Question

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: $PC{{l}_{5(s)}}+4{{H}_{2}}{{O}_{(l)}}\to {{H}_{3}}P{{O}_{4(aq)}}+5HC{{l}_{(aq)}}$ in an experiment , $~0.360$ mol of $PC{{l}_{5}}$ was added to $2.88$ mol of water.

Answer 1

Hint : When phosphorus pentachloride is reacted with the water, it results in the formation of the acid and on the other hand, when water is reacted with fluorine, it results in the formation of the acid halide. Now you can easily complete these reactions with the help of it. Solve it.

Complete Step By Step Answer:
Here given reaction $PC{{l}_{5(s)}}+4{{H}_{2}}{{O}_{(l)}}\to {{H}_{3}}P{{O}_{4(aq)}}+5HC{{l}_{(aq)}}$
This tells you that the reaction consumes five moles of water for each mole of phosphorus pentachloride that takes half within the reaction.
Now, your goal once working out if you are managing a limiting chemical agent is to select a chemical and see if you have got enough of the second chemical to permit for all the moles of the primary chemical to require half within the reaction.
Let's decide the phosphorus pentachloride initial. so as for $0.360$ moles of phosphorus pentachloride to react, you wish to possess
$0.360moles(PC{{l}_{5}})\cdot \dfrac{4{{H}_{2}}O}{1mole(PC{{l}_{5}})}=1.44moles({{H}_{2}}O)$
You offer the reaction with $2.88$ moles of water, over enough to permit for all the moles of phosphorus pentachloride to react. This means that phosphorus pentachloride can act as a limiting chemical agent, i.e. it'll be utterly consumed before all the moles of water get the prospect to react.
In other words, water is going to be in excess. You get a similar result by choosing water. during this case, $2.88$ moles of water would need
$2.88moles({{H}_{2}}O)\cdot \dfrac{1mole(PC{{l}_{5}})}{4mole\left( {{H}_{2}}O \right)}=0.720moles(PC{{l}_{5}})$
Since you simply have $0.360$ moles of phosphorus pentachloride out there, this can be your limiting chemical agent. Now, the theoretical yield corresponds to the number of products made if all the moles of reactants that really react find you manufacturing moles of product.
Notice that the reaction produces one mole of orthophosphoric acid, ${{H}_{2}}P{{O}_{4}}$ , and five moles of acid, for one mole of phosphorus pentachloride and five moles of water. Since all the moles of phosphorus pentachloride react, the reaction can turn out
$0.360moles(PC{{l}_{5}})\cdot \dfrac{1moles(HCl)}{1mole(PC{{l}_{5}})}=0.360moles({{H}_{3}}P{{O}_{4}})$ and $0.360moles(PC{{l}_{5}})\cdot \dfrac{5moles(HCl)}{1mole(PC{{l}_{5}})}=1.80moles(HCl)$
This will be the theoretical yield for the given following reaction.

Note :
Phosphoric acid is an inorganic compound and is also known as the orthophosphoric acid . It is weakly acidic in nature and consists of three $-OH$ bonds attached to the phosphorus and one oxygen atom which is doubly bonded to the phosphorus atom.