Question

What would be the stoichiometric coefficient of $P$ and $HN{O}_3$ respectively, in the net balanced equation for the given redox reaction:
$P+HN{O}_3\to HP{O}_3+NO+H_{2}O$

• A. $5,3$
• B. $1,1$
• C. $2,3$
• D. $3,5$

Answer 1

The correct option is D $3,5$

The redox reaction is -
$\stackrel{0}{P}+H\stackrel{+5}{N}{O}_3\to H\stackrel{+5}{P}{O}_3+\stackrel{+2}{N}O+H_{2}O$
$\stackrel{0}{P}\to H\stackrel{+5}{P}{O}_3$----- oxidation
So, $P$ , acts as a reducing agent.

$H\stackrel{+5}{N}{O}_3\to \stackrel{+2}{N}O$--- reduction
So, $HN{O}_3$ , acts as a oxidising agent.
n-factor calculation formula :
$n_f=(|O.S{.}_{Product}-O.S{.}_{Reactant}|\times \text{number of atom}$
For oxidation :
$n_f=(|5-0|\times 1=5$
For reduction:
$n_f=(|2-5|\times 1=3$

Balance atom undergoing oxidation and reduction.
$P+HN{O}_3\to HP{O}_3+NO+H_{2}O$

Simplest ratio of n- factor's $=5:3$

Cross mutiply the oxidising and reducing agents with ratio of n-factors. and balancing the main elements other than oxygen and hydrogen.
$3P+5HN{O}_3\to 3HP{O}_3+5NO+H_{2}O$

Balance atoms oxygen.
$3P+5HN{O}_3\to 3HP{O}_3+5NO+H_{2}O$

Balance hydrogen.
$3P+5HN{O}_3\to 3HP{O}_3+5NO+H_{2}O$

balance charge
charge in reactant side = 0
charge in product side = 0
so the balanced equation is $3P+5HN{O}_3\to 3HP{O}_3+5NO+H_{2}O$
the coefficient of $P$ and $HN{O}_3$ are 3 and 5 respectively.