Question

NX is produced by the following step of reactions.
$\begin{aligned} & M+{{X}_{2}}\to M{{X}_{2}} \\\ & M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\\ & {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\\ \end{aligned}$
How much M (in gm) is consumed to produce 206 gm of NX. (Take at wt. M=56, N=23, X=80).

Answer 1

Hint We should calculate the mole ratio of metal and NX in order to determine the M (in gm) is consumed to produce 206 gm of NX. We can calculate the moles of metal and NX by taking the ratio of given mass and molar mass of NX.

Complete Step by step solution:
- As we are being provided with following step of reactions
$\begin{aligned} & \Rightarrow M+{{X}_{2}}\to M{{X}_{2}} \\\ & \Rightarrow M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\\ & \Rightarrow {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\\ \end{aligned}$ - If we multiply the first equation by 3 and add all the equations then we get:
$\begin{aligned} & \Rightarrow 3M+3{{X}_{2}}\to M{{X}_{2}} \\\ & \Rightarrow 3M{{X}_{2}}+{{X}_{2}}\to {{M}_{3}}{{X}_{8}} \\\ & \Rightarrow {{M}_{3}}{{X}_{8}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}} \\\ \end{aligned}$
- We can write the resultant equation as:
$\Rightarrow 3M+4{{X}_{2}}+{{N}_{2}}C{{O}_{3}}\to NX+C{{O}_{2}}+{{M}_{3}}{{O}_{4}}$
- We can calculate the molar mass of NX that is given in data as: 80+20=103 gm.
- Now, we will calculate the moles of metal and NX by taking the ratio of given mass and molar mass of NX. Hence, we get the number of moles of NX as:
206/103 = 2 moles.
- The Mole ratio of metal M and NX is 3:1. Hence, we can calculate the moles of metal as:
$2\text{ }moles\text{ }NX\times \dfrac{3\text{ }mole\text{ }M}{1\text{ }mole\text{ }NX}=6\text{ }moles\text{ }M$
- As we can see that 3 moles of metal M is produced from 1 mole of NX. Hence, 6 moles of metal M is produced from 2 moles of NX.
- And as 1 mole of metal M is equal; to 56 gm, so 6 moles of metal M is equal to 6 moles X 56gm=336gm of metal.
- Hence, we can say that 336gm of metal is consumed to produce 206 gm of NX.

Note: As we know that equations should be multiplied and then added in order to get the mole ratio of metal M and NX. Then we can find the moles of metal M and moles of NX by dividing the given mass to molar mass. And the molar mass of NX can be found out by adding the atomic weight of N and X.