Question

what is the balanced chemical equation for this reaction?
$ce{h3po4 + hcl -> pcl5 + h2o}$
$ce{2h3po4 + 10hcl -> 2pcl5 + 4h2o}$
$ce{h3po4 + 5hcl -> pcl5 + 4h2o}$
$ce{h3po4 + 5hcl -> pcl5 + h2o}$
$ce{2h3po4 + 5hcl -> 2pcl5 + 3h2o}$

Explanation:

Step1: Count P atoms

Left: 1 (in $\text{H}_3\text{PO}_4$), Right: 1 (in $\text{PCl}_5$) → P is balanced for now.

Step2: Count Cl atoms

Left: 1 (in $\text{HCl}$), Right: 5 (in $\text{PCl}_5$). Multiply $\text{HCl}$ by 5:
$\text{H}_3\text{PO}_4 + 5\text{HCl}
ightarrow \text{PCl}_5 + \text{H}_2\text{O}$

Step3: Count H atoms

Left: $3 + 5 = 8$ (from $\text{H}_3\text{PO}_4$ and $\text{HCl}$), Right: 2 (in $\text{H}_2\text{O}$). Multiply $\text{H}_2\text{O}$ by 4:
$\text{H}_3\text{PO}_4 + 5\text{HCl}
ightarrow \text{PCl}_5 + 4\text{H}_2\text{O}$

Step4: Count O atoms

Left: 4 (in $\text{H}_3\text{PO}_4$), Right: 4 (in $4\text{H}_2\text{O}$) → O is balanced.

Step5: Verify all atoms

P: 1=1; Cl: 5=5; H: 8=8; O:4=4. All atoms balanced.

Answer:

$\text{H}_3\text{PO}_4 + 5\text{HCl}
ightarrow \text{PCl}_5 + 4\text{H}_2\text{O}$ (the second option)