To increase the solubility of a solute, the following options apply:
a. increasing the surface area of the solute - This allows more solute particles to be in contact with the solvent, facilitating dissolution.
b. heating the solution - For most solids, increasing temperature increases solubility. However, for gases, solubility typically decreases with increased temperature.
d. stirring the solution - Stirring helps distribute the solute and solvent more evenly, which can enhance the rate of dissolution.
So, the correct answers are a, b, and d.
Options c (cooling the solution) and e (decreasing the surface area of the solute) would generally not increase solubility. Cooling tends to decrease the solubility of solids, and decreasing surface area slows down the dissolution process.