Question

An element A reacts with compound BO₃ to produce A₃O₄ and B₂O₃. The number of moles of A₃O₄ produced if 1 mole each of A and BO₃ is reacted, is
(A) 3
(B) 1
(C) $\dfrac{1}{3}$
(D) $\dfrac{2}{3}$

Answer 1

Hint : According to the Principle of Atom Conservation (POAC), the total number of reactant atoms must equal the total number of product atoms. Elements are substances made up of just one atom form. Compounds are made up of atoms from various elements bound together by chemical bonds. A mixture is created by combining elements and compounds.

Complete Step By Step Answer:
According to the Principle of Atom Conservation (POAC), the total number of reactant atoms must equal the total number of product atoms. Elements are substances made up of just one atom form. Compounds are made up of atoms from various elements bound together by chemical bonds. A mixture is created by combining elements and compounds.
In this case, another material may be involved in the reaction between A and BO₃. As a result, we use POAC in these types of questions (Principle of Atom Conservation). A₃O₄ contains three A atoms, implying that three A atoms react to form one molecule of A₃O₄. In the same way, two molecules of BO₃ combine to form one molecule of B₂O₃.
$3A + 2B{O_3} \to {A_3}{O_4} + {B_2}{O_3}$

| A| BO₃| A₃O₄| B₂O₃
---|---|---|---|---
No. of moles of reactants| 1| 1| |
No. of moles of reactants /stoichiometric coefficient| $\dfrac{1}{3}$ | $\dfrac{1}{2}$ | |
No. of moles of substances after reaction| 0| $\dfrac{1}{3}$ | $\dfrac{1}{3}$ | $\dfrac{1}{3}$

Now, since three moles of A react with two moles of BO₃, one mole of A can react with two-thirds of a mole of BO₃.
1 mole of A yields $\dfrac{1}{3}$ mole of A₃O₄, while $\dfrac{2}{3}$ mole of BO₃ yields $\dfrac{1}{3}$ mole of B₂O₃.
Hence, option c is the answer.

Note :
According to the Principle of Atom Conservation (POAC), the total number of reactant atoms must equal the total number of product atoms. Elements are substances made up of just one atom form. Compounds are made up of atoms from various elements bound together by chemical bonds. A mixture is created by combining elements and compounds.