For the reaction : `N_2+3H_2 to 2NH_3`. If the rate of disappearance of hydrogen is `1.8 times 10^3 mol//l -sec`. What is the rate of formation of ammonia?

Options

A. `1.8 times 10^3 mol//l-sec`
B. `1.2 times 10^3 mol//l-sec`
C. `2.7 times 10^3 mol//l-sec`
D. `0.9 times 10^3 mol//l-sec`

Answer

To solve the problem, we need to determine the rate of formation of ammonia (\(NH_3\)) from the given rate of disappearance of hydrogen (\(H_2\)) for the reaction:

\[ N_2 + 3H_2 \rightarrow 2NH_3 \]

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The rate of disappearance of hydrogen (\(-\frac{d[H_2]}{dt}\)) is given as \(1.8 \times 10^3 \, \text{mol/L/s}\).

2. **Write the Rate Law Expression:**
- For the reaction, the rate of disappearance of reactants and the rate of formation of products can be expressed as:
\[ -\frac{1}{3} \frac{d[H_2]}{dt} = \frac{1}{2} \frac{d[NH_3]}{dt} \]
Here, the coefficients from the balanced equation are used to relate the rates.

3. **Relate the Rates:**
- Rearranging the above equation gives:
\[ \frac{d[NH_3]}{dt} = -\frac{2}{3} \frac{d[H_2]}{dt} \]

4. **Substitute the Given Rate:**
- Substitute the value of \(-\frac{d[H_2]}{dt}\):
\[ \frac{d[NH_3]}{dt} = -\frac{2}{3} \times (-1.8 \times 10^3) \]
- The negative sign indicates that \(H_2\) is disappearing, but since we are looking for the rate of formation of \(NH_3\), we take the positive value.

5. **Calculate the Rate of Formation of Ammonia:**
- Performing the calculation:
\[ \frac{d[NH_3]}{dt} = \frac{2}{3} \times 1.8 \times 10^3 = 1.2 \times 10^3 \, \text{mol/L/s} \]

6. **Final Answer:**
- The rate of formation of ammonia is:
\[ \frac{d[NH_3]}{dt} = 1.2 \times 10^3 \, \text{mol/L/s} \]

### Summary:
The rate of formation of ammonia (\(NH_3\)) is \(1.2 \times 10^3 \, \text{mol/L/s}\).

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