The hard white crust inside a kettle often comes from calcium carbonate deposited when hard water is heated. It is not simply “dried water”: calcium and bicarbonate species begin dissolved, but heating and the loss of carbon dioxide shift the balance, leaving sparingly soluble calcium carbonate on the surface. The US Geological Survey likewise notes that heating hard water can form such deposits.
Vinegar contains dilute acetic acid. Hydrogen ions supplied by the acid react with carbonate, ultimately producing water and carbon dioxide; calcium that was locked in the solid remains in solution as charged ions and is more readily rinsed away. The small bubbles seen during soaking are mainly carbon dioxide. Vinegar therefore does not mechanically “soften” the scale: it changes the chemical form of the material.
This also explains why vinegar is not equally effective on every deposit. Scale containing substantial silicates, iron compounds or other materials may respond differently, and some metals, stone surfaces and seals can be damaged by acid. Unplug and cool a kettle, follow the manufacturer’s instructions, and rinse it thoroughly afterwards. Because vinegar is acidic, it must never be mixed with chlorine bleach; the combination can release toxic chlorine gas.
https://www.usgs.gov/water-science-school/science/hardness-water
https://www.cdc.gov/chemical-emergencies/chemical-fact-sheets/chlorine.html
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