Answer
$P \space and \space O_2: $ $\frac{4 \space moles \space P}{5 \space moles \space O_2}$ and $\frac{5 \space moles \space O_2}{4 \space moles \space P}$
$P \space and \space P_2O_5:$ $ \frac{4 \space moles \space P}{2 \space moles \space P_2O_5}$ and $\frac{2 \space moles \space P_2O_5}{4 \space moles \space P}$
$O_2 \space and \space P_2O_5:$ $\frac{5 \space mole \space O_2}{2 \space moles \space P_2O_5}$ and $\frac{2 \space moles \space P_2O_5}{5 \space mole \space O_2}$
Work Step by Step
1. Use the balance coefficients to write the mole-mole equalities:
4 moles $P$ = 5 moles $O_2$
4 moles $P$ = 2 moles $P_2O_5$
5 moles $O_2$ = 2 moles $P_2O_5$
2. Use these equalities to write the conversion factors:
$\frac{4 \space moles \space P}{5 \space moles \space O_2}$ and $\frac{5 \space moles \space O_2}{4 \space moles \space P}$
$\frac{4 \space moles \space P}{2 \space moles \space P_2O_5}$ and $\frac{2 \space moles \space P_2O_5}{4 \space moles \space P}$
$\frac{5 \space mole \space O_2}{2 \space moles \space P_2O_5}$ and $\frac{2 \space moles \space P_2O_5}{5 \space mole \space O_2}$
