[mburt]

Hi,

In my textbook, they offer a quite complicated way of finding the limiting reactant. I think I may have found a simple way of discovering it but I want to make sure it works first.

The question:

What is the maximum mass of PCl₃ that can be obtained from 125g P₄ and 323g Cl₂?

P₄(s) + 6Cl₂(g) 4PCl₃(l)

My answer:

Of course you have to find the number of moles of limiting reactant, convert to moles of PCl₃, then convert to grams of. I did the procedure that the textbook laid out and I found some parts to be unnecessary. Here's what I tried: get number of moles of both reactants (to get a standardized measure of quantity), then divide each reactant by their mole ratio in the formula. The smaller number of "moles" between the two reactants must be limiting. Is this theory correct?

125g P₄ 1.01mol P₄ / 1 = 1.01mol P₄

323g Cl₂ 4.56mol Cl₂ / 6 = 0.759mol Cl₂

Therefore Cl₂ is limiting. An analogy that I thought of was if you had to build a cube requiring 2 red sides and 4 black sides. If you had 30 red sides, and 64 black sides, then you can only produce 15 boxes- red is completely used and black is in excess.

30 red / 2 = 15
64 black / 4 = 16

Therefore red is limiting.

The textbook's way:

Get moles of P₄ and Cl₂, calculate a mole ratio by dividing moles of Cl₂ and P₄. Next if the calculated mole ratio is < 6/1 then Cl₂ is limiting, and if the mole ratio is > 6/1 then P₄ is limiting.

It seems like the textbook's way requires memorizing of which reactant goes where in the mole ratio, and the > and < might get confusing.

Thanks and please let me know if my method is valid

[Hunter2]

It goes more faster.

The reaction says you need 1 mole P₄ and 6 mole Cl₂ to obtain 4 mole PCl₃

Calculation of the mole of phosphorous and chlorine give 1.01 mol P₄ and 4.56 mole Cl₂

You have instead of 1:6 only 1:4.56 , so chlorine will limit the reaction.

[camptzak]

Even simpler
The reactant with the higest number next to it is the limiting reagent.

[Hunter2]

No

in case of we would have let say 568 g equal 8 mole Chlorine, then Phosphorous is the limiting reactant.

[Borek]

The reactant with the higest number next to it is the limiting reagent.

So when you react hydrogen with oxygen to produce water

2H₂ + O₂ -> 2H₂O

hydrogen is always the limiting reactant?

[Borek]

125g P₄ 1.01mol P₄ / 1 = 1.01mol P₄

323g Cl₂ 4.56mol Cl₂ / 6 = 0.759mol Cl₂

OK. What you have calculated is the ratio of moles of the substance to so called "mole of reaction".

Mathematically it is equivalent to the book approach, just the numbers are rearranged. If you feel better solving it this way - go for it.

[mburt]

Yep I think I got it... Thanks again.

However I don't agree with camptzak saying that the limiting reactant is the reactant with the highest coefficient. In cases where the molar mass is different (it always is for different compounds) I don't see how there is any relation between coefficients in the chemical formula and the limiting reactant. A reactant with a low coefficient but a really high molar mass would result in a high number of moles (amount of substance), the converse also being true.