NX is produced by the following step of reactions
`M + X_(2) rightarrow MX_(2)`
`3MX_(2) + X_(2) rightarrow M_(3)X_(8)`
`M_(3)X_(8) + N_(2)CO_(3) rightarrow NX + CO_(2) + M_(3)O_(4)`
How much M (metal) is consumed to produce 206 gm of NX? (Take at. wt of M = 56, N=23, X = 80]

Options

A. 42gm
B. 56gm
C. 14/3 gm
D. 7/4gm

Answer

To determine how much metal M is consumed to produce 206 g of NX, we can follow these steps:

### Step 1: Write the balanced chemical equation for the final reaction
The final reaction is:
\[ M_3X_8 + N_2CO_3 \rightarrow NX + CO_2 + M_3O_4 \]

### Step 2: Determine the molar mass of NX
Given:
- Atomic weight of N = 23 g/mol
- Atomic weight of X = 80 g/mol

The molar mass of NX:
\[ \text{Molar mass of NX} = \text{Atomic weight of N} + \text{Atomic weight of X} = 23 + 80 = 103 \text{ g/mol} \]

### Step 3: Calculate the number of moles of NX produced
Using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Number of moles of NX} = \frac{206 \text{ g}}{103 \text{ g/mol}} = 2 \text{ moles} \]

### Step 4: Relate moles of NX to moles of M consumed
From the balanced equation, we see that:
- 8 moles of NX are produced from 3 moles of M.

To find how many moles of M are needed to produce 2 moles of NX, we set up a proportion:
\[ \frac{3 \text{ moles of M}}{8 \text{ moles of NX}} = \frac{x \text{ moles of M}}{2 \text{ moles of NX}} \]

Cross-multiplying gives:
\[ 8x = 6 \quad \Rightarrow \quad x = \frac{6}{8} = \frac{3}{4} \text{ moles of M} \]

### Step 5: Calculate the mass of M consumed
The molar mass of M is given as 56 g/mol. Thus, the mass of M consumed is:
\[ \text{Mass of M} = \text{Number of moles} \times \text{Molar mass} = \frac{3}{4} \text{ moles} \times 56 \text{ g/mol} = 42 \text{ g} \]

### Final Answer
The amount of metal M consumed to produce 206 g of NX is **42 g**.

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