Solubility

Solubility refers to the maximum amount of solute that can be dissolved into a solvent. The phases of the solute and solvent can be any of the three phases, but mostly we will be discussing aqueous solutions where the solvent is liquid water.

A solution can be in one of the three states: saturated; unsaturated; or hypersaturated. In a saturated solution, the solution has reached its maximum capacity to dissolve a certain solute, which is the solubility of that solute. Any more solute added into a saturated solution will not be dissolved. Microscopically, dissolution and separation occurs at the same rate so that it seems like nothing is happening in gross, which is the state of dynamic equilibrium. However, being saturated with a certain solute does not mean it cannot dissolve any more of other substances.

An unsaturated solution contains less amount of solute than the solubility, and thus it can dissolve more of that solute. When a solution is hypersaturated, it has more solute dissolved than the solubility. Hypersaturation is an extremely unstable state, and just a little bit of impulse will lead to the crystallization of the excess solute.

The solubility of solids is commonly represented by the amount in grams of the solid that can be dissolved into 100 grams of water. Molarity, or moles per liter, is also used for solids with relatively low solubility. The dissolution reactions of most highly soluble solids into water are endothermic processes. As a result, most solids tend to dissolve better into water at higher temperatures.

For gases, we normally represent their solubility by the volume of gas that can be dissolved into 1 ml of water. The mass in grams that can be dissolved into 100 grams of water is also often used. The dissolution of most gases into water are exothermic processes, which implies that gases usually dissolve better into water at lower temperatures.

A solubility curve illustrates the solubility of a substance according to temperature. As most solids become more soluble at higher temperatures, the solubility curve of a typical solid would look like the figure below.

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Note that any point on the curve indicates a saturated solution. Any point above the curve indicates a hypersaturated solution, whereas any point below the curve means the solution is unsaturated. Using the solubility curve, we can calculate the amount of solute additionally dissolved or crystallized according to change in temperature. Suppose we have a saturated solution containing $b$ grams of solute in 100 grams of water at ${t_2}^\circ\text{C}.$ If we lower the temperature to ${t_1}^\circ\text{C},$ then $b-a$ grams of solute will be crystallized.

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The figure above is the solubility curve of some solid compound $\ce{X}.$ Suppose we have 270 grams of a saturated $\ce{X}$ solution at $60^\circ\text{C}.$ Find the amount (in grams) of $\ce{X}$ that becomes crystallized when we lower the temperature of the solution to $30^\circ\text{C}.$

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Note that the mass ratio between the solute and solvent of a saturated $\ce{X}$ solution at $60^\circ\text{C}$ is $80:100=4:5.$ Thus a 270-gram-solution of $\ce{X}$ at $60^\circ\text{C}$ will contain 120 grams of $\ce{X}$ and 150 grams of water. At $30^\circ\text{C},$ 150 grams of water can dissolve up to $40\times\frac{3}{2}=60$ grams of $\ce{X},$ according to the given solubility curve. Therefore the amount of $\ce{X}$ that becomes crystallized when the temperature is decreased to $30^\circ\text{C}$ is $120\text{ g}-60\text{ g}=60\text{ g}.$ $_\square$