The Williamson ether synthesis is a reaction that involves the formation of an ether from an alkyl halide and an alkoxide ion. However, it is not possible to synthesize a symmetrical ether directly from two different alkyl halides using the Williamson ether synthesis. Instead, you can synthesize a symmetrical ether by using a two-step process involving the formation of an unsymmetrical ether first, followed by a reaction that converts the unsymmetrical ether into the desired symmetrical ether.Here's a stepwise mechanism for synthesizing a symmetrical ether from two different alkyl halides:1. Choose the appropriate alkyl halides R1-X and R2-X and a suitable base B for the Williamson ether synthesis.2. Perform the Williamson ether synthesis: a. Generate the alkoxide ion by reacting the base B with an alcohol R1-OH : B + R1-OH R1-O - + HB b. Perform the nucleophilic substitution reaction between the alkoxide ion R1-O - and the alkyl halide R2-X : R1-O - + R2-X R1-O-R2 + X - 3. Now, you have an unsymmetrical ether R1-O-R2 . To convert this unsymmetrical ether into the desired symmetrical ether R1-O-R1 , you can use a reaction such as the Ullmann ether synthesis or the Simmons-Smith reaction, depending on the specific alkyl halides and reaction conditions.For example, the Ullmann ether synthesis involves the reaction of an unsymmetrical ether with a copper catalyst and an additional equivalent of the alkyl halide R1-X to form the symmetrical ether:4. Perform the Ullmann ether synthesis: a. React the unsymmetrical ether R1-O-R2 with a copper catalyst Cu and the alkyl halide R1-X under appropriate conditions: R1-O-R2 + Cu + R1-X R1-O-R1 + R2-X + CuXNow, you have successfully synthesized the desired symmetrical ether R1-O-R1 from two different alkyl halides using a combination of the Williamson ether synthesis and the Ullmann ether synthesis.