At the beginning of the distillation(first drops distilling), the temperature of the boiling liquid will____than the temperature read on the properly positioned thermometer.
When we add heat to a system, that heat can do only 1 of 2 things. It can change the temperature or it can change the phase.
When we are doing a distillation, all the heat added to the system is busy turning the liquid into gas. So the temperature will stay constant at the boiling point of the substance, and a properly placed thermometer should read the same temperature.
The liquid in the distillation flask contains a combination of the high boiling point and low boiling point liquid, so it will boil at a temperature which is in between the high boiling point and low boiling point.
While the initial vapor is composed mostly of the low boiling component, thus the temperature will be the low boiling point.
You are overthinking it. What really happens is that the bp of the boiling liquid is raised because of a solute (the other liquid) but only slightly. So you are correct that the new bp of the boiling liquid is slightly (negligibly) higher. But really, you should only be concerned about bp elevation when a solution is made up of a volitlie solvent and a nonvolitile solute (like NaCl).
For a distillation, you can assume that each liquid's bp remains unchanged. The lower bp liquid will boil off first.
The question is asking "what is temp of the bp compared to the temp reading on the thermometer." The answering doesn't really have anything to do with bp elevation. It really is: how does the temp of the liquid compare to the temp reading of the thermometer, which should be the same because the temp of a boiling liquid doesn't change during its phase change.
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