(b) Calculate the amount of zirconium produced (in kg) if a reactor were charged with 310.0 kg and 29.0 kg Na.
To calculate the amount of zirconium produced, we need to determine the stoichiometric ratio between zirconium and sodium in the reaction.
The balanced equation for the reaction between sodium (Na) and zirconium (Zr) is as follows:
2 Na + ZrO2 ⟶ 2 Na2O + Zr
From the balanced equation, we can see that for every 2 moles of sodium (Na), 1 mole of zirconium (Zr) is produced.
Step 1: Convert the mass of sodium (Na) to moles:
Molar mass of sodium (Na) = 22.99 g/mol
Moles of sodium (Na) = Mass of sodium (Na) / Molar mass of sodium (Na)
Moles of sodium (Na) = 29.0 kg / (22.99 g/mol * 1000 g/kg)
Step 2: Use the stoichiometric ratio to determine the moles of zirconium (Zr):
Moles of zirconium (Zr) = (1/2) * Moles of sodium (Na)
Step 3: Convert moles of zirconium (Zr) to mass:
Molar mass of zirconium (Zr) = 91.22 g/mol
Mass of zirconium (Zr) = Moles of zirconium (Zr) * Molar mass of zirconium (Zr)
Now, we can plug in the values and calculate the amount of zirconium produced:
Mass of sodium (Na) = 29.0 kg
Molar mass of sodium (Na) = 22.99 g/mol
Molar mass of zirconium (Zr) = 91.22 g/mol
Moles of sodium (Na) = 29.0 kg / (22.99 g/mol * 1000 g/kg) = 1.26 mol
Moles of zirconium (Zr) = (1/2) * Moles of sodium (Na) = (1/2) * 1.26 mol = 0.63 mol
Mass of zirconium (Zr) = Moles of zirconium (Zr) * Molar mass of zirconium (Zr) = 0.63 mol * 91.22 g/mol = 57.49 g
Therefore, the amount of zirconium produced is 57.49 g (or 0.05749 kg).