Do I have this right?
Which one of these is the solute and which one is the solvent in a solution composed of a.) 25.0 g. of silver in 5.0 g. of mercury, and b.) 3.0 g. of iodine (I2) in 100.0 mL of ethanol?
a.) Mercury is the solute and silver is the solvent.
b.) Iodine is the solute and ethanol is the solvent.
b is correct.
Let me talk a little about (a). Many people classify the solute as the material present in smaller quantity and the solvent as the material present in the larger quantity. Under such rules your classification is correct. Others tend to classify the liquid as the solvent (unless there are two liquids) and the solid as the solute. Under this classification, mercury (a liquid) is the solvent and silver is the solute. Mercury "dissolves" many metals forming amalgams which are solids; i.e., silver and gold among others. I tend to go with the solid as the solute and the liquid as solute. Therefore, I would classify mercury as the solvent and silver as the solute. However, it makes little difference, which is called which, as long as people know what we are talking about.
I posted this answer but didn't identify myself properly.
No, your understanding is not correct for either part of the question.
In a solution, the solute is the substance that is dissolved in the solvent. The solvent is the substance that does the dissolving.
For part a) of the question, the solution is composed of 25.0 g of silver in 5.0 g of mercury. In this case, the solute is silver because it is the substance being dissolved, and the solvent is mercury because it is doing the dissolving. So, the correct answer for part a) is that silver is the solute and mercury is the solvent.
For part b) of the question, the solution is composed of 3.0 g of iodine (I2) in 100.0 mL of ethanol. In this case, the solute is iodine because it is being dissolved, and the solvent is ethanol because it is doing the dissolving. Therefore, the correct answer for part b) is that iodine is the solute and ethanol is the solvent.