What reaction happens when carboxylic acids are treated with calcium hydroxide and distilled?
Acetic acid (as an example of a typical carboxylic acid) reacts with calcium hydroxide to form calcium acetate. This is a simple acid-base reaction which forms a salt and water:

$$\ce{2CH3COOH + Ca(OH)2 -&gt; (CH3COO)2Ca + 2H2O}$$

Upon heating, calcium acetate undergoes decomposition to acetone and calcium carbonate. The acetone can be distilled off from the mixture, leaving behind solid calcium carbonate:

$$\ce{(CH3COO)2Ca -&gt;[\Delta] CaCO3 + 2(CH3)2C=O}$$

At even higher temperatures calcium carbonate itself can be decomposed to calcium oxide and carbon dioxide:

$$\ce{CaCO3 -&gt;[\Delta] CaO + CO2}$$

References


https://www.tut.fi/ms/muo/vert/3_organic_chemistry/carboxylic_reactions.htm
http://www.docbrown.info/page04/OilProducts10.htm