Why is the temperature graph sigmoidal in simple distillation of components with very different bps? I'm writing an organic chemistry lab report on distillation and I thought I understood this, but the more I look at my lab textbook, I realize I don't.  My textbook 1 explains that the temperature of a mixture will rise continuously while it boils and distills if it is composed of two components with similar boiling points, but take on a sigmoidal shape when they are

When a liquid mixture is distilled, often the temperature does not
remain constant but increases throughout the distillation. The reason
for this is that the composition of the vapor that is distilling
varies continuously during the distillation (see Figure 14.3B).


I don't understand this sentence: &quot;The reason for this is that the composition of the vapor that is distilling varies continuously during the distillation.&quot; I understand why it is true, but not why it is an explanation for the shape of these graphs. Let's say I'm distilling volatile component B from non-volatile component A. If the boiling point of the mixture is the point at which the vapor pressure of the mixture equals the atmospheric pressure, what does the composition of the vapor have to do with anything?  The relevant pressure is the atmospheric pressure, right?  I would think that as component B is boiled off, the vapor pressure of the mixture would decrease, because the mixture has less B, by Raoult's law, Ptotal = PA + PB = PA°NA + PB°NB, and as its vapor pressure goes down, its boiling point goes up.  I don't see why this isn't happening continuously.
Is the relevant pressure not the atmospheric pressure, but some additional pressure exerted by the vapor in the flask?  (It's been a long time since I took general chemistry.)

Pavia, D. L., Lampman, G. M., Kriz, G. S., &amp; Engell, R. G. (2011). A small-scale approach to: Organic laboratory techniques. Belmont, CA: Thomson Brooks/Cole
You must understand... in an experiment, the sigmoidal shape will never have infinite slope... This would be a discontinuity... the sigmoidal shape (rightmost) and the &quot;curve&quot; (middle image) are essentially representing identical phenomena... there is a transition from one pure component to another. The only difference is how abrupt the change is... and this is determined by the endpoints/boiling points for each component. The more abrupt the change from one to another pure component, the steeper the slope of the change. I hope this helps. I can speak to this further, if necessary.