Find the weight of `NH_3` in grams when 2.8 kg `N_2` reacts with 1Kg `H_2` ?

Options

A. 6000g
B. 3400g
C. 3000g
D. 5666g

Answer

To find the weight of ammonia (NH₃) produced when 2.8 kg of nitrogen (N₂) reacts with 1 kg of hydrogen (H₂), we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced reaction for the formation of ammonia from nitrogen and hydrogen is:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]

### Step 2: Calculate the molar masses
- Molar mass of \( N_2 \) = 28 g/mol (since nitrogen has an atomic mass of 14 g/mol)
- Molar mass of \( H_2 \) = 2 g/mol (since hydrogen has an atomic mass of 1 g/mol)
- Molar mass of \( NH_3 \) = 17 g/mol (14 g/mol for nitrogen + 3 g/mol for hydrogen)

### Step 3: Convert the masses from kg to grams
- Mass of \( N_2 \) = 2.8 kg = 2800 g
- Mass of \( H_2 \) = 1 kg = 1000 g

### Step 4: Determine the number of moles of each reactant
- Moles of \( N_2 \):
\[ \text{Moles of } N_2 = \frac{2800 \text{ g}}{28 \text{ g/mol}} = 100 \text{ moles} \]

- Moles of \( H_2 \):
\[ \text{Moles of } H_2 = \frac{1000 \text{ g}}{2 \text{ g/mol}} = 500 \text{ moles} \]

### Step 5: Identify the limiting reagent
From the balanced equation, 1 mole of \( N_2 \) reacts with 3 moles of \( H_2 \). Therefore, for 100 moles of \( N_2 \), we need:
\[ 100 \text{ moles of } N_2 \times 3 \text{ moles of } H_2/\text{mole of } N_2 = 300 \text{ moles of } H_2 \]
Since we have 500 moles of \( H_2 \), which is more than enough, \( N_2 \) is the limiting reagent.

### Step 6: Calculate the amount of \( NH_3 \) produced
From the balanced equation, 1 mole of \( N_2 \) produces 2 moles of \( NH_3 \). Therefore, 100 moles of \( N_2 \) will produce:
\[ 100 \text{ moles of } N_2 \times 2 \text{ moles of } NH_3/\text{mole of } N_2 = 200 \text{ moles of } NH_3 \]

### Step 7: Convert moles of \( NH_3 \) to grams
Now, we convert the moles of \( NH_3 \) to grams:
\[ \text{Mass of } NH_3 = 200 \text{ moles} \times 17 \text{ g/mol} = 3400 \text{ g} \]

### Final Answer
The weight of \( NH_3 \) produced is **3400 grams**.

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