Question

A \[{\text{NX}}\] is produced by the following step reactions
1. ${\text{M}} + {{\text{X}}_2} \to {\text{M}}{{\text{X}}_2}$
2. \[{\text{M}}{{\text{X}}_2} + {{\text{X}}_2} \to {{\text{M}}_3}{{\text{X}}_8}\]
3. \[{{\text{M}}_3}{{\text{X}}_8} + {{\text{N}}_2}{\text{C}}{{\text{O}}_3} \to {\text{NX}} + {\text{C}}{{\text{O}}_2} + {{\text{M}}_3}{{\text{O}}_4}\]
How much ${\text{M}}$ (metal) is consumed to produce $206{\text{ gm}}$ of \[{\text{NX}}\]. (Take at wt of ${\text{M}} = 56$, ${\text{N}} = 23$, ${\text{X}} = 80$)
a. $336{\text{ gm}}$
b. $56{\text{ gm}}$
c. $\dfrac{{14}}{3}{\text{ gm}}$
d. $\dfrac{7}{4}{\text{ gm}}$

Answer 1

Hint:We have to calculate the mass of ${\text{M}}$ (metal) consumed to produce $206{\text{ gm}}$ of \[{\text{NX}}\]. To solve this calculate the mole ratio of ${\text{M}}$ (metal) and \[{\text{NX}}\]. Calculate the number of moles of both ${\text{M}}$ (metal) and \[{\text{NX}}\] by taking the given mass the molar mass.

Formula Used: ${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {{\text{gm}}} \right)}}{{{\text{Molar mass}}\left( {{\text{gm/mol}}} \right)}}$

Complete answer:
First we have to determine a balanced chemical equation which gives the stoichiometry between ${\text{M}}$ (metal) and \[{\text{NX}}\].
We are given three equations as follows:
${\text{M}} + {{\text{X}}_2} \to {\text{M}}{{\text{X}}_2}$ …… (1)
\[{\text{M}}{{\text{X}}_2} + {{\text{X}}_2} \to {{\text{M}}_3}{{\text{X}}_8}\] …… (2)
\[{{\text{M}}_3}{{\text{X}}_8} + {{\text{N}}_2}{\text{C}}{{\text{O}}_3} \to {\text{NX}} + {\text{C}}{{\text{O}}_2} + {{\text{M}}_3}{{\text{O}}_4}\] …… (3)
Multiply equation (1) by 3. Thus,
${\text{3M}} + 3{{\text{X}}_2} \to 3{\text{M}}{{\text{X}}_2}$ …… (4)
Balance the equation (2) by changing the coefficient of ${\text{M}}{{\text{X}}_2}$ to 3. Thus,
\[{\text{3M}}{{\text{X}}_2} + {{\text{X}}_2} \to {{\text{M}}_3}{{\text{X}}_8}\] …… (5)
Add equation (4), equation (5) and equation (3). Thus,
${\text{3M}} + 43{{\text{X}}_2} + {{\text{N}}_2}{\text{C}}{{\text{O}}_3} \to {\text{NX}} + {\text{C}}{{\text{O}}_2} + {{\text{M}}_3}{{\text{O}}_4}$ …… (6)
Now, calculate the molar mass of \[{\text{NX}}\] from the given atomic weights. Thus,
Molar mass of \[{\text{NX}}\] $ = 23 + 80$
Molar mass of \[{\text{NX}}\] $ = 103{\text{ gm/mol}}$
Thus, the molar mass of \[{\text{NX}}\] is $103{\text{ gm/mol}}$.
Now, calculate the number of moles of \[{\text{NX}}\] using the equation as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {{\text{gm}}} \right)}}{{{\text{Molar mass}}\left( {{\text{gm/mol}}} \right)}}$
We are given that $206{\text{ gm}}$ of \[{\text{NX}}\] is produced. i.e. the mass of \[{\text{NX}}\] is $206{\text{ gm}}$. And the molar mass of \[{\text{NX}}\] is $103{\text{ gm/mol}}$. Thus,
${\text{Number of moles of NX}} = \dfrac{{206{\text{ gm}}}}{{103{\text{ gm/mol}}}}$
${\text{Number of moles of NX}} = 2{\text{ mol}}$
Thus, the number of moles of \[{\text{NX}}\] are $2{\text{ mol}}$.
From equation (6), we can see that the mole ratio of ${\text{M}}$ (metal) and \[{\text{NX}}\] is $3:1$. i.e. three moles of ${\text{M}}$ (metal) are required to produce one mole of \[{\text{NX}}\]. But the number of moles of \[{\text{NX}}\] are $2{\text{ mol}}$.
Thus, to produce $2{\text{ mol}}$ of \[{\text{NX}}\], $6{\text{ mol}}$ of ${\text{M}}$ (metal) are required.
Now, we will calculate the mass of ${\text{M}}$ (metal) using the equation as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {{\text{gm}}} \right)}}{{{\text{Molar mass}}\left( {{\text{gm/mol}}} \right)}}$
${\text{Mass}}\left( {{\text{gm}}} \right) = {\text{Number of moles}}\left( {{\text{mol}}} \right) \times {\text{Molar mass}}\left( {{\text{gm/mol}}} \right)$
We are given that the atomic mass of ${\text{M}}$ (metal) is $56{\text{ gm/mol}}$. And $6{\text{ mol}}$ of ${\text{M}}$ (metal) are required. Thus,
${\text{Mass}} = 6{\text{ mol}} \times 56{\text{ gm/mol}}$
${\text{Mass}} = 336{\text{ gm}}$
Thus, the mass of ${\text{M}}$ (metal) consumed to produce $206{\text{ gm}}$ of \[{\text{NX}}\] is $336{\text{ gm}}$.

Thus, the correct option is (a) $336{\text{ gm}}$.

Note:
Remember to balance the equations correctly. Unbalanced equations can lead to wrong mole ratios leading to wrong answers. The molar mass of \[{\text{NX}}\] can be calculated using the given atomic weights.