Answer:
The balanced chemical equation is:
2Br + 7O2 → 2Br2O7
From the equation, we can see that 7 moles of oxygen are required to react with 2 moles of bromine to form 2 moles of dibromine heptoxide.
First, we need to determine the limiting reagent:
The moles of oxygen gas can be calculated as:
n(O2) = m/M = 425 g / 32 g/mol = 13.28 mol
The moles of bromine can be calculated as:
n(Br) = m/M = 350 g / 80 g/mol = 4.375 mol
The limiting reagent is bromine because it is present in a smaller quantity.
Theoretical yield of dibromine heptoxide can be calculated using the moles of limiting reagent:
n(Br2O7) = n(Br) × (2 mol Br2O7 / 2 mol Br) × (7 mol O2 / 2 mol Br2O7) = 4.375 × 7 / 2 = 15.3125 mol
The molar mass of Br2O7 is:
M(Br2O7) = 2 × M(Br) + 7 × M(O) = 2 × 80 g/mol + 7 × 16 g/mol = 296 g/mol
The theoretical yield of dibromine heptoxide can be calculated as:
mass(Br2O7) = n(Br2O7) × M(Br2O7) = 15.3125 mol × 296 g/mol = 4534.375 g or 4.53 kg
Therefore, the theoretical yield of dibromine heptoxide is 4.53 kg.