
Adding salt to a pot does not make the water boil sooner. In fact, dissolved salt reduces the tendency of water molecules to escape from the liquid surface, so the solution must reach a higher temperature before its vapour pressure equals the surrounding pressure. This is boiling-point elevation, one of the colligative properties of solutions.
In an ordinary kitchen, however, the change is small. Using the ideal dilute-solution approximation, about 10 grams of table salt in one litre of water raises the boiling point by roughly 0.2°C. Heating the solution from room temperature to that slightly higher boiling point requires a little more energy, so the claim that salt makes water reach the boil faster has no physical basis. The pan, lid, heat source, altitude and amount of water usually matter much more.
Once boiling, salted water can indeed be slightly hotter than pure water, but the difference at normal cooking concentrations is too small to shorten pasta cooking noticeably. Enough salt to create a large increase would make the food unpalatable. The main reason to salt cooking water is flavour, not speed.
It is also worth separating “a higher boiling point” from “easier to boil”. The first means the liquid must reach a higher temperature; the second would mean sustained boiling begins sooner. The phrases sound similar, but their physical meanings point in opposite directions.
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Solutions_and_Mixtures/Colligative_Properties/Boiling_Point_Elevation
https://pubs.acs.org/doi/10.1021/cr900105w
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