We have to have the same number of atoms of each species in both sides of the reaction.
Lets call:
a: mols of H3PO4
b: mols of P2O5
c: mols of H2O
Balance for hydrogen H:
[tex]a\cdot3=c\cdot2[/tex]
Balance for Phosphorus P:
[tex]a\cdot1=b\cdot2[/tex]
Balance for Oxygen O:
[tex]a\cdot4=b\cdot5+c\cdot1[/tex]
We can express a b in function of c, and then solve backwards:
[tex]3a=2c\longrightarrow a=\frac{2}{3}c[/tex][tex]a=2b\longrightarrow b=\frac{1}{2}a=\frac{1}{2}\cdot\frac{2}{3}c=\frac{1}{3}c[/tex]
This system has infinite solutions. The third equation gives an identity, so we must fix a value for c and then calculate the others.
As b and c are "thirds" of c, we select c=3.
Then:
[tex]\begin{gathered} a=\frac{2}{3}c=\frac{2}{3}\cdot3=2 \\ b=\frac{1}{3}c=\frac{1}{3}\cdot3=1 \end{gathered}[/tex]
As b=1, we know that is the lowest possible combination of integers:
Answer:
- 2 mols of H3PO4
- 1 mol of P2O5
- 3 mols of H2O
