The rate of decomposition of `NH_(3)(g)` at 10 atm on platinum surface is zero order . What is rate of formation (in M `min^(-1)`) of `H_(2)`(g) , if rate constant of reaction `2NH_(3(g)) to N_(2)(g) +3H_(2)(g)` is 2.0 M `min^(-1)`?

Answer

To solve the problem, we need to determine the rate of formation of hydrogen gas (H₂) from the decomposition of ammonia (NH₃) given that the reaction is zero order and the rate constant is provided.

### Step-by-Step Solution

1. **Identify the Reaction**:
The decomposition of ammonia can be represented by the following balanced chemical equation:
\[ 2 \text{NH}_3(g) \rightarrow \text{N}_2(g) + 3 \text{H}_2(g) \]

2. **Understand Zero Order Kinetics**:
For a zero order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

3. **Given Data**:
- Rate constant \( k = 2.0 \, \text{M min}^{-1} \)
- The reaction is zero order.

4. **Calculate the Rate of Reaction**:
Since the reaction is zero order, the rate of decomposition of NH₃ is equal to the rate constant:
\[ \text{Rate of decomposition of NH}_3 = k = 2.0 \, \text{M min}^{-1} \]

5. **Relate the Rate of Decomposition to the Rate of Formation of H₂**:
From the balanced equation, we see that for every 2 moles of NH₃ decomposed, 3 moles of H₂ are produced. Therefore, the stoichiometric relationship can be used to find the rate of formation of H₂:
\[ \text{Rate of formation of H}_2 = \left(\frac{3}{2}\right) \times \text{Rate of decomposition of NH}_3 \]

6. **Substituting the Rate**:
Now substituting the rate of decomposition into the equation:
\[ \text{Rate of formation of H}_2 = \left(\frac{3}{2}\right) \times 2.0 \, \text{M min}^{-1} \]

7. **Calculate the Final Rate**:
\[ \text{Rate of formation of H}_2 = 3.0 \, \text{M min}^{-1} \]

### Final Answer:
The rate of formation of hydrogen gas (H₂) is \( 3.0 \, \text{M min}^{-1} \).