Question

The hydrated cation \(\mathrm{M}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) has \(K_{\mathrm{a}}=10^{-4}\), and the acid \(\mathrm{HA}\) has \(K_{\mathrm{a}}=10^{-5}\). Identify the principal reaction in an aqueous solution of each of the following salts, and classify each solution as acidic, basic, or neutral: (a) \(\mathrm{NaA}\) (b) \(\mathrm{M}\left(\mathrm{NO}_{3}\right)_{3}\) (c) \(\mathrm{NaNO}_{3}\) (d) \(\mathrm{M} A_{3}\)

Short answer

(a) Basic; (b) Acidic; (c) Neutral; (d) Acidic.

Step-by-step solution

Understand the Problem

We need to identify the principal reaction in aqueous solutions of given salts and classify the solution as acidic, basic, or neutral. This involves understanding the nature of each salt and determining whether it will form acidic, basic, or neutral solutions.

Analyze Salt (a) NaA

The salt NaA consists of Na+ and A-. Since Na+ is a cation from a strong base (NaOH), it does not affect the pH. A- comes from HA, a weak acid with a dissociation constant \( K_a = 10^{-5} \). In water, A- will react with water and shift the equilibrium of \( HA \leftrightarrow H^+ + A^- \) to the left. Thus, NaA forms a basic solution due to the anion's ability to accept protons.

Analyze Salt (b) M(NO₃)₃

M(NO₃)₃ consists of M³⁺ ions and NO₃⁻ ions. The cation \( \mathrm{M} \left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+} \) has \( K_a = 10^{-4} \), indicating that it releases protons in water, causing the solution to be acidic. The NO₃⁻ ion is from a strong acid (HNO₃) and does not affect the pH. Therefore, the solution is acidic due to \( \mathrm{M}^{3+} \).

Analyze Salt (c) NaNO₃

NaNO₃ contains the ions Na+ and NO₃⁻. Both come from strong bases and acids (NaOH and HNO₃) and do not significantly affect the pH of the solution. Therefore, the solution remains neutral.

Analyze Salt (d) M A₃

MA₃ contains \( \mathrm{M}^{3+} \) and \( \mathrm{A}^{-} \). The cation \( \mathrm{M}^{3+} \) is quite acidic \( K_a = 10^{-4} \), while the anion \( \mathrm{A}^- \) is less basic \( K_b = \frac{K_w}{K_a}=10^{-9} \) due to the weak acid HA. As \( \mathrm{M}^{3+} \) is a stronger acid than \( \mathrm{A}^- \) is a base, the solution is acidic.

Key concepts

Salt Solutions

Salt solutions are formed when salts dissolve in water, leading to the dissociation of the constituent ions. The properties of these ions determine the resultant pH of the solution. Let's consider different types of salt solutions:

• An acidic salt solution occurs when the salt is composed of ions that generate H⁺ ions in water, leading to an acidic pH. For example, the salt M(NO₃)₃ contains M³⁺ ions, which are derived from M(H₂O)₆³⁺, releasing protons into the solution.
• A basic salt solution forms when the salt ions tend to accept protons from water, reducing the concentration of H⁺ ions. An example is NaA, where A⁻ ions, derived from the weak acid HA, interact with water resulting in a basic pH.
• Neutral salt solutions occur when neither the cations nor the anions impact the pH significantly. NaNO₃ is a good example since both Na⁺ and NO₃⁻ originate from strong bases and acids, respectively, which means they don't alter the pH of the solution.

In each case, understanding the nature of the ions—whether they are from strong or weak acids and bases—helps in predicting the resultant acidity or basicity of the salt solution.

pH Classification

The pH scale is a measure of acidity or basicity of an aqueous solution. pH values range from 0 to 14, where:

• A pH lower than 7 indicates an acidic solution.
• A pH greater than 7 indicates a basic solution.
• A pH of 7 is considered neutral.

pH classification can be determined by assessing the ion composition of a salt in a solution. Each ion can influence the pH based on its ability to donate or accept protons:

- **Acidic Solutions:** Salts like M(NO₃)₃ release ions that donate protons, making the solution acidic. These have a significant Ka value showing a propensity to dissociate in water and lower the pH.
- **Basic Solutions:** In the case of NaA, the anion A⁻ preferentially accepts protons from water. This reduces the concentration of H⁺ ions, increasing the pH.
- **Neutral Solutions:** Salts like NaNO₃ neither donate nor accept protons significantly, thus maintaining a neutral pH. Understanding the source and nature of the salt ions helps in predicting whether the solution will be acidic, basic, or neutral in nature.

Dissociation Constants

Dissociation constants, represented as Ka for acids and Kb for bases, measure how completely an acid or base dissociates in water. This is crucial for understanding the behavior of salts in solution:

• The dissociation constant Ka represents the acid strength. A higher Ka value, like for M(H₂O)₆³⁺ with a Ka of 10⁻⁴, indicates stronger acidic properties, making the solution more acidic. On the other hand, HA has a lower Ka of 10⁻⁵, showing it's a weaker acid.
• Kb, calculated as Kw/Ka for acids, provides the basic nature of the conjugate base. For instance, A⁻, with a calculated Kb of 10⁻⁹, demonstrates its weak basicity, which affects the overall pH of the salt solution NaA.

Understanding dissociation constants is fundamental in predicting the behavior of ions in a solution, whether they will act predominantly as acids or bases. This forms the basis for predicting the resulting pH when such salts are dissolved in water. The comparison of Ka and Kb values provides insights into whether an ion will increase or reduce the pH, influencing whether the solution classifies as acidic, basic, or neutral.