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The Corey-House alkane synthesis is carried out by treating an alkyl halide with
(A) Lithium metal
(B) Copper metal
(C) Lithium metal following by reaction with cuprous iodide and then treating the product with an alkyl halide
(D) Cuprous iodide followed by reaction with alkyl halide

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Hint: In organic chemistry, an alkane or paraffin is an acyclic saturated alkane consisting of hydrogen and carbon bonds arranged in different structures. All carbon bonds in alkane are single carbon bonds only. The Corey-House alkane synthesis is carried out in three steps.

Complete Step by step solution:
Alkane synthesis:
It's a process of synthesis or producing or manufacturing of alkanes.
Alkane can be produced in many different ways which are as follows,
Petroleum refining: alkanes are separated in an oil refinery by fractional distillation and processed into many products.
Fischer-Tropsch: is a method to synthesize liquid hydrocarbons from carbon monoxide and hydrogen.
Laboratory preparation- There is usually no need of preparing alkane in the laboratory as alkane is produced commercially, although when alkane is produced in the laboratory there is usually a side-product.
Preparation of alkane from other organic compounds:
From alkenes and alkynes: when alkenes or alkynes are subjected to hydrogenation reaction by treating them with hydrogen in presence of palladium or platinum or nickel as catalyst. In this, powdered catalyst is preferred to increase the surface area so that adsorption of hydrogen on catalyst increases. Hydrogen gets attached to the catalyst to form hydrogen-catalyst bond which leads to weakening of hydrogen- hydrogen bond, thereby leading to addition of hydrogen on alkane and alkynes. The reaction is exothermic as alkane is more stable as it has sigma bonds.
From haloalkanes: Alkanes are manufactured from haloalkanes using different methods.
Corey- House- Synthesis: When haloalkane is treated with dialkyl lithium cuprate which is also known as Gilman's reagent. By this reaction higher alkane is obtained. Steps of Corey-House-synthesis reaction:
Alkyl halide reacts with Lithium in presence of dry ether to form alkyl lithium
 $ R - X + 2Li \to R - Li + LiX $
Alkyl lithium reacts with CuI and forms dialkyl lithium cuprate.
 $ 2R - Li + CuI \to {R_2}CuLi + LiI $
Dialkyl lithium cuprate reaction with alkyl halide to give alkane.
 $ {R_2}CuLi + {R^1}X \to R - {R^1} + R - Cu + LiX $
Therefore, the correct option is C.

Note:
Some uses of alkane are:
-They are important raw materials of the chemical industry.
-Natural gas mainly contains methane and ethane.