Solubility

The solubility of a solute in a given solvent is the maximum concentration that the solute can have when the dissolution is at equilibrium. If that was a mouthful, let's break it down. Imagine dissolving a solute, like sugar, into water. If you stir it, you can get the sugar to dissolve a lot more quickly. Note that stirring does not affect the solubility of a solute by any means. It simply increases the reaction rate of a dissolution process.

By the way, the molar concentration of solubility described by the definition above can be converted to a mass solubility through the molar mass of the solute.

However, if you stir for long enough, you'll notice that stirring no longer helps as the solution is pretty much as dissolved as it can get. If dissolving no longer works, then your solute has reached its solubility concentration.

If your solution involves dissolving a gas in a liquid, the gas's solubility is given by Henry's Law:

This states that the solubility concentration of a gas in liquid s proportional to its partial pressure. The constant k is a constant that is unique to each gas, in mol/(L atm) or any equivalent unit of molar concentration/pressure.

Note that the formation of a solution as described below is the same as a dissolution process

The formation of viable solutions is considered to be spontaneous, meaning the change in Gibbs Free Energy of a dissolution process is negative. Why is this? Well, remember that the change in Gibbs Free Energy of a process can be expressed through the following equation:

So, the temperature of a solution is of course always positive in Kelvins. The change in entropy of a dissolution process is positive. This is because before you dissolve the solute, it still has molecular order. Once it dissolves, the ions dissociate and disperse throughout the solvent, making the resulting solution very disordered. This means the change in entropy is positive as the system's entropy increased.

Next, for enthalpy, the enthalpy of the dissolution is negative. This is kind of tricky to explain but follow the diagram above for a better intuition as to why the enthalpy of dissolution is negative.

The equilibrium for a dissolution process can be expressed through saturated solutions. A saturated solution is one in which the solute ions are at their maximum concentration before they precipitate. To conceptualize this, imagine a solution with water and sugar. If you pour enough sugar into the water, almost every water molecule will bond with the ions of a sugar molecule. But because you poured extra, there will be a few sugar molecules with nothing to bond with so they'll precipitate. A saturated solution is one in which the sugar is fully dissolved but if even a bit more is poured, a precipitate will form.

Saturated solutions are thus at equilibrium, as the reaction rates of dissolution(the solid dissociating into aqueous solute ions) and precipitation(the formation of solid precipitate from the aqueous ions) are equal.

Let's take an example with AgCl(Silver chloride) dissolved in water. The dissolution equation is:

AgCl(s) ⇌ Ag⁺(aq) + Cl^-(aq)

The reaction going right to left is the precipitation reaction while the reaction going left to right is the dissolution reaction where the solid solute dissociates into the ions that comprise it. The solubility product(solubility equilibrium constant) for this reaction is:

Now, let's take our AgCl-water solution and add some FeCl₃ to it. You may think nothing happens, but if you thought so, you'd be incorrect. Note that there are Cl^- ions in both AgCl and FeCl₃, which means the addition of FeCl₃ to our solution will increase the Cl^- ions in solution. Since Fe isn't in the original solution, it is a spectator ion. This effect is known as the common ion effect.

Since the amount of Cl^- ions in solutions increases, by Le Chatelier's Principle, the equilibrium of the dissolution process will shift to the left away from the ions to the precipitate. This means that at equilibrium, the concentration of Cl ions will be slightly higher and the concentration of Ag ions will be lower. However, the amount of ions that actually dissolved will be less. The equilibrium concentration of Cl is only higher because it was technically added to the solution. However, the amount of Cl ions that dissolved from the original solute is less, so the solubility of the solute decreases while keeping the solubility product the same.

A similar effect is observed with hydroxide ions and hydrogen cations if those ions are part of the original solute compound. If you add hydroxide ions to a solution with hydrogen ions, or vice versa, the the ion in the original solute gets neutralized, which means its equilibrium concentration decreases. This shifts the equilibrium to the right, increasing the solubility.

So, if you know about the equilibrium constant, you'll know about the reaction quotient, which is found in the same way the solubility product is. This is denoted by Q_sp, the solubility reaction quotient. If:

Q_sp is less than K_sp, the system will dissociate into more ions so more ions will dissolve and no precipitation will be observed.

Q_sp is more than K_sp, the system is past the solubility so precipitate will form as the system shifts left to restore equilibrium.

Of course, if Q_sp is equal to K_sp, then the system is at equilibrium.