Answer:
152.57 g
Step-by-step explanation:
The balanced chemical equation for the reaction between calcium and nitrogen gas to form calcium nitride is:
3Ca + N2 → Ca3N2
From the balanced equation, we can see that the mole ratio between calcium and calcium nitride is 3:1. This means that 3 moles of calcium react to form 1 mole of calcium nitride.
First, let's calculate the number of moles of calcium and nitrogen gas given:
Mass of calcium = 56.6 g
Molar mass of calcium (Ca) = 40.08 g/mol
Moles of calcium = Mass of calcium / Molar mass of calcium = 56.6 g / 40.08 g/mol = 1.41 mol
Mass of nitrogen gas = 30.5 g
Molar mass of nitrogen gas (N2) = 28.02 g/mol
Moles of nitrogen gas = Mass of nitrogen gas / Molar mass of nitrogen gas = 30.5 g / 28.02 g/mol = 1.09 mol
Since the reaction has a 90% yield, only 90% of the limiting reactant (which is calcium in this case) will be converted to product. Therefore, we need to multiply the moles of calcium by 0.90 to account for the yield:
Moles of calcium nitride formed = Moles of calcium x Yield = 1.41 mol x 0.90 = 1.27 mol
Now, using the mole ratio from the balanced equation, we can determine the mass of calcium nitride formed:
Molar mass of calcium nitride (Ca3N2) = 40.08 g/mol (molar mass of calcium) x 3 + 14.01 g/mol (molar mass of nitrogen) x 2 = 120.25 g/mol
Mass of calcium nitride formed = Moles of calcium nitride formed x Molar mass of calcium nitride = 1.27 mol x 120.25 g/mol = 152.57 g
So, the mass of calcium nitride formed in the reaction is 152.57 g.