In the Haber process for the industrial manufacturing of ammonia involving the reaction, `N_2(g)+3H_2(g)hArr 2NH_3(g)` at 200 atm pressure in the presence of a catalyst, a temperature of about `500^@C` is used. This considered as optimum temperature for the process because :

Options

A. yield is maximum at this temperature
B. catalyst is active only at this temperature
C. energy needed for the reaction is easily obtained at this temperature
D. rate of the catalytic reaction is fast enough while the yield is also appreciable for this exothermic reaction at this temperature.

Answer

To determine why a temperature of about 500°C is considered optimum for the Haber process of ammonia synthesis, we can analyze the factors affecting the yield and rate of the reaction. The reaction is as follows:

\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The Haber process synthesizes ammonia from nitrogen and hydrogen gases. It is an equilibrium reaction, meaning that both the forward and reverse reactions occur simultaneously.

2. **Effect of Temperature on Yield**:
The reaction is exothermic, meaning it releases heat. According to Le Chatelier's principle, lowering the temperature favors the formation of products (in this case, ammonia). However, if the temperature is too low, the reaction rate will be very slow.

3. **Finding a Balance**:
At 500°C, the reaction is sufficiently fast, allowing for a reasonable production rate of ammonia while still providing a good yield. This temperature is a compromise between maximizing yield and maintaining a practical reaction rate.

4. **Role of the Catalyst**:
A catalyst is used in the Haber process to increase the rate of the reaction without affecting the equilibrium position. The catalyst remains active at 500°C, ensuring that the reaction proceeds quickly.

5. **Comparison with Other Temperatures**:
- At lower temperatures, the yield of ammonia is higher, but the reaction rate is too slow for industrial applications.
- At higher temperatures, the reaction rate increases, but the yield of ammonia decreases due to the shift in equilibrium towards the reactants.

6. **Conclusion**:
Therefore, 500°C is considered the optimum temperature because it provides a good balance between a high yield of ammonia and a fast reaction rate, making the process efficient for industrial production.

### Final Answer:
The optimum temperature of 500°C in the Haber process is chosen because it allows for a good yield of ammonia while ensuring that the reaction proceeds at a practical rate.

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