26. a) Y is the condenser*. Its function is to cool the hot vapor, causing it to condense back into liquid. X is a thermometer*. Its function is to measure the temperature of the vapor that is distilling. The final answer is $\boxed{\text{Y: Condenser, X: Thermometer}}$ b) The method illustrated is distillation, which is used to separate miscible liquids with different boiling points. i. Ethanol and water ii. Methanol and water The final answer is $\boxed{\text{i. Ethanol and water, ii. Methanol and water}}$ c) The property that makes it possible to separate the mixture using distillation is the difference in their boiling points. The final answer is $\boxed{\text{Difference in boiling points}}$