Question

In redox reaction: $Fe + HN{O_3} \to Fe{(N{O_3})_2} + N{H_4}N{O_3} + {H_2}O$, what would be the coefficient of $HN{O_3},Fe{(N{O_3})_2},N{H_4}N{O_3}$?
(A) $1:10:4$
(B) $10:4:1$
(C) $4:10:4$
(D) $4:1:4$

Answer 1

As we are very well aware with the term coefficient which is basically a multiplier or any factor that is responsible for measuring any particular property of any substance such as the number of moles, number of atoms or molecules as well as any volume. It is considered the stoichiometric ratio.

Complete step-by-step answer: As we know that a redox reaction is the one that involves the processes of oxidation and reduction taking place simultaneously in the same reaction. And we also know that the coefficient ratio of any reaction is basically the ratio or its moles or molecules telling us about the amount of reactants which are used to form one or more than one products. For instance: a classical balancing method involves the balancing by adding the stoichiometric coefficient on the reactant and product sides.
A very common example involves:
${H_2} + {O_2} \to {H_2}O$
We can balance it by the classical method where we can add a stoichiometric before hydrogen and water to balance the whole equation. So, we will get:
$2{H_2} + {O_2} \to 2{H_2}O$
Similarly, in the above given redox reaction we will first try to balance this equation as we can see that the number of atoms are different in reactants and products. We see that only one iron atom is present in the reactant side but two atoms of iron are present in product, same way only one molecule of nitrate is present in the reactant and more than in product. So, we can add stoichiometric coefficients on both sides and then balance this equation as:
$4Fe + 10HN{O_3} \to 4Fe{(N{O_3})_2} + N{H_4}N{O_3} + 3{H_2}O$
Thus, we can say that four moles or atoms or molecules of iron reacts with ten moles, atoms or molecules of nitric acid resulting in the formation of four moles or molecules of iron nitrate, one mole of ammonium nitrate and three moles or molecules of water.
Hence, the coefficient ratio of $HN{O_3}:Fe{(N{O_3})_2}:N{H_4}N{O_3}$ will be equivalent to $10:4:1$.

Therefore, the correct answer is (B).

Note: Always remember that the given redox reactions should be balanced to calculate the ratio of their coefficient or simply their stoichiometric coefficients. For balancing, count the number of atoms on the right hand side and the left hand side and then equalise the number of atoms or molecules accordingly.