Question

In the reaction;
$CO + \dfrac{1}{2}{O_2} \to C{O_2};{N_2} + {O_2} \to 2NO$
${\text{10 mL}}$ of the mixture containing carbon monoxide and nitrogen required ${\text{7 mL}}$ oxygen to form $C{O_2}$ and ${\text{NO}}$, on combustion.
The volume of ${N_2}$ in the mixture will be:
A) $\dfrac{7}{2}mL$
B) $\dfrac{{17}}{2}mL$
C) ${\text{4 mL}}$
D) ${\text{7 mL}}$

Answer 1

Analyze the reactions given in the question and try to relate the elements with others according to the use of the number of moles. One can also find out the relation between oxygen and nitrogen elements and relate them with the reaction of formation of nitrogen oxide and find out the correct choice.

Complete answer:

1. First of all let us analyze the given reactions in the question. The reaction of formation of carbon dioxide is as,
   $CO + \dfrac{1}{2}{O_2} \to C{O_2}$
   In the above reaction, one mole of carbon monoxide is reacted with a half mole of an oxygen molecule to form one mole of carbon dioxide.
2. Now as we know the number of moles is always directly proportional to the volume. Now let us consider the volume of ${N_2}$ as ${\text{x}}$ and this volume will be equal to the volume of ${O_2}$ which is required to react with it.
3. Now let us consider the volume of ${\text{CO}}$ as ${\text{y}}$ and the volume of ${O_2}$ reacting with it will be $\dfrac{y}{2}$. By the statement of ${\text{10 mL}}$ of mixture containing carbon monoxide and nitrogen required ${\text{7 mL}}$ oxygen we can say that,
   $x + y = 10$
   As $\dfrac{y}{2} = 7$
   Therefore, we can get values of ${\text{x}}$ and $y$ as ${\text{4}}$ and ${\text{6}}$ respectively.
4. We get the volume of ${N_2}$ as ${\text{4 mL}}$. And by the above reaction $\dfrac{1}{2}{N_2} + \dfrac{1}{2}{O_2} \to NO$
   In the above reaction if there is $\dfrac{1}{2}$ mole of ${O_2}$ is used by ${\text{CO}}$ then there will be $\dfrac{1}{2}$ mole of ${O_2}$ is used by ${N_2}$ and therefore, the volume of ${N_2}$ in the mixture can be $\dfrac{7}{2}$ which shows option A as the correct choice.

Note:
The volume of the above reactions is measured in identical conditions and hence can be related to each other. The products formed in both the reactions are oxides and both reactions are carried in presence of oxygen molecules and one can relate this volume of oxygen used for the determination of the volume of nitrogen in the mixture.