The Haber's process of production of ammonia involves the equilibrium:
`N_(2)(g)+3H_(2)(g)hArr2NH_(2)(g)`
Assuming `DeltaH^(@)` and `DeltaS^(@)` for the reaction do not change with temperature, which of the statements is true?
`(DeltaH^(@)=-95kJ and DeltaS^(@)=-198JK^(-1))`

Options

A. Ammonia dissociates spontaneously below 500 K
B. Ammonia dissociates spontaneously above 500 K
C. Ammonia dissociates at all temperatures.
D. Ammonia does not dissociates at any temperatures.

Explanation

To solve the problem regarding the Haber process of ammonia production, we need to analyze the given thermodynamic parameters: ΔH° and ΔS°. The reaction is:

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

Given:
- ΔH° = -95 kJ (which is -95000 J when converted to joules)
- ΔS° = -198 J/K

We need to determine the spontaneity of the reaction at a specific temperature (500 K) using the Gibbs free energy equation:

### Step 1: Write the Gibbs Free Energy Equation
The Gibbs free energy change (ΔG°) is given by the equation:

\[ \Delta G° = \Delta H° - T \Delta S° \]

### Step 2: Substitute the Values
We will substitute the values of ΔH°, ΔS°, and T into the equation. Remember to convert ΔH° to joules:

\[ \Delta G° = -95000 \, \text{J} - (500 \, \text{K}) \times (-198 \, \text{J/K}) \]

### Step 3: Calculate TΔS°
Now calculate \( T \Delta S° \):

\[ T \Delta S° = 500 \, \text{K} \times (-198 \, \text{J/K}) = -99000 \, \text{J} \]

### Step 4: Substitute TΔS° into ΔG°
Now substitute this value back into the Gibbs free energy equation:

\[ \Delta G° = -95000 \, \text{J} + 99000 \, \text{J} \]

### Step 5: Simplify the Equation
Now, simplify the equation:

\[ \Delta G° = -95000 + 99000 = 4000 \, \text{J} \]

### Step 6: Analyze the Result
Since ΔG° is positive (4000 J), this indicates that the reaction is non-spontaneous at 500 K.

### Conclusion
The reaction is at equilibrium at 500 K, and ammonia will dissociate spontaneously below this temperature.

### Final Answer
The correct statement is that ammonia dissociates only when its temperature is below 500 K.