We have the following chemical reaction:
P₄ + 10 Cl₂ → 4 PCl₅
Identifying the limiting reactant.
mass of  P₄ = 28 g
mass of Clâ‚‚ = 53 g
number of moles = mass / molecular weight
number of moles of Pâ‚„ = 28 / 124 = 0.226 moles
number of moles of Clâ‚‚ = 53 / 71 = 0.746 moles
From the reaction we see that 1 mole of Pâ‚„ will react with 10 moles of Clâ‚‚ so 0.226 moles of Pâ‚„ will react with 2.226 moles of Clâ‚‚, but we have only 0.746 moles of Clâ‚‚. So the limiting reactant will be Clâ‚‚.
Part B
From the previous calculations we know that 28 g of Pâ‚„ are equal to 0.226 moles moles of Pâ‚„.
Now, knowing the chemical reaction, we devise the following reasoning:
if     1 mole of P₄ produces 4 moles of PCl₅
then  0.226 moles of P₄ produces X moles of PCl₅
X = (0.226 Ă— 4) / 1 = 0.904 moles of PClâ‚…
Part C
From the previous calculations we know that 53 g of Clâ‚‚ are equal to 0.746 moles moles of Clâ‚‚.
Now, knowing the chemical reaction, we devise the following reasoning:
if     10 moles of Cl₂ produces 4 moles of PCl₅
then  0.746 moles of Cl₂ produces X moles of PCl₅
X = (0.746 Ă— 4) / 10 = 0.298 moles of PClâ‚…