Which shows equilibrium between solute and solvent? I'm stumped.

a. 2 M CaCl2
b. 1 g Na2CO3 & 100 mL H2O
c. 2 mL methanol & 4 mL hexane
d. 1 mL H2O & 3 mL ethanol

I was stumped, also, but after thinking long and hard I believe the answer is C. Choices a, b, and d are cases in which the solute is completely soluble in the solvent. Methanol and hexane are not miscible so there is an equilibrium set up between the two for the solubility of one in the other.

To determine which option shows equilibrium between solute and solvent, we need to consider the properties of solutes and solvents.

A solute is a substance that gets dissolved in a solvent, and a solvent is the substance in which the solute is dissolved. Equilibrium occurs when the rate of dissolution of the solute is equal to the rate of precipitation (re-crystallization of the solute). In other words, it is the point at which the dissolved solute and the undissolved solute are in balance.

Let's analyze each option to find the one that best represents equilibrium.

a. 2 M CaCl2:
CaCl2 is a soluble compound. The concentration of 2 M indicates that there are 2 moles of CaCl2 dissolved in 1 liter of water (the solvent). This option is not at equilibrium because all the solute has dissolved in the solvent without any undissolved solute remaining.

b. 1 g Na2CO3 & 100 mL H2O:
Na2CO3 is also a soluble compound. However, the given quantity of 1 g is insufficient to establish equilibrium in 100 mL of water (the solvent). This option is not at equilibrium because some of the solute has dissolved, but there is still undissolved solute remaining.

c. 2 mL methanol & 4 mL hexane:
Methanol and hexane are both organic solvents and do not typically form a solution with each other. In this case, they are immiscible, meaning they do not freely mix or dissolve. This option does not indicate equilibrium between solute and solvent.

d. 1 mL H2O & 3 mL ethanol:
Water (H2O) and ethanol are both polar solvents that can dissolve in each other. However, the given amounts of 1 mL and 3 mL are not sufficient to establish equilibrium. This option is not at equilibrium because there is more solvent than solute.

In conclusion, none of the given options (a, b, c, d) represents equilibrium between solute and solvent.