Titanium (Ti) can be produced by the reaction of metallic sodium (Na) with titanium tetrachloride vapor (TiCl4). The byproduct of this reaction is sodium chloride (NaCl). Calculate the amount of titanium produced (in kg) when a reactor is charged with 87.0 kg of TiCl4 and 20.0 kg of Na.
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To calculate the amount of titanium produced in this reaction, we need to determine the limiting reactant. The limiting reactant is the one that is completely consumed first, thus determining the maximum amount of product that can be formed.
Let's start by writing the balanced chemical equation for the reaction:
2 Na + TiCl4 -> Ti + 2 NaCl
According to the stoichiometry of the balanced equation, 2 moles of Na react with 1 mole of TiCl4 to produce 1 mole of Ti.
First, we need to convert the masses of TiCl4 and Na to moles using their respective molar masses:
Molar mass of TiCl4 = 47.867 + (4 × 35.453) = 189.948 g/mol
Molar mass of Na = 22.990 g/mol
Moles of TiCl4 = Mass of TiCl4 / Molar mass of TiCl4
= 87.0 kg × 1000 g/kg / 189.948 g/mol
= 458.54 mol
Moles of Na = Mass of Na / Molar mass of Na
= 20.0 kg × 1000 g/kg / 22.990 g/mol
= 869.08 mol
To determine the limiting reactant, we compare the moles of Na and TiCl4 in a 2:1 ratio. Since the ratio is 2:1, if the moles of Na are more than half the moles of TiCl4, then Na is the limiting reactant. Otherwise, TiCl4 is the limiting reactant.
Moles of Na required for complete reaction = 1/2 × Moles of TiCl4
= 1/2 × 458.54 mol
= 229.27 mol
Since we have 869.08 mol of Na present, which is greater than 229.27 mol, Na is the excess reactant and TiCl4 is the limiting reactant.
The moles of Ti produced will be equal to the moles of TiCl4 used in the reaction:
Moles of Ti = Moles of TiCl4 used = 458.54 mol
Finally, we need to convert moles of Ti to kilograms using the molar mass of titanium:
Molar mass of Ti = 47.867 g/mol
Mass of Ti = Moles of Ti × Molar mass of Ti
= 458.54 mol × 47.867 g/mol
= 21,955.20 g
Converting grams to kilograms:
Mass of Ti = 21,955.20 g / 1000
= 21.96 kg
Therefore, the amount of titanium produced in this reaction is approximately 21.96 kg.