fill in the gaps to balance the equation. use the smallest set of whole numbers to balance the equation and…

Explanation:

Step1: Balance phosphorus atoms

Let the coefficient of $HPO_2$ be $a$, the coefficient of $P_2O_3$ be $b$ and the coefficient of $H_2O$ be $c$. For phosphorus atoms, we have $a = 2b$.

Step2: Balance hydrogen atoms

For hydrogen atoms, $a=2c$.

Step3: Balance oxygen atoms

For oxygen atoms, $2a = 3b + c$. Substitute $a = 2b$ into $2a=3b + c$, we get $4b=3b + c$, so $b = c$. Let $b = 1$, then $a = 2$. The balanced equation is $2HPO_2\rightarrow P_2O_3+H_2O$.

Step4: Count atoms in reactants and products

• For phosphorus ($P$) in reactants: In $2HPO_2$, the number of $P$ atoms is $2$. In products, in $P_2O_3$ the number of $P$ atoms is $2$.
• For oxygen ($O$) in reactants: In $2HPO_2$, the number of $O$ atoms is $2\times2 = 4$. In products, in $P_2O_3$ there are 3 $O$ atoms and in $H_2O$ there is 1 $O$ atom, so total $3 + 1=4$.
• For hydrogen ($H$) in reactants: In $2HPO_2$, the number of $H$ atoms is $2$. In products, in $H_2O$ the number of $H$ atoms is $2$.

Answer:

The balanced - equation coefficients: 2, 1, 1

Element	Reactant	Products
P	2	2
O	4	4
H	2	2