How do you determine the limiting reagent and what is the theoretical yield of the following problem?

Question

Phosphorus pentachloride reacts with water to give phosphoric acid and hydrogen chloride according to the following reaction:
#PCl_5 +4H_2O -> H_3PO_4+5HCl# in an experiment , 0.360 mol of #PCl_5# was added to 2.88 mol of water.

Noah Aldrich · Accepted Answer

Here's how you can do that.

The mole ratios in which the chemical species involved in the reaction find themselves are indicated by the stoichiometric coefficients that appear in the balanced chemical equation. As for you, you've #"PCl"_ (5(s)) + color(red)(4)"H"_ 2"O"_ ((l)) -> "H"_ 3 "PO"_ (4(aq)) + 5 "HCl"_ ((aq))# This tells you that the reaction consumes #color(red)(5)# moles of water for every mole of phosphorus pentachloride that takes part in the reaction. Choosing a reactant and determining if there is enough of the second reactant to enable all the moles of the first reactant to participate in the reaction is the aim of determining if you are working with a limiting reagent. Let's pick phosphorus pentachloride first. In order for #0.360# moles of phosphorus pentachloride to react, you need to have #0.360 color(red)(cancel(color(black)("moles PCl"_5))) * (color(red)(4)color(white)(a)"H"_2"O")/(1color(red)(cancel(color(black)("mole PCl"_5)))) = "1.44 moles H"_2"O"# You supply the reaction with #2.88# moles of water, more than enough to allow for all the moles of phosphorus pentachloride to react. This indicates that the phosphorus pentachloride will function as a limiting reagent, meaning that it will be consumed entirely before every mole of water has an opportunity to react. That is, there will be an abundance of water. You get the same result by picking water. In this case, #2.88# moles of water would require #2.88color(red)(cancel(color(black)("moles H"_2"O"))) * ("1 mole PCl"_5)/(color(red)(4)color(red)(cancel(color(black)("moles H"_2"O")))) = "0.720 moles PCl"_5# Since you only have #0.360# moles of phosphorus pentachloride available, this will be your limiting reagent. The amount of product produced if every mole of reactant that truly reacts yields a mole of product is known as the theoretical yield. Notice that the reaction produces #1# mole of phosphoric acid, #"H"_2"PO"_4#, and #5# moles of hydrochloric acid, for #1# mole of phosphorus pentachloride and #color(red)(5)# moles of water. Since phosphorus pentachloride reacts in all of its moles, the reaction will result in #0.360 color(red)(cancel(color(black)("moles PCl"_5))) * ("1 mole H"_3"PO"_4)/(1color(red)(cancel(color(black)("mole PCl"_5)))) = "0.360 moles H"_3"PO"_4# and #0.360 color(red)(cancel(color(black)("moles PCl"_5))) * "5 moles HCl"/(1color(red)(cancel(color(black)("mole PCl"_5)))) = "1.80 moles HCl"# This is the theoretical yield of the reaction.

Cooper Anderson · Answer

undefined To determine the limiting reagent in a chemical reaction, you compare the stoichiometry of the reactants to the actual amounts available. The reactant that produces the least amount of product is the limiting reagent.

To find the theoretical yield, use the amount of the limiting reagent and its stoichiometric ratio with the desired product. This calculation assumes that all reactants are completely consumed and no side reactions occur.

How do you determine the limiting reagent and what is the theoretical yield of the following problem?

Phosphorus pentachloride reacts with water to give phosphoric acid and hydrogen chloride according to the following reaction: #PCl_5 +4H_2O -> H_3PO_4+5HCl# in an experiment , 0.360 mol of #PCl_5# was added to 2.88 mol of water.

Phosphorus pentachloride reacts with water to give phosphoric acid and hydrogen chloride according to the following reaction:
#PCl_5 +4H_2O -> H_3PO_4+5HCl# in an experiment , 0.360 mol of #PCl_5# was added to 2.88 mol of water.