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NX is produced by the following step of reactions:
\[\begin{align}
& 3M+3{{X}_{2}}\to 3M{{X}_{2}} \\
& 3M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\
& {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\
\end{align}\]
How much M (metal) is consumed to produce 206gm of NX?
(Take atomic weight of M=56M, N=23, X=80)
(A) $42$ gm
(B) $336$ gm
(C) \[\dfrac{14}{3}\]gm
(D) $\dfrac{7}{4}$gm

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: In order to determine the amount of metal M consumed to produce 206gm of NX, the mole ratio of metal and NX shall be calculated. Moles of metal M and moles of NX can be calculated by taking the ratio of given mass and molar mass. The molar mass of NX can be calculated by adding the Atomic weight of N and X.

Complete step by step solution:
\[\begin{align}
& M+{{X}_{2}}\to M{{X}_{2}} \\
& 3M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\
& {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\
\end{align}\]
If equation 1 is multiplied by 3 and all equations are added, we get
\[\begin{align}
& 3M+3{{X}_{2}}\to 3M{{X}_{2}} \\
& 3M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\
& {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\
\end{align}\]
Resultant equation will be: \[3M+4{{X}_{2}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}}\]
Mass of NX is 206gm as given in data.
Molar Mass of NX can be calculated as given in data: $23+80=103gm$
Moles of NX can be calculated by taking the ratio of the mass of NX and molar mass of NX.
So, the number of moles of NX will be: $\dfrac{206}{103}=2 moles$
A mole ratio of Metal M and NX is 3:1
So, the number of moles of Metal M can be calculated as:
\[2moles\text{ NX}\times \dfrac{3\text{ }mole\text{ M}}{1\text{ mole NX}}\]=$6 moles M$
As 1 mole of NX is produced by 3 moles of metal M
So, 2 moles of NX will be produced by 6 moles of metal M.
As given in data, the atomic weight of metal M is $56gm$
So, 1 mole of metal M is equal to $56gm$, so $6 moles$ of metal $M$ is equal to $6moles\times 56gm=336gm$ of metal.

So (B) 336gm of metal M is consumed to produce 206gm of NX.

Note: In order to calculate mole ratio of metal M and NX, Equations should be multiplied and added. Then moles of metal M and moles of NX can be calculated by dividing given mass to molar mass. Value of 1 Mole is given in data so that it can be used to calculate the weight of 6 moles of metal M. Molar mass of NX can be calculated by adding the Atomic weight of N and X.