Final answer:
By identifying chlorine as the limiting reactant and using stoichiometry based on the balanced chemical equation, the maximum amount of phosphorus trichloride produced from reacting white phosphorus with chlorine gas is calculated to be 59.87 grams.
Step-by-step explanation:
To calculate the maximum amount of phosphorus trichloride (PCl3) produced, we must first identify the limiting reactant. We start by calculating the moles of the reactants using the given molar masses. For white phosphorus (P4), which has a molar mass of 124 g/mol, we have:
moles of P4 = mass of P4 / molar mass of P4
= 12.4 g / 124 g/mol
= 0.1 moles
For chlorine gas (Cl2), which has a molar mass of 71 g/mol, we have:
moles of Cl2 = mass of Cl2 / molar mass of Cl2
= 46.6 g / 71 g/mol
= 0.656 moles
The balanced chemical equation P4(s) + 6 Cl2(g) → 4 PCl3(l) shows that 1 mole of P4 reacts with 6 moles of Cl2 to produce 4 moles of PCl3. Using stoichiometry, we can calculate how much PCl3 can be formed from the moles of the limiting reactant:
For every 1 mole of P4, 4 moles of PCl3 are produced. Given we have 0.1 moles of P4, we could produce 0.4 moles of PCl3 if P4 is limiting. However, the reaction also requires 6 moles of Cl2 to completely react with 1 mole of P4, which means we need 0.6 moles of Cl2 for the available P4. Since we only have 0.656 moles of Cl2, chlorine is not limiting.
Chlorine is the limiting reactant since 6 moles of Cl2 would be required to react with 0.1 moles of P4, and we have less than 6 moles (0.656 moles) of Cl2. We can now calculate the mass of PCl3 produced from the moles of the limiting reactant (Cl2):
moles of PCl3 produced = (moles of Cl2 / 6) x 4
= (0.656 moles / 6) x 4
= 0.437 moles
The mass of PCl3 can then be found using the molar mass of PCl3 (137 g/mol):
mass of PCl3 = moles of PCl3 x molar mass of PCl3
= 0.437 moles x 137 g/mol
= 59.87 g
Therefore, the maximum amount of phosphorus trichloride that can be produced is 59.87 g.