A pure liquid has a constant boiling point (at constant pressure). A change in boiling during distillation is an indication of impurity. The opposite, proposition, however, is not always true, and a constant boiling point does not necessarily mean that the liquid is pure.
This is because, at the boiling point, vapor and liquid are in equilibrium, and, if the composition of the vapor and liquid remains constant through the process, the temperature will also remain constant.
The boiling point can differ by location depending on pressure. Why does not a pure liquid in a distilling flask vaporize all at once whilst the boiling temperature is reached? Additional heat must be supplied for a phase change to occur.
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