In my lab report, I am asked to

"Find the solubility of Ca(OH)2 in H2O as the temperature increases. Explain (in terms of energy) the reasons for this trend."

From what I have found, Ca(OH)2's solubility goes down, but I have no idea why! It isn't a gas... it's a solid dissolved in liquid, right?
Thank you for your time.

Here is a site that has a graph of a number of salts versus temperature.

http://galileo.phys.virginia.edu/education/outreach/8thgradesol/TempSolubility.htm

Note that KNO3, NH4Cl, NaCl and some others increase solubility with increasing temperature (although to different extents). These salts are endothermic when dissolved in water. (Next time you're in the lab add a little KNO3 or NH4Cl to H2O in a test tube and shake it. Feel that it gets cold.) So the solution process is endothermic as shown by the following simplistic equation.
solid + heat ==> ions(aq). By Le Chatelier's Principle, adding heat increases solubility and that's what the graph shows.

There are some compounds, notably gases but not all are gases, in which the solution process is exothermic. NH3, HCl, and a few others are in this category. These equations look like this.
gas(or solid) ==> solution + heat
and Le Chatelier's principle tells us that heat will favor the reverse direction. The solution of Ca(OH)2 is exothermic so we would expect the solubility to decrease at higher temperatures. Having said all of that we need to remember that solution, although it sounds simple enough, is a complicated process involving several discrete steps. For example, NaOH and KOH are EXTREMELY exothermic when dissolved but the solubility increases with higher temperatures. Other processes must be at work with those examples.

You're correct that Ca(OH)2 is a solid and it dissolves in water (H2O) to form a solution. The solubility of a solid in a liquid, like water, generally varies with temperature.

To understand why the solubility of Ca(OH)2 decreases as the temperature increases, we need to consider the concept of energy. When a solid dissolves in a liquid, energy changes occur at the molecular level.

The dissolution process involves breaking the bonds holding the solid particles together and forming new interactions between the solute particles and the solvent molecules. This process requires energy, which is called the lattice energy or enthalpy of dissolution. The lattice energy represents the energy required to separate the ions in the solid compound.

As temperature increases, the energy supplied to the system also increases. This added energy enhances the kinetic energy of the molecules, making them move more rapidly and collide more frequently. The increased molecular motion helps to overcome the attractive forces holding the solid particles together, facilitating the dissolution process.

However, in the case of Ca(OH)2, there is an opposing effect related to the solute-solvent interactions. When Ca(OH)2 dissolves in water, the Ca2+ and OH- ions are surrounded by water molecules due to the electrostatic attractions between the ions and the polar water molecules. This process is called solvation or hydration.

The hydration process releases energy, known as the hydration energy or enthalpy of hydration. The strength of the hydration interaction between the ions and water molecules is influenced by temperature. As temperature increases, the thermal motion of water molecules becomes more pronounced, leading to weaker and less favorable solute-solvent interactions.

This decrease in solute-solvent interaction strength results in a decrease in the solubility of Ca(OH)2 as temperature increases. The decrease occurs because the energy released during hydration becomes less significant compared to the energy required to break the lattice energy of the solid at higher temperatures.

In summary, while the increased kinetic energy at higher temperatures promotes the dissolution of solid Ca(OH)2, the weakening of solute-solvent interactions due to enhanced thermal motion of water molecules reduces the solubility. This overall effect causes the solubility of Ca(OH)2 to decrease as temperature increases.