Question

why alkali metals prepared by electrolysis of there fused chlorides

Answer 1

chlorides in the fused state.....the ions become free and mobile and it is thus easy to discharge at the electrolyte
See....say NaCl for example...is in solid state then the ions would not be able to move freely in the electrodes and electrolysis would be VERY DIFFICULT...thus to make the ions free n mobile... is in fused or molten state

Answer 2

 I. Alkali metals are strong reducing agents, hence cannot be extracted by reduction of their oxides and other compounds.
II. Being highly positive in nature it is not possible to displace them from their salt solutions by any other element.
III. Alkali metals cannot be obtained by the electrolysis of the aqueous solution of their salts because H2 is liberated at cathode instead of alkali metal. That’s why alkali metals are prepared by electrolysis of their fused chloride.