Question

Calculate the solubility, in moles per liter, of iron(II) hydroxide, \(\mathrm{Fe}(\mathrm{OH})_{2},\) in a solution buffered to a pH of 7.00.

Short answer

The solubility of \(\mathrm{Fe(OH)}_2\) at pH 7.00 is \(4.87 \times 10^{-3}\) M.

Step-by-step solution

Determine the relationship between solubility and pH

The solubility of iron(II) hydroxide, \(\mathrm{Fe(OH)}_2\), can be affected by the pH of the solution according to the following equation: \[\mathrm{Fe(OH)}_2 (s) \rightleftharpoons \mathrm{Fe}^{2+}(aq) + 2\mathrm{OH}^- (aq)\]. From this reaction, we see that increased \([\mathrm{OH}^-]\) from high pH decreases solubility due to the common-ion effect.

Calculate hydroxide ion concentration at pH 7

Since the pH is 7, we find the pOH using the relationship: \( \text{pOH} = 14.00 - 7.00 = 7.00 \). The \([\mathrm{OH}^-]\) concentration is then \( 10^{-7.00} = 1.0 \times 10^{-7} \) M.

Write the solubility product expression

The solubility product \(K_{sp}\) for \(\mathrm{Fe(OH)}_2\) is defined as: \[K_{sp} = [\mathrm{Fe}^{2+}][\mathrm{OH}^-]^2\]. This expression represents the equilibrium condition when \(\mathrm{Fe(OH)}_2\) is dissolved in a solution.

Solve for the solubility in terms of Ksp

Assuming that the additional concentration of \([\mathrm{OH}^-]\) from \(\mathrm{Fe(OH)}_2\) dissolution is negligible compared to the existing \([\mathrm{OH}^-]\), substitute \( 1.0 \times 10^{-7} \) M for \([\mathrm{OH}^-]\) into the \(K_{sp}\) expression. Let \(s\) be the solubility of \(\mathrm{Fe(OH)}_2\) in \(\mathrm{mol/L}\). Thus, \[ K_{sp} = s \cdot (1.0 \times 10^{-7})^2 \].

Use the value of Ksp to find solubility

For \(\mathrm{Fe(OH)}_2\), \(K_{sp} = 4.87 \times 10^{-17}\) (a known constant). Solving for \(s\), the solubility: \[ s = \frac{K_{sp}}{(1.0 \times 10^{-7})^2} = \frac{4.87 \times 10^{-17}}{1.0 \times 10^{-14}} = 4.87 \times 10^{-3} \text{ M} \].

Conclusion

The solubility of \(\mathrm{Fe(OH)}_2\) at pH 7.00 is \(4.87 \times 10^{-3}\) moles per liter.

Key concepts

iron(II) hydroxide

Iron(II) hydroxide, denoted as \( \mathrm{Fe(OH)}_2 \), is an important chemical compound commonly discussed in chemistry, particularly regarding its solubility and reactions in aqueous solutions. It is a slightly soluble compound that forms a pale green precipitate in water. The solubility of \( \mathrm{Fe(OH)}_2 \) in water is influenced by the solution's pH level, which is a measure of the acidity or basicity of the solution. A pivotal role in its solubility is played by the hydroxide ions (\( \mathrm{OH}^- \)); the balance of these ions in solution affects how much \( \mathrm{Fe(OH)}_2 \) can dissolve into its constituent ions: \( \mathrm{Fe}^{2+} \) ions and \( \mathrm{OH}^- \) ions. Understanding the solubility behavior of \( \mathrm{Fe(OH)}_2 \) provides insights into broader chemistry concepts like solubility equilibrium and the effects of ion concentration on solubility.

pH and pOH

The concepts of pH and pOH are central to understanding the behavior of acids and bases in solution. The pH scale measures how acidic or basic a solution is, with a range from 0 (most acidic) to 14 (most basic). A pH of 7 is neutral, which is the pH of pure water. Alternatively, pOH is a measure related to the concentration of hydroxide ions (\( \mathrm{OH}^- \)) in a solution. pH and pOH are inversely related and summed to 14:

• \( \text{pH} + \text{pOH} = 14.00 \)

Understanding pH and pOH is crucial when calculating the solubility of compounds like \( \mathrm{Fe(OH)}_2 \), as pH changes affect the concentration of hydroxide ions in solution. For instance, a solution with a pH of 7 has a corresponding pOH of 7, indicating a low concentration of \( \mathrm{OH}^- \), thus impacting the precipitation or dissolution of hydroxide compounds.

solubility product constant (Ksp)

The solubility product constant, represented by the symbol \( K_{sp} \), describes the equilibrium between a solid and its ions in a solution. For \( \mathrm{Fe(OH)}_2 \), the expression is: \[ K_{sp} = [\mathrm{Fe}^{2+}][\mathrm{OH}^-]^2 \] This expression quantifies the extent to which \( \mathrm{Fe(OH)}_2 \) can dissolve in water before the solution becomes saturated. The \( K_{sp} \) value is determined experimentally and is specific to each compound. It helps predict whether a precipitate will form when solutions of ions are mixed. For instance, a low \( K_{sp} \) value indicates that only a small amount of \( \mathrm{Fe(OH)}_2 \) will dissolve, meaning the compound is poorly soluble. When solving solubility problems, the \( K_{sp} \) value of \( \mathrm{Fe(OH)}_2 \) is used to determine the maximum concentration of dissolved ions in equilibrium with the undissolved solid. This becomes especially important in buffered solutions, where the concentration of ions is influenced by the added components in the system.

common-ion effect

The common-ion effect is an important principle in chemistry that affects the solubility of ionic compounds. It is all about the influence an ion, already present in solution, has on a dissolving compound. Consider the dissolution of \( \mathrm{Fe(OH)}_2 \): its solubility is impacted by the concentration of \( \mathrm{OH}^- \) ions in the solution. When the concentration of \( \mathrm{OH}^- \) ions increases, due to a common ion present from another source, it suppresses further dissolution of \( \mathrm{Fe(OH)}_2 \). This occurs because the system reaches equilibrium faster with fewer ions needing to dissolve to satisfy the \( K_{sp} \) condition.

• Adding base to the solution increases \( \mathrm{OH}^- \) and decreases solubility.
• Reduction in solubility is due to the shift in equilibrium towards the solid form, limiting further ionization.

Through strategies like buffering, where the pH is controlled, the common-ion effect becomes a powerful tool in controlling solubility and stability of compounds in a variety of chemical processes.