In the industrial preparation of acrylic acid, there are two main steps. In the first step, calcium carbide (CaC₂) reacts with water to produce acetylene (C₂H₂) and calcium hydroxide:
CaC₂(s)+2H2O(g)→C₂H₂(g)+Ca(OH)₂(s)
In the second step, acetylene (C₂H₂), carbon dioxide (CO₂), and water react to form acrylic acid:
(CH₂CHCOOH): 6₂2H₂(g)+3CO₂(g)+4H₂O(g) → 5CH₂CHCOOH(g).
Given that the yield of the first step is 85% and the yield of the second step is 89%, calculate the mass of calcium carbide required to produce 5.0 kg of acrylic acid.