Limestone is composed primarily of calcium carbonate, A \(1.0-\mathrm{mm}^{3}\) chip of limestone was accidentally dropped into a water-filled swimming pool, measuring \(10 \mathrm{~m} \times 7 \mathrm{~m} \times 2 \mathrm{~m}\). Assuming that the carbonate ion does not function as a Bronsted base and that the \(\mathrm{pH}\) of the water is 7 , will the pebble dissolve entirely? The density of calcium carbonate is \(2.71 \mathrm{~g} \cdot \mathrm{cm}^{-3}\).

Calcium carbonate ((CaCO_3)) is an ionic compound widely found in geological formations such as limestone and chalk, and also in organisms like mollusks and corals. Solubility is an important property that dictates how much of this compound can dissolve in water. Calcium carbonate is considered to be only slightly soluble in water, meaning that only a small amount of this compound can be dissolved at a given time under standard conditions.

{(CaCO_3 (s) ↔ Ca^{2+} (aq) + CO_3^{2-} (aq))}
The solubility is often expressed as the solubility product constant ((K_{sp})), which for calcium carbonate at room temperature is approximately 3.3 x 10^{-9}, a low value reflecting its limited solubility. This equilibrium process is influenced by various factors, such as temperature and the presence of other ions in solution.

In the context of the educational problem, the mass of a 1.0 mm³ limestone chip can be calculated, but when it comes to dissolving in a large body of water like a swimming pool, calcium carbonate's low solubility means that it is unlikely the chip will dissolve entirely. When students tackle homework involving solubility, understanding the concept of solubility product and the equilibrium process is essential for explaining the behavior of such sparingly soluble compounds in water.

The Bronsted-Lowry theory defines an acid as a substance that can donate a proton ((H^+)), while a base is a substance that can accept a proton. This theory expands the definition of acids and bases beyond those simply containing hydrogen or hydroxide ions.

For instance, in aqueous solutions, water can act as both a Bronsted acid and a Bronsted base. This dual behavior is fundamental to many chemical reactions in water. When a substance like calcium carbonate is introduced to water, we'd consider whether the carbonate ion ((CO_3^{2-})) could act as a Bronsted base and thus alter the water's pH. In the textbook exercise, it is assumed that the carbonate ion does not act as a Bronsted base; if it did, it would accept a proton and potentially change the pH value by forming bicarbonate ((HCO_3^-)).

Understanding this aspect of the Bronsted base theory is crucial to determining the subsequent chemical reactions that might influence solubility and the pH of the solution. In the given scenario, assuming that the carbonate ion doesn't behave as a base simplifies the problem by eliminating the need to consider changes in pH due to the dissolution of the limestone chip.

The pH of a solution is a measure of its acidity or basicity, which in turn can impact the solubility of certain compounds. For calcium carbonate, pH plays a critical role. As a rule of thumb, the solubility of calcium carbonate decreases as the pH of the solution increases, meaning it is less soluble in more alkaline conditions. Conversely, in an acidic environment, increased solubility is observed because the excess (H^+) ions react with the carbonate ions to form bicarbonate, which is more soluble.

In a neutral pH of 7, like the water in the swimming pool from our exercise, calcium carbonate has a very low solubility. No additional protons are available from the water to react with (CO_3^{2-}), and consequently, there's little to no increase in solubility that would result from a decrease in pH. It is, therefore, pretty safe to conclude that, with a neutral pH and a carbonate ion not acting as a Bronsted base, the limestone chip in the exercise would not completely dissolve in the pool's large volume of water.

Students learning about solubility should consider how pH affects ionic compounds like calcium carbonate. This is not only crucial for chemistry and environmental science courses but also for practical situations, such as understanding water quality and treatment processes in real-life applications.