Answer
a. $ SO_2 $ and $ O_2 $: $$ \frac{ 2 \space moles \space SO_2 }{ 1 \space mole \space O_2 } \space and \space \frac{ 1 \space mole \space O_2 }{ 2 \space moles \space SO_2 }$$
$ SO_2 $ and $ SO_3 $: $$ \frac{ 2 \space moles \space SO_2 }{ 2 \space moles \space SO_3 } \space and \space \frac{ 2 \space moles \space SO_3 }{ 2 \space moles \space SO_2 }$$
$ O_2 $ and $ SO_3 $: $$ \frac{ 1 \space mole \space O_2 }{ 2 \space moles \space SO_3 } \space and \space \frac{ 2 \space moles \space SO_3 }{ 1 \space mole \space O_2 }$$
b. $ P $ and $ O_2 $: $$ \frac{ 4 \space moles \space P }{ 5 \space moles \space O_2 } \space and \space \frac{ 5 \space moles \space O_2 }{ 4 \space moles \space P }$$
$ P $ and $ P_2O_5 $: $$ \frac{ 4 \space moles \space P }{ 2 \space moles \space P_2O_5 } \space and \space \frac{ 2 \space moles \space P_2O_5 }{ 4 \space moles \space P }$$
$ O_2 $ and $ P_2O_5 $: $$ \frac{ 5 \space moles \space O_2 }{ 2 \space moles \space P_2O_5 } \space and \space \frac{ 2 \space moles \space P_2O_5 }{ 5 \space moles \space O_2 }$$
Work Step by Step
1. Identify all pairs:
a. We can find the mole-mole factors between: $SO_2$ and $O_2$, $SO_2$ and $SO_3$, $O_2$ and $SO_3$ .
b. We can find the mole-mole factors between: $P$ and $O_2$, $P$ and $P_2O_5$, $O_2$ and $P_2O_5$.
2. Use the coefficients of the balanced equation to write the conversion factors.
a. $2SO_2(g) + O_2(g) \longrightarrow 2SO_3(g)$
Thus, if we use 2 $SO_2$ moles, we will need 1 $O_2$ mole to react with it, and it will produce 2 $SO_3$ moles.
2 $SO_2$ moles = 1 $O_2$ mole
2 $SO_2$ moles = 2 $SO_3$ moles
1 $O_2$ mole = 2 $SO_3$ moles
b. $4P(s) + 5O_2(g) \longrightarrow 2P_2O_5(s)$
Thus, if we use 4 $P$ moles, we will need 5 $O_2$ moles to react with it, and it will produce 2 $P_2O_5$ moles.
4 $P$ moles = 5 $O_2$ mole
4 $P$ moles = 2 $P_2O_5$ moles
5 $O_2$ mole = 2 $P_2O_5$ moles
