Question

Balance the following equation:
 $ Zn + HN{O_3} \to 4Zn{(N{O_3})_2} + {N_2}O + {H_2}O $
(A) $ 4Zn + 10HN{O_3} \to 4Zn{(N{O_3})_2} + {N_2}O + 5{H_2}O $
(B) $ 4Zn + 5HN{O_3} \to 4Zn{(N{O_3})_2} + 3{N_2}O + 5{H_2}O $
(C) $ 4Zn + 15HN{O_3} \to 4Zn{(N{O_3})_2} + 2{N_2}O + 5{H_2}O $
(D) None of these

Answer 1

Hint: Any chemical reaction can be expressed in the form of a chemical equation in which the reactants and products are expressed as their chemical symbols. A balanced equation gives us the information about the molar ratios in which reactants react and the products are produced according to their stoichiometric coefficients.

Complete answer:
The given chemical equation represents the reaction that is taking place between zinc metal and nitric acid to produce zinc nitrate, dinitrogen oxide and water as the products.
The chemical reactions follow the laws of chemical combination and one of these laws known as the law of definite proportion states that the atoms combine to form molecules only in specific proportions. Another such law is called the law of Conservation of mass that states that the mass remains conserved throughout the reaction. This means that no new element can be formed in a chemical reaction. Thus the atoms of each element are only present in a fixed amount and the reaction only causes a rearrangement of atoms.
These laws indicate the need to balance the chemical equations in such a manner that the number of atoms of each element remain same on the reactant as well as the product side which ensures that the total mass of reactants and the total mass of products remains unchanged and equal.
The reaction given is:
 $ Zn + HN{O_3} \to 4Zn{(N{O_3})_2} + {N_2}O + {H_2}O $
To have a balanced equation, we first multiply $ HN{O_3} $ by a factor of ten, so that the number of nitrogen atoms becomes equal on both sides.
Ton doing so, the number of hydrogen atoms and oxygen atoms change. Therefore, the water molecule is multiplied by a factor of five to obtain ten hydrogens and thirty oxygen atoms on each side.
Lastly, the zinc atoms need to be multiplied by a factor of four to balance them.
The final balance equation is:
 $ 4Zn + 10HN{O_3} \to 4Zn{(N{O_3})_2} + {N_2}O + 5{H_2}O $
The correct option is (a).

Note:
The moles of products produced in and reactants consumed can be calculated by keeping the ratio of stoichiometric coefficients in mind but this is only applicable for a balanced chemical equation and not any chemical equation.