High-purity silicon is obtained using a three-step process. The first step involves heating solid silicon dioxide, SiO₂, with solid carbon to give solid silicon and carbon monoxide gas. In the second step, solid silicon is converted into liquid silicon tetrachloride, SiCl₄, by treating it with chlorine gas. In the last step, SiCl₄ is treated with hydrogen gas to give ultrapure solid silicon and hydrogen chloride gas. 

(a) Write balanced chemical equations for the steps involved in this three-step process. 

(b) Calculate the masses of carbon, chlorine, and hydrogen required per kilogram of silicon.