Question

Sodium chloride is listed in the solubility rules as a soluble compound. Therefore, the \(K_{\mathrm{sp}}\) value for \(\mathrm{NaCl}\) is infinite. Is this statement true or false? Explain.

Short answer

The statement is false. Although sodium chloride (NaCl) is soluble in water according to solubility rules, this does not mean its \(K_{\mathrm{sp}}\) value is infinite. No compound has infinite solubility in water, and solubility rules only help to determine if a compound is soluble or not, without providing a specific \(K_{\mathrm{sp}}\) value.

Step-by-step solution

Understanding Solubility Rules

Solubility rules are general guidelines to determine which ionic compounds are soluble in water. According to the solubility rules, all salts containing alkali metal ions, like sodium (Na\(^+\)), and nitrates, are soluble in water. This means that sodium chloride (NaCl) is indeed soluble in water.

Understanding the Solubility Product Constant, \(K_{\mathrm{sp}}\)

The solubility product constant (\(K_{\mathrm{sp}}\)) is an equilibrium constant that quantifies the solubility of a slightly soluble compound. The larger the \(K_{\mathrm{sp}}\) value, the more soluble the compound is in water. For a salt reaction of the form \(\mathrm{AB} \leftrightarrow \mathrm{A}^+ + \mathrm{B}^-\), the \(K_{\mathrm{sp}}\) can be written as: \[K_{\mathrm{sp}} = [\mathrm{A}^+][\mathrm{B}^-]\]

Relating Solubility Rules and \(K_{\mathrm{sp}}\) values

While it is true that a higher \(K_{\mathrm{sp}}\) value indicates greater solubility, the statement that the \(K_{\mathrm{sp}}\) value for NaCl is "infinite" is incorrect. In reality, no compound has infinite solubility, as there would be a limit to how much of a compound can dissolve in a given volume of water. The solubility rules merely help us determine if a compound is soluble or not, but they do not provide us with the specific value of \(K_{\mathrm{sp}}\). In fact, sodium chloride has a finite solubility in water, and its \(K_{\mathrm{sp}}\) value is not infinite.

Conclusion

The statement "Sodium chloride is listed in the solubility rules as a soluble compound. Therefore, the \(K_{\mathrm{sp}}\) value for \(\mathrm{NaCl}\) is infinite." is false. While sodium chloride is indeed soluble, its \(K_{\mathrm{sp}}\) value is not infinite, as no compound has infinite solubility in water.

Key concepts

Ksp

The Solubility Product Constant, often abbreviated as \(K_{\mathrm{sp}}\), is a critical concept in understanding how substances dissolve in water. Essentially, \(K_{\mathrm{sp}}\) is the equilibrium constant that describes the saturated solution of a slightly soluble salt. In chemical terms, it indicates to what extent a compound will dissolve in water.
For a generic salt \(\mathrm{AB}\), which dissociates into \(\mathrm{A}^+\) and \(\mathrm{B}^-\) ions, the \(K_{\mathrm{sp}}\) formula is written as:

• \(K_{\mathrm{sp}} = [\mathrm{A}^+][\mathrm{B}^-]\)

The values within brackets represent the concentration of ions at equilibrium. Larger \(K_{\mathrm{sp}}\) values signify greater solubility, while smaller values indicate limited solubility.
It is essential to note that \(K_{\mathrm{sp}}\) is specific to slightly soluble salts, hence it does not apply to substances that are considered highly soluble, as they are assumed to dissolve completely under normal conditions.

Sodium Chloride

Sodium chloride, commonly known as table salt, is a ubiquitous substance that most know dissolves readily in water. According to solubility rules, sodium chloride (NaCl) is classified as a soluble ionic compound, meaning that it dissolves almost completely in water.
Solubility rules simplify the process of determining whether compounds dissolve in water by providing a set of general guidelines. For example, all ionic compounds containing sodium (Na\(^+\)) are tagged as soluble. Hence, it is predictable that NaCl will dissolve efficiently in water.
Despite its high solubility, stating that sodium chloride has an infinite solubility is incorrect. There's always a physical limit to solubility, marked by how much solute can be dissolved in a solvent at a given temperature. Sodium chloride's solubility reaches this limit due to its ionic nature and water's polar properties.

Equilibrium Constant

An Equilibrium Constant is a key concept in chemistry, representing the ratio of product concentrations to reactant concentrations at equilibrium for a reversible reaction. It reflects the balance point of the reaction, which is reached when the forward and reverse reactions occur at the same rate.
For a general reaction where two substances AB and CD produce AD and BC, the equilibrium constant \(K\) can be depicted as:

• \(K = \frac{[AD][BC]}{[AB][CD]}\)

This equation reveals the concentrations of the products over the reactants, all raised to the power of their stoichiometric coefficients.
When discussing solubility, the \(K_{\mathrm{sp}}\) can be seen as a specific kind of equilibrium constant relevant to the solubility of salts in water. Its magnitude gives insight into the extent of the salt's dissolution in a solvent, serving as a benchmark for comparing different salts' solubilities.