# Diphosphorus pentoxide reacts with water to produce phosphoric acid (H_3PO_4). How do you write the balanced equation for this reaction?

Jan 15, 2016

${\text{P"_4"O"_text(10(s]) + 6"H"_2"O"_text((l]) -> 4"H"_3"PO}}_{\textrm{4 \left(a q\right]}}$

#### Explanation:

The interesting thing about diphosphorus pentoxide, ${\text{P"_2"O}}_{5}$, is that it usually exists as a dimer.

This implies that ${\text{P"_2"O}}_{5}$ is actually the compound's empirical formula and that you should use ${\text{P"_4"O}}_{10}$ as its molecular formula.

Now, diphosphorus pentoxide reacts violently with water to form phosphoric acid, ${\text{H"_3"PO}}_{4}$. The reaction is highly exothermic and leads to the formation of toxic fumes.

The unbalanced chemical equation for this reaction looks like this

${\text{P"_4"O"_text(10(s]) + "H"_2"O"_text((l]) -> "H"_3"PO}}_{\textrm{4 \left(a q\right]}}$

To balance this equation, start by multiplying the phosphoric acid by $4$ to get equal numbers of atoms of phosphorus on both sides of the equation

${\text{P"_4"O"_text(10(s]) + "H"_2"O"_text((l]) -> 4"H"_3"PO}}_{\textrm{4 \left(a q\right]}}$

Notice that you have $2$ atoms of hydrogen on the reactants' side and $12$ on the products' side. Multiply the water molecule by $6$ to balance the hydrogen atoms out.

Incidentally, this will also balance out the atoms of oxygen, since you'd now have $16$ on the reactants' side and $16$ on the products' side.

The balanced chemical equation for this reaction will thus be

${\text{P"_4"O"_text(10(s]) + 6"H"_2"O"_text((l]) -> 4"H"_3"PO}}_{\textrm{4 \left(a q\right]}}$

It's worth mentioning that diphosphorus pentoxide is a very powerful dehydrating agent.

SIDE NOTE You'll sometimes see this reaction written using the empirical formula of diphosphorus pentoxide, ${\text{P"_2"O}}_{5}$. In that case, the balanced chemical equation will be

${\text{P"_2"O"_text(5(s]) + 3"H"_2"O"_text((l]) -> 2"H"_3"PO}}_{\textrm{4 \left(a q\right]}}$