In the synthesis of ammonia from nitrogen and hydrogen gases, if `6xx10^(-2)` mole of hydrogen disappears in 10 minutes, the number of moles of ammonia formed in 0.3 minutes is

Options

A. `1.8xx10^(-2)`
B. `1.2xx10^(-3)`
C. `4xx10^(-2)`
D. `3.6xx10^(-2)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write the balanced chemical equation
The synthesis of ammonia from nitrogen and hydrogen can be represented by the balanced equation:
\[ \text{N}_2 + 3 \text{H}_2 \rightarrow 2 \text{NH}_3 \]

### Step 2: Determine the relationship between the moles of reactants and products
From the balanced equation, we can see that:
- 3 moles of hydrogen (\( \text{H}_2 \)) produce 2 moles of ammonia (\( \text{NH}_3 \)).
- Therefore, the ratio of moles of hydrogen to moles of ammonia is:
\[ \frac{3 \text{ moles H}_2}{2 \text{ moles NH}_3} \]

### Step 3: Calculate the rate of disappearance of hydrogen
We are given that \( 6 \times 10^{-2} \) moles of hydrogen disappear in 10 minutes. The rate of disappearance of hydrogen can be calculated as:
\[ \text{Rate} = \frac{\text{Moles of } H_2}{\text{Time}} = \frac{6 \times 10^{-2} \text{ moles}}{10 \text{ minutes}} = 6 \times 10^{-3} \text{ moles/minute} \]

### Step 4: Relate the rate of hydrogen disappearance to ammonia formation
Using the stoichiometric coefficients from the balanced equation, we can relate the rate of disappearance of hydrogen to the rate of formation of ammonia:
\[ \frac{-1}{3} \frac{d[\text{H}_2]}{dt} = \frac{1}{2} \frac{d[\text{NH}_3]}{dt} \]

### Step 5: Calculate the amount of ammonia formed in 0.3 minutes
We need to find out how many moles of ammonia are formed in 0.3 minutes. First, we calculate the amount of hydrogen that would disappear in 0.3 minutes:
\[ \text{Moles of } H_2 \text{ in } 0.3 \text{ minutes} = \text{Rate} \times \text{Time} = 6 \times 10^{-3} \text{ moles/minute} \times 0.3 \text{ minutes} = 1.8 \times 10^{-3} \text{ moles} \]

### Step 6: Use stoichiometry to find moles of ammonia formed
Using the stoichiometric relationship:
From 3 moles of \( H_2 \), we get 2 moles of \( NH_3 \). Therefore, the moles of ammonia formed from \( 1.8 \times 10^{-3} \) moles of hydrogen is:
\[ \text{Moles of } NH_3 = \frac{2}{3} \times 1.8 \times 10^{-3} = 1.2 \times 10^{-3} \text{ moles} \]

### Final Answer
The number of moles of ammonia formed in 0.3 minutes is:
\[ \text{Moles of } NH_3 = 1.2 \times 10^{-3} \]

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