The carbonate ion concentration is gradually increased in a solution containing divalent cations of magnesium, calcium, strontium, barium, and manganese. Which of the following carbonates will form first? Which of the following will form last? Explain. \(\begin{array}{ll}\text { (a) } \mathrm{MgCO}_{3} & K_{\mathrm{sp}}=3.5 \times 10^{-8}\end{array}\) (b) \(\mathrm{CaCO}_{3} \quad K_{\mathrm{sp}}=4.2 \times 10^{-7}\) (c) \(\operatorname{Sr} \mathrm{CO}_{3} \quad K_{\mathrm{sp}}=3.9 \times 10^{-9}\) \(\begin{array}{ll}\text { (d) } \mathrm{BaCO}_{3} & K_{\mathrm{sp}}=4.4 \times 10^{-5}\end{array}\) (e) \(\mathrm{MnCO}_{3} \quad K_{\mathrm{sp}}=5.1 \times 10^{-9}\)

The solubility product constant, commonly abbreviated as Ksp, is a crucial parameter in the study of solution chemistry. It provides a numerical value that reflects the extent to which a compound can dissolve in a solution. The concept of Ksp becomes particularly important when dealing with sparingly soluble salts.

For instance, a salt with a high Ksp value indicates that the compound is comparatively soluble and will dissolve more readily in water. In contrast, salts with low Ksp values are much less soluble and are more likely to precipitate out of solution. Precipitation occurs when the product of the concentrations of the ions in the solution exceeds the Ksp value, resulting in the formation of a solid compound.

Understanding how to compare and use Ksp values is essential when trying to predict which compounds will precipitate first in a solution with multiple potential precipitates. It's an invaluable tool in the study and application of chemistry, from laboratory experiments to geochemical predictions and beyond.

Precipitation is the process in which dissolved ions in a solution form a solid compound. The likelihood of a compound precipitating is directly related to its solubility product constant, or Ksp. To understand when precipitation occurs, one must consider the concept of 'ionic product' which is the product of concentrations of the precipitating ions in the solution.

If the ionic product is less than the Ksp, the solution is 'unsaturated' and no precipitation occurs. If the ionic product equals the Ksp, the solution is 'saturated', and the system is at equilibrium, meaning the solid phase is in dynamic balance with its dissolved ions. However, if the ionic product exceeds the Ksp, the solution becomes 'supersaturated', and precipitation ensues, resulting in the formation of a solid from the ions in solution.

This concept helps explain why, in a mixture of different potential precipitates, the ion with the lowest solubility product constant will precipitate first. Its lower threshold for exceeding the Ksp is met sooner as ion concentrations increase in solution.

The concentration of carbonate ions, CO3^2-, in a solution plays a pivotal role in chemical equilibria involving carbonates. As the concentration of carbonate ions is increased, the potential for precipitation of carbonate compounds also increases, especially if divalent cations such as Ca^2+, Mg^2+, or Ba^2+ are present.

This rise in carbonate ion concentration can tip the balance of a saturated solution towards precipitation. Specifically, for each carbonate compound, the product of the concentration of the carbonate ion and the divalent cation in solution must not exceed the compound's respective Ksp for the solution to remain free of solid precipitate. Understanding the interplay between carbonate ion concentration and the Ksp values of different carbonate compounds is key in predicting and controlling the formation of precipitates in commercial, environmental, or biological systems.