Robert S. answered • 04/05/21

Patient PhD Chemist with 40 Years of R&D And Teaching

Hello, Caitlyn,

The balanced equation tells us that, under ideal conditions (theoretical) we'll get 4 moles of PCl_{3} for every 1 mole of P_{4}. The molar ratio is 4 moles PCl_{3}/mole P_{4}. Or, 0.25 moles P_{4}/mole PCl_{3}.

We want to wind up with 512g of PCl_{3}, but we're told this reaction only has a 78% yield. Phooey. (the technical term for this level of yield). So let's plan ahead and adjust the amount of ending material we should target for by dividing the 512 grams by 0.78, which tells us we should target for 656.4 grams of PCl_{3}, so that we wind up with (0.78*656.4) 512 grams.

656.4 grams of PCl_{3} is 4.78 moles of the material (656.4~~g~~/137.3~~g~~/mole). Multiply this by the molar ratio we deduced earlier (0.25 moles P_{4}/PCl_{3}) to find the moles P_{4} we need.

(0.25 moles P_{4}/PCl_{3})*(4.78 moles PCl_{3}) = 1.195 moles P_{4}. Convert to grams by multiplying by the molar mass of P_{4}. That gives us 148.1 grams P_{4}. Slightly different than option 2, but that may be due to a difference in atomic masses or rounding.

Bob