp_{Mn}/[Mn^{2+}]\). Substitute into \(Kws \cdot [H2S]/ h = Ksp_{Fe}/[Fe^{2+}] \)Solving for h, we get, h = \(Kws \cdot [H2S] \cdot [Fe^{2+}]/Ksp_{Fe}\)

Evaluate the completeness of the separation

To evaluate if the separation is complete, compare hs needed for precipitation of FeS with that of MnS. If hs needed for MnS precipitation is larger than that of FeS, then separation is complete. On the other hand, if hs needed for MnS precipitation is smaller than that required for FeS, then separation will not be complete.

Key concepts

Solubility product

The solubility product ( K_{sp}) is a crucial equilibrium constant in chemistry that helps predict the solubility of compounds. It defines the extent to which a salt can dissolve in a solution. For an ionic compound like FeS, K_{sp} represents the product of the molar concentrations of the ions at saturation. This constant varies for different compounds and is essential for determining whether a compound will precipitate under certain conditions.

In the case of FeS and MnS, the respective solubility product expressions are K_{sp} = [Fe^{2+}][HS^-] for iron(II) sulfide, and K_{sp} = [Mn^{2+}][HS^-] for manganese(II) sulfide. The solubility product helps us understand that when the product of concentrations of ions in solution exceeds the K_{sp} value, the salt will precipitate. Understanding K_{sp} is key to manipulating the precipitation of different ions to achieve separation.

• Higher K_{sp} values mean more solubililty.
• Predicting the solubilites of compounds helps in separation processes.
• K_{sp} varies with temperature and the type of solvent.

Hydronium ion concentration

Hydronium ion concentration ([H_{3}O^+]) plays a vital role in the solubility of sulfide salts. In acidic solutions, the equilibrium between H_{2}S and hydrosulfide ions (HS^-) is influenced by the concentration of hydronium ions. Essentially, [H_{3}O^+] dictates how much of the H_2S dissociates to produce HS^-, which is necessary for forming precipitates like FeS.

The presence of [H_{3}O^+] shifts the equilibrium and affects the concentration of ions available in the solution. By calculating the appropriate [H_{3}O^+], we can manage the ion concentrations such that certain compounds precipitate while others remain dissolved. In the provided exercise, calculating [H_{3}O^+] ensures maximum precipitation of FeS without forming MnS, achieving effective ion separation.

• [H_{3}O^+] is a measure of acidity in a solution.
• It influences chemical equilibria, especially in acid-base reactions.
• Adjusting [H_{3}O^+] can control precipitate formation.

Ion precipitation

Precipitation occurs when the product of the ionic concentrations in a solution exceeds the compound's solubility product threshold ( K_{sp}). This process is used to separate ions in a mixture by selectively precipitating one ion while keeping others dissolved. The manipulation of conditions such as ionic concentrations and [H_{3}O^+] allows for precise control over which salts will form a solid and precipitate out of the solution.

In the analyzed exercise, the goal is to selectively precipitate FeS while leaving MnS dissolved. By adjusting the hydronium ion concentration, the solution conditions can promote the precipitation of FeS because it reaches its K_{sp} value before MnS does. The selective precipitation based on differing K_{sp} values allows for the effective separation of these ions in the lab.

• Precipitation is a reversible process influenced by concentration and temperature.
• Selectivity in precipitation can be achieved through understanding K_{sp}.
• Precipitate formation is often visual, indicating changes in solution composition.

Chemical equilibrium

Chemical equilibrium in a solution occurs when the forward and reverse reactions balance each other out, resulting in a stable condition where the concentrations of reactants and products remain unchanged over time. It is represented in reactions where the rate of dissolution of a salt matches the rate of its precipitation.

Understanding chemical equilibrium is essential in separating ions using precipitation. For FeS and MnS, the equilibrium involves the saturation point of dissolved ions and their salts forming in the solution. By manipulating external conditions, such as pH or ionic strength, it is possible to shift the equilibrium towards one side to facilitate specific precipitate formation. This leveraging of equilibrium helps predict and control which ions will precipitate out and which will stay dissolved, allowing for selective separations like the one desired in the exercise.

• Equilibrium occurs when the concentrations of ions and compounds in solution stabilize.
• Shifting equilibrium is essential for controlled ion precipitation.
• External factors like pressure and temperature can influence equilibrium.