56 g of nitrogen and 8 g hydrogen gas are heated in a closed vessel. At equilibrium 34 g of ammnia are present. The equilibrium number of moles of nitrogen, hdregen and ammonia are respectively

Options

A. 1,2,2
B. 2,2,1
C. 1,1,2
D. 2,1,2

Explanation

To solve the problem step by step, we will calculate the number of moles of nitrogen (N₂), hydrogen (H₂), and ammonia (NH₃) at equilibrium.

### Step 1: Calculate the moles of nitrogen (N₂)
- Given mass of nitrogen = 56 g
- Molar mass of nitrogen (N₂) = 28 g/mol (since atomic mass of N = 14 g/mol)

Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Moles of } N_2 = \frac{56 \text{ g}}{28 \text{ g/mol}} = 2 \text{ moles} \]

### Step 2: Calculate the moles of hydrogen (H₂)
- Given mass of hydrogen = 8 g
- Molar mass of hydrogen (H₂) = 2 g/mol (since atomic mass of H = 1 g/mol)

Using the same formula:
\[ \text{Moles of } H_2 = \frac{8 \text{ g}}{2 \text{ g/mol}} = 4 \text{ moles} \]

### Step 3: Calculate the moles of ammonia (NH₃) at equilibrium
- Given mass of ammonia = 34 g
- Molar mass of ammonia (NH₃) = 17 g/mol (14 g/mol for N + 3 g/mol for H)

Using the formula:
\[ \text{Moles of } NH_3 = \frac{34 \text{ g}}{17 \text{ g/mol}} = 2 \text{ moles} \]

### Step 4: Write the balanced chemical equation
The balanced equation for the formation of ammonia is:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]

### Step 5: Determine the change in moles
From the balanced equation, we see that:
- 1 mole of N₂ reacts with 3 moles of H₂ to produce 2 moles of NH₃.

### Step 6: Calculate the remaining moles of nitrogen and hydrogen at equilibrium
- Initially, we had 2 moles of N₂ and 4 moles of H₂.
- At equilibrium, we have 2 moles of NH₃, which means:
- For every 2 moles of NH₃ produced, 1 mole of N₂ is consumed and 3 moles of H₂ are consumed.

Thus, the changes are:
- N₂: \(2 - 1 = 1\) mole remaining
- H₂: \(4 - 3 = 1\) mole remaining

### Final Result
At equilibrium, the number of moles of nitrogen, hydrogen, and ammonia are:
- Moles of N₂ = 1
- Moles of H₂ = 1
- Moles of NH₃ = 2

### Summary
The equilibrium number of moles of nitrogen, hydrogen, and ammonia are respectively:
**1 mole of N₂, 1 mole of H₂, and 2 moles of NH₃.**

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