Solubility and solubility curves Knowledge-Based Study

Study notes

1. What is Solubility?

   Solubility is defined as the maximum mass of a solute that can dissolve in a specified volume or mass of a solvent at a given temperature and pressure to produce a stable solution. In general chemistry, solubility is most frequently expressed as the number of grams of solute dissolved in 100 g of water (g solute / 100 g H2O).

   States of Saturation

   Depending on the quantity of dissolved solute relative to its solubility limit at a constant temperature, solutions are categorized into three distinct states:

   • Unsaturated Solution: Contains less solute than the maximum equilibrium amount that can dissolve at that temperature. Additional solute added will continue to dissolve.
   • Saturated Solution: Contains the exact maximum amount of dissolved solute in dynamic equilibrium with undissolved solute at that temperature. Any extra solute added remains undissolved at the bottom.
   • Supersaturated Solution: An unstable state containing more dissolved solute than a saturated solution could typically hold at that temperature. It is prepared by dissolving solute at an elevated temperature and carefully cooling the solution without mechanical disturbance. Adding a seed crystal or agitating the solution induces rapid precipitation of the excess solute.

   Key Variables Influencing Solubility

   Several fundamental factors govern the extent to which a solute dissolves in a given solvent:

   • Nature of Solute and Solvent: Guided by the principle "like dissolves like", polar solutes (such as ionic salts) dissolve readily in polar solvents like water, whereas nonpolar solutes dissolve in nonpolar solvents like hexane.
   • Temperature:
     • Solids and Liquids: For most solid solutes whose dissolution process is endothermic ($\Delta H > 0$), solubility increases as temperature rises. For solutes that dissolve exothermically ($\Delta H < 0$), solubility decreases with increasing temperature.
     • Gases: The dissolution of a gas in a liquid solvent is almost universally exothermic. Consequently, increasing the temperature decreases gas solubility, allowing gas molecules to escape into the vapor phase.
   • Pressure: Pressure has a negligible effect on the solubility of liquids and solids because they are virtually incompressible. However, it profoundly affects gas solubility according to Henry's Law, which states that the solubility of a gas is directly proportional to the partial pressure of that gas above the liquid.

   Reading a Solubility Curve

   A solubility curve is a graphical representation plotting solubility (typically in g solute / 100 g H2O on the y-axis) against temperature (in °C on the x-axis). It enables the quantitative prediction of solution behavior across varying temperatures.

   Regions on the Graph

   • Points on the Curve: Any coordinate lying directly on the solubility curve represents a saturated solution at that specific temperature.
   • Points Below the Curve: Any point falling beneath the curve represents an unsaturated solution. The vertical distance from that point up to the curve indicates how many additional grams of solute can be dissolved before reaching saturation.
   • Points Above the Curve: A coordinate above the curve represents either a supersaturated solution (if all solute remains homogeneously dissolved) or a heterogeneous mixture containing a saturated solution alongside precipitated solid.

   Curves with a positive slope (sloping upward to the right) indicate endothermic dissolution, while curves with a negative slope (sloping downward to the right) reflect exothermic dissolution.

   Quantitative Analysis Using Solubility Curves

   Solubility curves allow chemists to calculate exact quantities involved during heating, cooling, and crystallization processes.

   Example: Determining Mass of Precipitate

   Consider a salt $X$ with a solubility of 80 g per 100 g of water at 60 °C and 35 g per 100 g of water at 20 °C.

   • If a saturated solution prepared in 100 g of water at 60 °C (containing 80 g of $X$) is cooled to 20 °C, the water can hold only 35 g of $X$ at the lower temperature.
   • The mass of salt that crystallizes out is: $$80\text{ g} - 35\text{ g} = 45\text{ g of } X\text{ precipitate}$$
   • If the initial mass of water is different (e.g., 250 g of water), the quantities scale proportionally using basic stoichiometric ratios: $$\text{Precipitate} = 45\text{ g} \times \frac{250\text{ g H}_2\text{O}}{100\text{ g H}_2\text{O}} = 112.5\text{ g}$$

   Fractional Crystallization

   When a mixture contains two different soluble salts, fractional crystallization can separate them by exploiting differences in their solubility curves. By heating the mixture to dissolve both components and then carefully cooling the solution, the compound with the steeper temperature dependence or lower solubility precipitates first in high purity.